# Chapter 8: Trendlines and Regression Analysis

Common Mathematical Functions Used in Predictive Analytical Models:

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Modeling Relationships and Trends in Data

Create charts to better understand data sets.

For cross-sectional data, use a scatter chart.

For time series data, use a line chart.

Right click on data series and choose Add trendline from pop-up menu

Check the boxes Display Equation on chart and Display R-squared value on chart

Excel Trendline Tool

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R2 (coefficient of determination) is a measure of the “fit” of the line to the data. The value of R2 will be between 0 and 1. A value of 1.0 indicates a perfect fit and all data points would lie on the line; the larger the value of R2 the better the fit.

Example 8.1: Modeling a Price-Demand Function

Scatter chart with the linear demand function

Sales = 20,512 – 9.5116(Price)

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Predicted Sales decreases by 9.5116 per \$1 increase

in Price.

Regression analysis is a tool for building mathematical and statistical models that characterize relationships between a dependent (ratio) variable and k independent, or explanatory variables (ratio or categorical), all of which are numerical.

Simple linear regression involves a single independent variable; the k = 1 case.

Multiple regression involves two or more independent variables; the k > 1 case

Regression Analysis

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Finds a linear relationship between:

– one dependent variable Y and

– one independent variable X

First prepare a scatter plot to verify the data has a linear trend.

Use alternative approaches if the data is not linear.

Simple Linear Regression

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Example 8.3: Home Market Value Data

Size of a house is typically related to its market value.

X = Square Footage

Y = Market Value (\$)

The scatter plot of the full data set (42 homes) indicates a linear trend.

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Finding the Best-Fitting Regression Line

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Predicted Market Value = 32,673 + 35.036(Square Feet)

The estimated market value of a home with 2,200 square feet would be: \$32,673 + \$35.036(2,200) = \$109,752

Example 8.4: Using Excel to Find the Best Regression Line

The regression model explains variation in market value due to size of the home.

It provides better estimates of market value than simply using its average.

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Least-Squares Regression

Note: The error term ε is assumed to be normally distributed with a zero mean and a constant unknown standard deviation σ.

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Residuals are the observed errors associated with estimating the value of the dependent variable using the regression line:

Residuals

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The best-fitting line minimizes the sum of squares of residuals (RSS = residual sum of squares):

Least Squares Regression

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Data > Data Analysis >

Regression

Check Labels

Excel outputs a table with many useful regression statistics. The regression

equation is shown by the column “Coefficients”

Simple Linear Regression With Excel

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Home Market Value Regression Results

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Predicted home market value increases by \$35.04 per

1 square foot increase in Home Size

Multiple R: If k = 1, R = | r |, where r is the sample correlation coefficient. The value of r varies from -1 to +1 (r is negative if slope is negative)

R Square: coefficient of determination, R2, which

varies from 0 (no fit) to 1 (perfect fit). If k =1, R2 = r2

Adjusted R Square: adjusts R2 for sample size and number of X variables

Standard Error s: the estimated standard deviation of the error term ε; variability between observed and predicted Y values. This is formally called the standard error (of the estimate), s = SYX.

Regression Statistics

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Example 8.6: Interpreting Regression Statistics for Simple Linear Regression

53.47 % of the variation in home market values can be explained by home size.

The standard error s = \$7287.7

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Example 8.7: Testing Significance of the X Variable

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(8.7)

Example 8.8: Hypothesis Test for the significance of Home Size (Square Feet)

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 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 32673.2 8831.95 3.6994 0.0006496 14823.18 50523.29 Square Feet 35.0364 5.1673 6.7803 3.798E-08 24.5927 45.4800

Residual = Actual Y value − Predicted Y value

Standard residual = residual / (standard deviation)

Rule of thumb: Standard residuals outside of ±3 show potential outliers.

Excel provides a table and a plot of residuals.

Residual Analysis and Regression Assumptions

This point has a standard residual of 4.53

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Linearity

examine scatter diagram (should appear linear)

examine residual plot (should appear random)

Normality of Errors

view a histogram of standard residuals

regression is robust to departures from normality

examine the normality plot in Excel’s Regression

Homoscedasticity (a constant variance of the error term ε): variation about the regression line is constant

examine the residual plot

Independence of Errors: successive observations should not be related.

This is important when one of the independent variable is time.

Checking Assumptions

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Examples of Diagnostic Scatter Charts of Residuals when the Regression Assumptions Are Not Met

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Linearity – linear trend in scatterplot

– no pattern in residual plot

Example 8.11: Checking Regression Assumptions for the Home Market Value Data

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Normality of Errors – residual histogram appears slightly skewed but is not a serious departure. Excel’s normal probability plot looks OK.

Example 8.11 Continued

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Constant Error Variance – residual plot shows no serious difference in the spread of the data for different X values.

Example 8.11 Continued

Independence of Errors – Because the data is cross-sectional, we can assume this assumption holds.

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The Need for Variable Transformation; file UN11

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ppgdp Residual Plot

499 3677.2 4473 4321.8999999999996 13750.1 9162.1 3030.7 22851.5 57118.9 45158.8 5637.6 22461.599999999999 18184.099999999999 670.4 14497.3 5702 43814.8 4495.8 741.1 92624.7 2047.2 1977.9 4477.7 7402.9 10715.6 32647.599999999999 6365.1 519.70000000000005 176.6 797.2 1206.5999999999999 46360.9 3244 57047.9 450.8 727.4 11887.7 4354 6222.8 736.6 2665.1 12212.1 7703.8 1154.0999999999999 13819.5 5704.4 28364.3 18838.8 200.6 55830.2 1282.5999999999999 7020.8 5195.3999999999996 706.1 4072.6 2653.7 3425.6 16852.400000000001 429.1 14135.4 324.60000000000002 3545.7 44501.7 39545.9 24669 12468.8 579.1 2680.3 39857.1 1333.2 26503.8 35292.699999999997 7429 2882.3 427.5 539.4 2996 612.70000000000005 2026.2 31823.7 12884 39278 1406.4 2949.3 5227.1000000000004 888.5 46220.3 29311.599999999999 33877.1 4899 43140.9 4445.3 9166.7000000000007 801.8 1468.2 45430.400000000001 865.4 1047.5999999999999 10663 9283.7000000000007 980.7 218.6 11320.8 10975.5 105095.4 49990.2 421.9 357.4 8372.7999999999993 4684.5 598.79999999999995 19599.2 3069.4 1131.0999999999999 7488.3 9100.7000000000007 2678.2 1625.8 2246.6999999999998 6509.8 2865 407.5 876.2 5124.7 6190.1 534.70000000000005 20321.099999999999 46909.7 35319.5 32372.1 1131.9000000000001 357.7 1239.8 504 84588.7 20791 1003.2 10821.8 1819.5 7614 1428.4 2771.1 5410.7 2140.1 12263.2 21437.599999999999 26461 72397.899999999994 21052.2 7522.4 10351.4 532.29999999999995 6677.1 3343.3 1283.3 15835.9 1032.7 5123.2 11450.6 351.7 43783.1 15976 23109.8 1193.5 114.8 7254.8 30542.799999999999 2375.3000000000002 6171.7 1824.9 7018 3311.2 48906.2 68880.2 2931.5 816 516 4434.5 4612.8 524.6 3543.1 15205.1 4222.1000000000004 10095.1 4587.5 3187.2 509 3035 39624.699999999997 36326.800000000003 46545.9 11952.4 1427.3 2963.5 13502.7 1182.7 1437.2 1237.8 573.1 2.8060619532387685 -1.5352000086793103 -0.89272548514221617 2.0954376205294913 -0.73775425831892294 -0.71262170489870202 -1.3458952580720365 -0.77540740167088429 0.59953364866214143 -0.38632366342129698 -0.84944522614334694 -0.58188857373310232 -0.16581653858598022 -0.99945132480312893 -1.1388354797477789 -1.5163837040073971 5.965326591540232E-2 -0.35499562947917829 1.9238118679765552 1.5471173855349225 -0.85437828634387891 0.11440333657504498 -1.9005750324397477 -0.32393583132048676 -1.0348922850509064 -0.14882235514948672 -1.4281570684740383 2.5887245853538952 0.87874153807370314 -0.73039230295781143 1.1477130877635835 -2.8429839240102783E-3 -0.79506726627703506 0.24826085251846997 1.2595190127581355 2.5823733143544665 -0.96537194195235387 -1.4795348195238625 -0.68571226412536834 1.5876678175167451 1.3494014423487206 -0.25618122026659584 -1.1193036572411807 1.0830324990657987 -1.2345326801165175 -1.5443068770954986 -0.81193598503945341 -1.073858797244267 2.3135098071926907 0.49428079809384085 0.45214593997371066 4.6832684080966303E-2 -0.5216005846606917 2.7626914755113652 -0.65454277494399138 -0.45696348548279841 -0.89725402994336312 2.3415541286742005 1.0788243694297179 -1.0234203378378446 0.68047919764079268 -0.46240948322709619 0.12164176832509033 7.500059749682797E-2 -0.35522702151422614 0.41622977409113115 1.5296260514233895 -1.5641119872092539 -0.44503751292696747 0.85276570736624269 -0.78949284736763081 0.16885050512692468 -0.76910033865358818 0.75435427787555742 1.8677731514884517 1.7163552062557308 -0.89200604717323939 7.0162818997188126E-4 -0.11705052182299269 -1.0221963937800616 -1.335479170150385 0.17742479345612971 -0.59489107182084533 -1.0285009708339357 -1.4235858291993628 1.3855303208156702 0.39865623948725459 0.66938823731124941 -0.617464568408022 -0.75908870828018804 -0.37891909072150143 -0.14661219575038098 -0.40347445331756315 1.4707549486233278 0.3690872211605476 0.5273705821085779 -0.52920913821135551 -0.6013766951497086 -1.3305760748700208 -1.1167291413624987 -9.5518245318886308E-2 1.8670860090319312 -0.40551909876710468 -1.3315725707165376 1.8693196231248199 -0.41466468752645325 1.3285938886940216 2.801529165436742 -0.33788815554940399 -1.3599551135311387 2.9582566723252248 -1.2665174706576792 1.3048098344105714 1.219296241160102 -1.3482020737054226 -0.65958719339477856 0.21482078924283465 -1.6758678116247678 -0.65999204929229505 -1.3395250459108095 -0.90319951611437954 1.5481329272226287 -1.2108634171078112 4.1136222559623903E-2 0.32024096920001099 -0.57379524644673729 -0.62740857578280096 0.11772476993017067 4.3708405643127612E-2 -6.6414444111977389E-3 -0.64167814986926475 3.7585387688007295 2.2927758600448498 -1.1737779906947758 1.4778752755272708 -0.36636650665729142 5.520200698016442E-2 -0.83149269419938676 1.1503327603897269 -0.52517826419472602 0.66681317487155978 -0.23120536904241806 -0.59470857043910819 -5.9404444629131525E-2 -1.3703517313615285 -1.179668056143236 -0.57386292729649191 1.343632976537565 -1.1150051777456438 -1.5091104913321947 -1.3175507689315422 2.1211279266413636 -1.0571695699272006 0.69211144720277584 0.35116834782301476 -3.1985269636250369E-2 1.4601463377722537 -1.4519117942603128 -0.47136404328191395 1.5613467015209825 -0.40936148954592722 -1.2945004986541606 -0.96113890527778145 0.90129374086947012 3.1087632450923106 -0.56267669200890547 -0.69619955688469126 -0.86687540726305379 -0.98534803712454577 1.1055056209414991 -0.68725694731624909 0.10208388725612982 0.31263515726594426 0.56302713154329975 -0.31207077043051834 1.0209507852061872E-2 2.3376061438647175 -1.6389579168539254 -1.5022503175241138 0.70288144029902178 0.7185072876183467 -1.0591779429803052 -1.1337570985569647 -0.83275524289806269 -0.71506020122038016 0.62411449680802811 2.7393820653716801 -1.5977576098548845 -0.20247691889582975 -0.14804669920870106 0.38907909053485179 -0.75230081645241675 -0.86822203746306048 0.66695358839479857 -0.35467383248715256 -1.3900519802340745 1.8060948735485218 3.1617118376182671 -5.0566015856357449E-2ppgdp

Residuals

fertility

fertility 499 3677.2 4473 4321.8999999999996 13750.1 9162.1 3030.7 22851.5 57118.9 45158.8 5637.6 22461.599999999999 18184.099999999999 670.4 14497.3 5702 43814.8 4495.8 741.1 92624.7 2047.2 1977.9 4477.7 7402.9 10715.6 32647.599999999999 6365.1 519.70000000000005 176.6 797.2 1206.5999999999999 46360.9 3244 57047.9 450.8 727.4 11887.7 4354 6222.8 736.6 2665.1 12212.1 7703.8 1154.0999999999999 13819.5 5704.4 28364.3 18838.8 200.6 55830.2 1282.5999999999999 7020.8 5195.3999999999996 706.1 4072.6 2653.7 3425.6 16852.400000000001 429.1 14135.4 324.60000000000002 3545.7 44501.7 39545.9 24669 12468.8 579.1 2680.3 39857.1 1333.2 26503.8 35292.699999999997 7429 2882.3 427.5 539.4 2996 612.70000000000005 2026.2 31823.7 12884 39278 1406.4 2949.3 5227.1000000000004 888.5 46220.3 29311.599999999999 33877.1 4899 43140.9 4445.3 9166.7000000000007 801.8 1468.2 45430.400000000001 865.4 1047.5999999999999 10663 9283.7000000000007 980.7 218.6 11320.8 10975.5 105095.4 49990.2 421.9 357.4 8372.7999999999993 4684.5 598.79999999999995 19599.2 3069.4 1131.0999999999999 7488.3 9100.7000000000007 2678.2 1625.8 2246.6999999999998 6509.8 2865 407.5 876.2 5124.7 6190.1 534.70000000000005 20321.099999999999 46909.7 35319.5 32372.1 1131.9000000000001 357.7 1239.8 504 84588.7 20791 1003.2 10821.8 1819.5 7614 1428.4 2771.1 5410.7 2140.1 12263.2 21437.599999999999 26461 72397.899999999994 21052.2 7522.4 10351.4 532.29999999999995 6677.1 3343.3 1283.3 15835.9 1032.7 5123.2 11450.6 351.7 43783.1 15976 23109.8 1193.5 114.8 7254.8 30542.799999999999 2375.3000000000002 6171.7 1824.9 7018 3311.2 48906.2 68880.2 2931.5 816 516 4434.5 4612.8 524.6 3543.1 15205.1 4222.1000000000004 10095.1 4587.5 3187.2 509 3035 39624.699999999997 36326.800000000003 46545.9 11952.4 1427.3 2963.5 13502.7 1182.7 1437.2 1237.8 573.1 5.968 1.5249999999999999 2.1419999999999999 5.1349999999999998 2 2.1720000000000002 1.7350000000000001 1.671 1.9490000000000001 1.3460000000000001 2.1480000000000001 1.877 2.4300000000000002 2.157 1.575 1.4790000000000001 1.835 2.6789999999999998 5.0780000000000003 1.76 2.258 3.2290000000000001 1.1339999999999999 2.617 1.8 1.984 1.546 5.75 4.0510000000000002 2.4220000000000002 4.2869999999999999 1.6910000000000001 2.2789999999999999 1.6 4.423 5.7370000000000001 1.8320000000000001 1.5589999999999999 2.2930000000000001 4.742 4.4420000000000002 2.5308062840941101 1.8120000000000001 4.2240000000000002 1.5009999999999999 1.4510000000000001 1.458 1.5009999999999999 5.4850000000000003 1.885 3.589 3 2.4900000000000002 5.9180000000000001 2.3929999999999998 2.6360000000000001 2.1709999999999998 4.9800000000000004 4.2430000000000003 1.702 3.8479999999999999 2.6019999999999999 1.875 1.9870000000000001 2.0329999999999999 3.1949999999999998 4.6890000000000001 1.528 1.4570000000000001 3.988 1.54 2.2170000000000001 2.1709999999999998 3.84 5.032 4.8769999999999998 2.19 3.1589999999999998 2.996 1.137 1.43 2.0979999999999999 2.5379999999999998 2.0550000000000002 1.587 4.5350000000000001 2.097 2.9089999999999998 1.476 2.262 1.4179999999999999 2.8889999999999998 2.4809999999999999 4.6230000000000002 3.5 2.2509999999999999 2.621 2.5430000000000001 1.506 1.764 3.0510000000000002 5.0380000000000003 2.41 1.4950000000000001 1.6830000000000001 1.163 4.4930000000000003 5.968 2.5720000000000001 1.6679999999999999 6.117 1.284 4.3844662585282403 4.3609999999999998 1.59 2.2269999999999999 3.3069999999999999 1.45 2.4460000000000002 1.63 2.1829999999999998 4.7130000000000001 1.9390000000000001 3.0550000000000002 3.3 2.5870000000000002 1.9 1.794 2.0910000000000002 2.1349999999999998 2.5 6.9249999999999998 5.431 1.988 1.948 2.1459999999999999 3.2010000000000001 2 4.2699999999999996 2.4089999999999998 3.7989999999999999 2.8580000000000001 2.41 3.05 1.415 1.3120000000000001 1.7569999999999999 2.2040000000000002 1.389 1.4279999999999999 1.5289999999999999 5.282 1.907 3.7629999999999999 3.488 2.6389999999999998 4.6050000000000004 1.5620000000000001 2.34 4.7279999999999998 1.367 1.3720000000000001 1.4770000000000001 4.0410000000000004 6.2830000000000004 2.383 1.504 2.2349999999999999 1.9950000000000001 4.2249999999999996 2.266 3.1739999999999999 1.925 1.536 2.7719999999999998 3.1619999999999999 5.4989999999999997 1.397 1.528 3.8639999999999999 3.7829999999999999 1.6319999999999999 1.909 2.0219999999999998 2.3159999999999998 3.7 5.9009999999999998 1.4830000000000001 1.7070000000000001 1.867 2.077 2.0430000000000001 2.2639999999999998 3.75 2.391 1.75 4.9379999999999997 6.3 3.109

Variable Transformation; file UN11

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ln(ppgdp) Residual Plot

6.2126060957515188 8.2099068719895989 8.405814603432848 8.371450399362784 9.5288013757955436 9.1228306890345792 8.0165488949239982 10.036772039682001 10.952890339124952 10.717940445722775 8.6372137220128131 10.019562463511157 9.8083028648573372 6.5078745491678731 9.5817177041734567 8.6485722694726181 10.687726938832723 8.4108989065983195 6.6081355689573131 11.436311123726746 7.6242282848455787 7.5897909547873637 8.406864800720653 8.9096270943145814 9.2794559026068608 10.393526625111543 8.7585852217871807 6.2532517220143964 5.1738872881698592 6.6811055883386397 7.0955617660066617 10.74421171055257 8.0845624152353039 10.951646544796773 6.1110237821656215 6.5894765325528883 9.3832595311074911 8.3788502417944919 8.7359752452129662 6.6020450040109653 7.8879968593481156 9.4101825424881262 8.9494689926010018 7.0510760984263587 9.5338359172170968 8.6489930858626121 10.252886591155431 9.8436738518342715 5.3013128755278354 10.930070220601412 7.1566445467147624 8.8566324506408556 8.5555288976818105 6.5597568705223015 8.3120368951164139 7.8837101715776026 8.1390319178354176 9.7322483588722797 6.0616899919974792 9.5564375682769942 5.7825936550804906 8.1734908806863054 10.703282669671836 10.585217301576824 10.113302673639005 9.4309848030892969 6.3614751742317441 7.8936840075385621 10.593055836478793 7.1953373464335844 10.185043397920472 10.471431422668699 8.913146539151807 7.9663438655209271 6.0579542883768145 6.2904574107056295 8.0050333446371109 6.417875419731609 7.613917396619577 10.367966574201658 9.46374151045109 10.578419844675169 7.2487885269309125 7.9893231330409886 8.5616119099628634 6.7895346475947056 10.741174374503975 10.285738621092536 10.430494548880466 8.4967863816385751 10.672226782034295 8.399602637234107 9.1233326313435779 6.6868592002084064 7.2917924396766809 10.723936763469254 6.7631918277907843 6.9542571126335568 9.2745350840181793 9.1360154532143234 6.888266602398275 5.3872435757424384 9.3343970206381623 9.3034207949921939 11.56262378806705 10.819582265199772 6.0447683191302932 5.878855602725328 9.032743635617944 8.4520144653912421 6.3949276525454728 9.8832440280590692 8.0292373817409946 7.0309458895373353 8.9210970814574466 9.1161066126234367 7.8929002060614657 7.3937552813124716 7.7172177519234308 8.7810640127644799 7.9603236291488395 6.0100409326809174 6.7755943753797983 8.5418272657079104 8.7307065206370034 6.2817058419546861 9.9194150340855014 10.755979756077155 10.472190498332305 10.385052219700158 7.0316529156383742 5.879694646264972 7.1227053552678186 6.2225762680713688 11.34555596693313 9.9422754797433885 6.9109501698786566 9.2893178971596093 7.5063170170522149 8.937743936942443 7.2643102157202932 7.926999632266674 8.5961337534888447 7.6686078358960952 9.4143581868518975 9.9729016686204481 10.183427229849748 11.189932572428278 9.9547603467135506 8.9256405149628666 9.2448770552464179 6.2772072401787113 8.8064390405316999 8.1147136221484395 7.157190164250415 9.6700347934801432 6.9399320106773583 8.5415345228023956 9.3457974093561873 5.8627785394799368 10.687003177158442 9.6788428750956506 10.048012048968754 7.084645445778885 4.7431914838854663 8.8894185977432674 10.326884257608627 7.7728790242810479 8.7277296056912128 7.5092804699947697 8.8562335561431595 8.1050659404345229 10.797659456791925 11.140124042697861 7.9832695164042695 6.7044143549641069 6.2461067654815627 8.3971701488165067 8.4365903268841382 6.2626360674327737 8.1727573291355231 9.6293861768737905 8.3480879135848998 9.2198054365918818 8.4310904923628254 8.0668980673902784 6.2324480165505225 8.0179667034935989 10.587207940173004 10.500311039860483 10.74819420148998 9.3886873740147259 7.2635398266357232 7.994126281227893 9.5106449444291865 7.0755552392570715 7.2704520552393639 7.1210908893052611 6.3510602215576917 1.8106849777263925 -1.3938154881382361 -0.65533572053759448 2.3163554955085583 -0.10098662231564681 -0.18072362277537968 -1.303714187105425 -0.11500079841647204 0.73107192281384159 -1.7617367945772067E-2 -0.50584821781884459 8.0327773261949398E-2 0.50232851785326238 -1.817222998101963 -0.49317391387238563 -1.1678049342509489 0.45264763998237623 -0.11518301205384818 1.1659475211200041 0.84183469447228032 -1.0239869573333529 -7.4341085735734502E-2 -1.6626845072265248 0.13207167582053447 -0.45560241982442284 0.41921795496896053 -1.0325873719231204 1.6178887876833628 -0.75041068107096187 -1.4448047444952734 0.67719399553835391 0.34367309247958855 -0.71753991159189212 0.38130066256384021 0.20269514186927573 1.8133773018674875 -0.35923517625796442 -1.2550559610365053 -0.29960751640367178 0.82617084314620293 1.323572412656099 0.35626570759254328 -0.64822289520559839 0.58660902725046338 -0.59686477042465436 -1.1955439916282029 -0.19399105161015862 -0.40473840555956864 0.76260422367314273 0.65292147211730112 1.7070611995273044E-2 0.48221040510836755 -0.21449988635242612 1.9759485363968858 -0.46248602491035129 -0.48508570517468907 -0.79176410055861934 3.0051681345239158 -7.8960824807481345E-3 -0.38184978848433015 -0.57595999321613167 -0.33939655795044255 0.50229354090355027 0.54108278310341174 0.29445482550881286 1.0333586274490965 0.62399670490260206 -1.5869010627121463 1.5943353899703583E-2 0.44006350029545827 -0.15405970957864579 0.70052567938850396 -0.31174596344382932 0.77015434473179223 0.77878745760049384 0.76795953829813346 -0.85585482602936613 -0.87103025618021057 -0.29238060140356525 -0.44363149120408574 -0.71132937583511491 0.64786777086982017 -0.97679213660585384 -1.0005965184046191 -1.1137278916854976 0.73543066690245773 0.74778968096443288 1.2773800533613917 -6.5858729268853722E-2 -0.478925335948714 2.6036199781548808E-2 8.7812322193507431E-2 0.12858762494617171 0.75976299337629705 1.1874015300394447E-2 0.89110086859821491 -1.1949041638066249 -1.1544271326641669 -0.75265375370570475 -0.58054792661155319 -0.68734696665015704 0.36888870313154687 0.18846583363853675 -0.74574211014650693 0.84315949051802996 -0.13759063328038335 0.23161101419085384 1.6037307547830988 0.16341459866051267 -1.1006878032117122 2.07274013989253 -0.5972014678068216 1.3536200326225956 0.71112655359015609 -0.88781593835256323 -0.1298931327469206 0.19161291246085321 -1.9749001884813231 -0.77832543082439409 -0.93464857387901823 -0.89057872343246292 0.43007702569448991 -1.8692135097029317 0.34200391466820301 0.70412541785918403 -1.5274671925928494 4.1227689907380682E-2 0.45397030032793984 0.57499637206881182 0.56496308936286876 -1.1494350289680764 2.5612510344752373 1.8380253726922859 -2.1631326515859839 0.97355863392771758 0.30140314692129522 -0.52328118943161739 -0.24948712872528755 0.91489784040529987 -5.849344561222658E-2 0.29383265529496816 -0.23624248880275678 -0.26932135761056841 -0.20446779048822439 -0.75695131520413383 -0.51360596241875034 6.1938126187259579E-2 1.1330586455995459 -0.44785515382627072 -1.0469986159208178 -0.74804430121572185 1.1647432845320331 -0.6419138580854522 0.78515644909639182 -8.359105785848131E-2 0.62559033358789984 0.89869006294789866 -1.1511776112974472 0.12553506241179591 0.35376158260003621 -1.5801154964828257E-2 -0.63594789264862128 -0.30203101878641481 0.42442493117037294 1.2145206033373031 -0.11445934298590199 -0.1021060870020718 -0.95481061928252275 -0.60272052733714521 0.87173543799323028 -0.25203694404176691 0.19017405052611869 0.61081532604077737 0.43417304158787617 -0.28735028522512396 -0.69035128963742043 1.3624582955699021 -1.4056960313843956 -1.2502521054854374 -0.26229210506594214 0.84114857653069519 -0.40661533064111821 -0.92413126987820049 -0.27059087707103613 -0.46566247941284278 0.6925066622455871 1.7559886877926356 -1.5548350229485624 0.26231715150867729 0.36843354427473329 0.7321425819172136 -0.14486944336888374 -1.2416450526865703 0.69738184963220107 0.27875481710283267 -1.8722117844792674 1.4366411279464586 2.7060242639127301 -0.96246146814189615ln(ppgdp)

Residuals

fertility

fertility6.2126060957515188 8.2099068719895989 8.405814603432848 8.371450399362784 9.5288013757955436 9.1228306890345792 8.0165488949239982 10.036772039682001 10.952890339124952 10.717940445722775 8.6372137220128131 10.019562463511157 9.8083028648573372 6.5078745491678731 9.5817177041734567 8.6485722694726181 10.687726938832723 8.4108989065983195 6.6081355689573131 11.436311123726746 7.6242282848455787 7.5897909547873637 8.406864800720653 8.9096270943145814 9.2794559026068608 10.393526625111543 8.7585852217871807 6.2532517220143964 5.1738872881698592 6.6811055883386397 7.0955617660066617 10.74421171055257 8.0845624152353039 10.951646544796773 6.1110237821656215 6.5894765325528883 9.3832595311074911 8.3788502417944919 8.7359752452129662 6.6020450040109653 7.8879968593481156 9.4101825424881262 8.9494689926010018 7.0510760984263587 9.5338359172170968 8.6489930858626121 10.252886591155431 9.8436738518342715 5.3013128755278354 10.930070220601412 7.1566445467147624 8.8566324506408556 8.5555288976818105 6.5597568705223015 8.3120368951164139 7.8837101715776026 8.1390319178354176 9.7322483588722797 6.0616899919974792 9.5564375682769942 5.7825936550804906 8.1734908806863054 10.703282669671836 10.585217301576824 10.113302673639005 9.4309848030892969 6.3614751742317441 7.8936840075385621 10.593055836478793 7.1953373464335844 10.185043397920472 10.471431422668699 8.913146539151807 7.9663438655209271 6.0579542883768145 6.2904574107056295 8.0050333446371109 6.417875419731609 7.613917396619577 10.367966574201658 9.46374151045109 10.578419844675169 7.2487885269309125 7.9893231330409886 8.5616119099628634 6.7895346475947056 10.741174374503975 10.285738621092536 10.430494548880466 8.4967863816385751 10.672226782034295 8.399602637234107 9.1233326313435779 6.6868592002084064 7.2917924396766809 10.723936763469254 6.7631918277907843 6.9542571126335568 9.2745350840181793 9.1360154532143234 6.888266602398275 5.3872435757424384 9.3343970206381623 9.3034207949921939 11.56262378806705 10.819582265199772 6.0447683191302932 5.878855602725328 9.032743635617944 8.4520144653912421 6.3949276525454728 9.8832440280590692 8.0292373817409946 7.0309458895373353 8.9210970814574466 9.1161066126234367 7.8929002060614657 7.3937552813124716 7.7172177519234308 8.7810640127644799 7.9603236291488395 6.0100409326809174 6.7755943753797983 8.5418272657079104 8.7307065206370034 6.2817058419546861 9.9194150340855014 10.755979756077155 10.472190498332305 10.385052219700158 7.0316529156383742 5.879694646264972 7.1227053552678186 6.2225762680713688 11.34555596693313 9.9422754797433885 6.9109501698786566 9.2893178971596093 7.5063170170522149 8.937743936942443 7.2643102157202932 7.926999632266674 8.5961337534888447 7.6686078358960952 9.4143581868518975 9.9729016686204481 10.183427229849748 11.189932572428278 9.9547603467135506 8.9256405149628666 9.2448770552464179 6.2772072401787113 8.8064390405316999 8.1147136221484395 7.157190164250415 9.6700347934801432 6.9399320106773583 8.5415345228023956 9.3457974093561873 5.8627785394799368 10.687003177158442 9.6788428750956506 10.048012048968754 7.084645445778885 4.7431914838854663 8.8894185977432674 10.326884257608627 7.7728790242810479 8.7277296056912128 7.5092804699947697 8.8562335561431595 8.1050659404345229 10.797659456791925 11.140124042697861 7.9832695164042695 6.7044143549641069 6.2461067654815627 8.3971701488165067 8.4365903268841382 6.2626360674327737 8.1727573291355231 9.6293861768737905 8.3480879135848998 9.2198054365918818 8.4310904923628254 8.0668980673902784 6.2324480165505225 8.0179667034935989 10.587207940173004 10.500311039860483 10.74819420148998 9.3886873740147259 7.2635398266357232 7.994126281227893 9.5106449444291865 7.0755552392570715 7.2704520552393639 7.1210908893052611 6.3510602215576917 5.968 1.5249999999999999 2.1419999999999999 5.1349999999999998 2 2.1720000000000002 1.7350000000000001 1.671 1.9490000000000001 1.3460000000000001 2.1480000000000001 1.877 2.4300000000000002 2.157 1.575 1.4790000000000001 1.835 2.6789999999999998 5.0780000000000003 1.76 2.258 3.2290000000000001 1.1339999999999999 2.617 1.8 1.984 1.546 5.75 4.0510000000000002 2.4220000000000002 4.2869999999999999 1.6910000000000001 2.2789999999999999 1.6 4.423 5.7370000000000001 1.8320000000000001 1.5589999999999999 2.2930000000000001 4.742 4.4420000000000002 2.5308062840941101 1.8120000000000001 4.2240000000000002 1.5009999999999999 1.4510000000000001 1.458 1.5009999999999999 5.4850000000000003 1.885 3.589 3 2.4900000000000002 5.9180000000000001 2.3929999999999998 2.6360000000000001 2.1709999999999998 4.9800000000000004 4.2430000000000003 1.702 3.8479999999999999 2.6019999999999999 1.875 1.9870000000000001 2.0329999999999999 3.1949999999999998 4.6890000000000001 1.528 1.4570000000000001 3.988 1.54 2.2170000000000001 2.1709999999999998 3.84 5.032 4.8769999999999998 2.19 3.1589999999999998 2.996 1.137 1.43 2.0979999999999999 2.5379999999999998 2.0550000000000002 1.587 4.5350000000000001 2.097 2.9089999999999998 1.476 2.262 1.4179999999999999 2.8889999999999998 2.4809999999999999 4.6230000000000002 3.5 2.2509999999999999 2.621 2.5430000000000001 1.506 1.764 3.0510000000000002 5.0380000000000003 2.41 1.4950000000000001 1.6830000000000001 1.163 4.4930000000000003 5.968 2.5720000000000001 1.6679999999999999 6.117 1.284 4.3844662585282403 4.3609999999999998 1.59 2.2269999999999999 3.3069999999999999 1.45 2.4460000000000002 1.63 2.1829999999999998 4.7130000000000001 1.9390000000000001 3.0550000000000002 3.3 2.5870000000000002 1.9 1.794 2.0910000000000002 2.1349999999999998 2.5 6.9249999999999998 5.431 1.988 1.948 2.1459999999999999 3.2010000000000001 2 4.2699999999999996 2.4089999999999998 3.7989999999999999 2.8580000000000001 2.41 3.05 1.415 1.3120000000000001 1.7569999999999999 2.2040000000000002 1.389 1.4279999999999999 1.5289999999999999 5.282 1.907 3.7629999999999999 3.488 2.6389999999999998 4.6050000000000004 1.5620000000000001 2.34 4.7279999999999998 1.367 1.3720000000000001 1.4770000000000001 4.0410000000000004 6.2830000000000004 2.383 1.504 2.2349999999999999 1.9950000000000001 4.2249999999999996 2.266 3.1739999999999999 1.925 1.536 2.7719999999999998 3.1619999999999999 5.4989999999999997 1.397 1.528 3.8639999999999999 3.7829999999999999 1.6319999999999999 1.909 2.0219999999999998 2.3159999999999998 3.7 5.9009999999999998 1.4830000000000001 1.7070000000000001 1.867 2.077 2.0430000000000001 2.2639999999999998 3.75 2.391 1.75 4.9379999999999997 6.3 3.109

Variable Transformation; file UN11

27

ppgdp Residual Plot

499 3677.2 4473 4321.8999999999996 13750.1 9162.1 3030.7 22851.5 57118.9 45158.8 5637.6 22461.599999999999 18184.099999999999 670.4 14497.3 5702 43814.8 4495.8 741.1 92624.7 2047.2 1977.9 4477.7 7402.9 10715.6 32647.599999999999 6365.1 519.70000000000005 176.6 797.2 1206.5999999999999 46360.9 3244 57047.9 450.8 727.4 11887.7 4354 6222.8 736.6 2665.1 12212.1 7703.8 1154.0999999999999 13819.5 5704.4 28364.3 18838.8 200.6 55830.2 1282.5999999999999 7020.8 5195.3999999999996 706.1 4072.6 2653.7 3425.6 16852.400000000001 429.1 14135.4 324.60000000000002 3545.7 44501.7 39545.9 24669 12468.8 579.1 2680.3 39857.1 1333.2 26503.8 35292.699999999997 7429 2882.3 427.5 539.4 2996 612.70000000000005 2026.2 31823.7 12884 39278 1406.4 2949.3 5227.1000000000004 888.5 46220.3 29311.599999999999 33877.1 4899 43140.9 4445.3 9166.7000000000007 801.8 1468.2 45430.400000000001 865.4 1047.5999999999999 10663 9283.7000000000007 980.7 218.6 11320.8 10975.5 105095.4 49990.2 421.9 357.4 8372.7999999999993 4684.5 598.79999999999995 19599.2 3069.4 1131.0999999999999 7488.3 9100.7000000000007 2678.2 1625.8 2246.6999999999998 6509.8 2865 407.5 876.2 5124.7 6190.1 534.70000000000005 20321.099999999999 46909.7 35319.5 32372.1 1131.9000000000001 357.7 1239.8 504 84588.7 20791 1003.2 10821.8 1819.5 7614 1428.4 2771.1 5410.7 2140.1 12263.2 21437.599999999999 26461 72397.899999999994 21052.2 7522.4 10351.4 532.29999999999995 6677.1 3343.3 1283.3 15835.9 1032.7 5123.2 11450.6 351.7 43783.1 15976 23109.8 1193.5 114.8 7254.8 30542.799999999999 2375.3000000000002 6171.7 1824.9 7018 3311.2 48906.2 68880.2 2931.5 816 516 4434.5 4612.8 524.6 3543.1 15205.1 4222.1000000000004 10095.1 4587.5 3187.2 509 3035 39624.699999999997 36326.800000000003 46545.9 11952.4 1427.3 2963.5 13502.7 1182.7 1437.2 1237.8 573.1 0.73367060008076335 -0.59505905508598511 -0.24637750753361176 0.62626567191123272 -0.21079835644876599 -0.17981548360433197 -0.47330555750360292 -0.28832426852870385 0.25035627141619443 -0.25412209005231912 -0.23050308650933582 -0.17644992185959918 3.3734813192667135E-2 -0.28209825614567874 -0.44130000533176578 -0.60295093608505623 4.0693473089380094E-2 -2.241786930410461E-2 0.57489474535550311 0.54704594069753676 -0.22087716165148064 0.13603769927891252 -0.88231349826434613 -1.3189202619627638E-2 -0.35023307198256248 -6.6317500421754216E-3 -0.55120026358892193 0.6966910309199954 0.34260229311512713 -0.16479914960509856 0.41079151841262118 -1.2440949934485857E-2 -0.19818108904107146 5.2246225830625825E-2 0.43353570145220544 0.69675985129851736 -0.31945003722538601 -0.56540913261592041 -0.15860808717031105 0.50638571951374489 0.46268645634122096 7.3223040091969782E-3 -0.37740783234066022 0.39539735817174559 -0.49703469634572317 -0.62203719647034261 -0.36277801783074581 -0.44067330849353747 0.64592511703502264 0.20249694469232227 0.23393134193755993 0.11910388686277085 -8.7722987243567307E-2 0.72758280336503711 -0.14006573576074244 -5.928366233705018E-2 -0.24469077401483208 0.73631987562126688 0.39174440092088525 -0.36781499863139233 0.29285394391310815 -6.2249689861008095E-2 6.9970805691265681E-2 7.2339759288123862E-2 -7.1825396158602728E-2 0.24325391783311801 0.49337751489099224 -0.60428789859162424 -0.23441223284327745 0.33991576592629524 -0.32895266648590493 0.13410982475022037 -0.19973686009706659 0.31949302190858142 0.56227338780461977 0.5322426628361987 -0.24080107107984761 9.8790988782048839E-2 6.1685630664423785E-2 -0.57260506276483514 -0.55599647237524707 0.12369007430458689 -0.11117575892067222 -0.30495115817251828 -0.53780429897173687 0.46345749049485963 0.20116794396453297 0.33860289716571779 -0.28860505851418317 -0.18708457602995809 -0.22467075885274956 5.2481900456297081E-2 -4.6750527870483172E-2 0.4817027033659631 0.2109047883966324 0.26316501909307932 -8.5071057103729197E-2 -0.11323658325105246 -0.52915324942936426 -0.38651448973092783 6.8137120366548176E-2 0.56111932204818893 -5.1597238594529471E-2 -0.53297513012515418 0.64234271266377829 -0.34600497656325369 0.44891361646474359 0.73208058304255696 -1.9643076816582616E-2 -0.49411725610580148 0.75945116504151811 -0.5882861745504534 0.45418948742071041 0.42705793514904489 -0.51052485898166267 -0.15549795394136878 0.16777026390254268 -0.66852494368587601 -0.13866241780378519 -0.49666637220222937 -0.24547352767946884 0.49655593767036121 -0.38633333269851899 0.11598000927766039 0.20508619128829564 -0.10184148667708715 -0.18830632627378563 5.2849182702113695E-2 7.5898249990677846E-2 6.3626316490237866E-2 -0.12934373869032068 0.88081014089466514 0.64770041045449278 -0.36555600991688608 0.55829962416282808 -6.1278092204811951E-2 0.1163836266321685 -0.24368004354608142 0.41370037161582229 -9.3635674591643903E-2 0.29243278253810456 2.2894077368538657E-2 -0.11796136075204189 8.0828131198345199E-2 -0.57351230770806638 -0.5460704172409675 -0.19760787207678798 0.54488062302011031 -0.49336667511018317 -0.61760110465091 -0.5174953876589059 0.61193747455263581 -0.33783645976355081 0.30441370544152546 0.20539409607254289 8.9875830811140589E-2 0.48039428890133906 -0.55484937532923251 -7.9615541109127164E-2 0.49910699532174596 -0.25408840787951575 -0.56268152376897485 -0.40883308097005716 0.35154941785921601 0.78079215420125103 -0.10852063315949445 -0.30725319341970053 -0.22743118610554081 -0.29839883922580779 0.40316644142740876 -0.16152368021440411 0.13382936715671345 0.14574595330793416 0.14428834572541183 -5.8577998162239187E-3 0.10202304800833129 0.65201588658103704 -0.67422271323894112 -0.58258798385762778 0.29924911423704748 0.31195808047146789 -0.39780118166319195 -0.36435527432746506 -0.24090016976244066 -0.16699020691851452 0.28577717690085591 0.72249285459319146 -0.630197623330922 -7.866392047906412E-2 -2.6100400793229506E-2 0.19524087781188915 -0.20971247561943862 -0.22518428315372185 0.29668828472277919 -3.501188677583067E-2 -0.48544825278766268 0.55475411387379725 0.79610430693150014 8.2391932256846045E-2ppgdp

Residuals

ln(ferility)

ln(ferility) 499 3677.2 4473 4321.8999999999996 13750.1 9162.1 3030.7 22851.5 57118.9 45158.8 5637.6 22461.599999999999 18184.099999999999 670.4 14497.3 5702 43814.8 4495.8 741.1 92624.7 2047.2 1977.9 4477.7 7402.9 10715.6 32647.599999999999 6365.1 519.70000000000005 176.6 797.2 1206.5999999999999 46360.9 3244 57047.9 450.8 727.4 11887.7 4354 6222.8 736.6 2665.1 12212.1 7703.8 1154.0999999999999 13819.5 5704.4 28364.3 18838.8 200.6 55830.2 1282.5999999999999 7020.8 5195.3999999999996 706.1 4072.6 2653.7 3425.6 16852.400000000001 429.1 14135.4 324.60000000000002 3545.7 44501.7 39545.9 24669 12468.8 579.1 2680.3 39857.1 1333.2 26503.8 35292.699999999997 7429 2882.3 427.5 539.4 2996 612.70000000000005 2026.2 31823.7 12884 39278 1406.4 2949.3 5227.1000000000004 888.5 46220.3 29311.599999999999 33877.1 4899 43140.9 4445.3 9166.7000000000007 801.8 1468.2 45430.400000000001 865.4 1047.5999999999999 10663 9283.7000000000007 980.7 218.6 11320.8 10975.5 105095.4 49990.2 421.9 357.4 8372.7999999999993 4684.5 598.79999999999995 19599.2 3069.4 1131.0999999999999 7488.3 9100.7000000000007 2678.2 1625.8 2246.6999999999998 6509.8 2865 407.5 876.2 5124.7 6190.1 534.70000000000005 20321.099999999999 46909.7 35319.5 32372.1 1131.9000000000001 357.7 1239.8 504 84588.7 20791 1003.2 10821.8 1819.5 7614 1428.4 2771.1 5410.7 2140.1 12263.2 21437.599999999999 26461 72397.899999999994 21052.2 7522.4 10351.4 532.29999999999995 6677.1 3343.3 1283.3 15835.9 1032.7 5123.2 11450.6 351.7 43783.1 15976 23109.8 1193.5 114.8 7254.8 30542.799999999999 2375.3000000000002 6171.7 1824.9 7018 3311.2 48906.2 68880.2 2931.5 816 516 4434.5 4612.8 524.6 3543.1 15205.1 4222.1000000000004 10095.1 4587.5 3187.2 509 3035 39624.699999999997 36326.800000000003 46545.9 11952.4 1427.3 2963.5 13502.7 1182.7 1437.2 1237.8 573.1 1.7864118629014598 0.42199441005937488 0.76173997202555699 1.6360798433805215 0.69314718055994529 0.77564840207168906 0.55100741339882253 0.51342224961325666 0.66731642052542384 0.2971372312225361 0.76453717664661835 0.62967475760437175 0.88789125735245711 0.76871836740701938 0.45425527227759638 0.39136618372866283 0.60704448150653356 0.98544359056247166 1.6249174832824866 0.56531380905006046 0.81447946572747032 1.1721724917761382 0.12575120530556025 0.96202862354800878 0.58778666490211906 0.68511500886268106 0.43567095016523022 1.7491998548092591 1.3989637642205535 0.88459364513090055 1.4555871876158399 0.52532006991644331 0.8237367502635472 0.47000362924573563 1.4868181988861897 1.7469364256197339 0.60540826625193855 0.44404459007563946 0.82986100387576744 1.5564589876432138 1.4911047254722358 0.92853794133402046 0.5944312076207876 1.4407825464039603 0.40613155265132483 0.37225297390205087 0.37706563358646639 0.40613155265132483 1.7020170937271937 0.63392782089997413 1.2778736121654701 1.0986122886681098 0.91228271047661635 1.7779985539780179 0.87254780892623618 0.96926261664026081 0.7751878908961547 1.6054298910365616 1.4452705662201879 0.53180403015118238 1.34755353280346 0.95628038009031346 0.62860865942237409 0.68662596356967986 0.70951253464620956 1.161587087829498 1.5452193401074492 0.42395969074432877 0.37637952721306783 1.383289852099592 0.43178241642553783 0.79615493063417442 0.7751878908961547 1.3454723665996355 1.6158175193981394 1.5845302767279155 0.78390154382840938 1.1502555218199482 1.097278065654973 0.12839321476839899 0.35767444427181588 0.74098450997410537 0.9313763692921958 0.72027584794819799 0.46184544154427198 1.5118250835670999 0.74050775191978291 1.0678093795130645 0.38933572617828072 0.81624937769392869 0.3492474281099357 1.0609104214840981 0.9086617047096639 1.5310438450060884 1.2527629684953681 0.81137456192459512 0.96355592434126924 0.93334448643998269 0.40945712937770185 0.56758395758459956 1.1154694057345327 1.6170091779304185 0.87962674750256364 0.40212620684264982 0.52057791520866903 0.15100287353652742 1.5025206300880229 1.7864118629014598 0.94468380637537297 0.51162530393655492 1.8110717802604279 0.24998020526776946 1.4780678985817615 1.4727013888606293 0.46373401623214022 0.80065538827523053 1.1960414339996557 0.37156355643248301 0.89445403726498074 0.48858001481867092 0.78070007756780679 1.5503246479415937 0.66217237626051473 1.1167795926235586 1.1939224684724346 0.95049890320389219 0.64185388617239469 0.58444776363660444 0.73764242044649664 0.75846664668058783 0.91629073187415511 1.9351380520734023 1.6921232790527083 0.68712910823438234 0.66680320522034331 0.76360564420850674 1.163463260987726 0.69314718055994529 1.451613827240533 0.87921172363273425 1.3347378742054885 1.0501220795076758 0.87962674750256364 1.1151415906193203 0.34712953109520095 0.27155269052189734 0.56360780920496012 0.79027389129066816 0.32858406377220672 0.3562748639173926 0.42461392694692518 1.6643048138749406 0.64553132661828205 1.3252165116113002 1.2493285060467332 0.97040005752118697 1.5271426697072703 0.44596705141749426 0.85015092936961001 1.553502280103797 0.31261855774181252 0.31626952930369356 0.39001300354924279 1.3964921860963366 1.83784757342081 0.86836019811660503 0.4081282255276481 0.80424122806553211 0.69064405034182685 1.441019260809137 0.81801616260581456 1.1549926221042173 0.65492596773974754 0.42918163472548043 1.0195690813276568 1.1512047387872804 1.7045662575256777 0.33432708027482477 0.42395969074432877 1.3517029163502716 1.3305173456508921 0.48980625654191517 0.64657954474361057 0.7040871205982796 0.8398415597107487 1.3083328196501789 1.7751218280750316 0.39406706315579509 0.53473744381230359 0.62433286455958559 0.73092454489397518 0.71441931583548512 0.81713316034093642 1.3217558399823195 0.87171168847618763 0.55961578793542266 1.5969603909229877 1.8405496333974869 1.1343011310766167

Variable Transformation; file UN11

28

ln(ppgdp) Residual Plot

6.2126060957515188 8.2099068719895989 8.405814603432848 8.371450399362784 9.5288013757955436 9.1228306890345792 8.0165488949239982 10.036772039682001 10.952890339124952 10.717940445722775 8.6372137220128131 10.019562463511157 9.8083028648573372 6.5078745491678731 9.5817177041734567 8.6485722694726181 10.687726938832723 8.4108989065983195 6.6081355689573131 11.436311123726746 7.6242282848455787 7.5897909547873637 8.406864800720653 8.9096270943145814 9.2794559026068608 10.393526625111543 8.7585852217871807 6.2532517220143964 5.1738872881698592 6.6811055883386397 7.0955617660066617 10.74421171055257 8.0845624152353039 10.951646544796773 6.1110237821656215 6.5894765325528883 9.3832595311074911 8.3788502417944919 8.7359752452129662 6.6020450040109653 7.8879968593481156 9.4101825424881262 8.9494689926010018 7.0510760984263587 9.5338359172170968 8.6489930858626121 10.252886591155431 9.8436738518342715 5.3013128755278354 10.930070220601412 7.1566445467147624 8.8566324506408556 8.5555288976818105 6.5597568705223015 8.3120368951164139 7.8837101715776026 8.1390319178354176 9.7322483588722797 6.0616899919974792 9.5564375682769942 5.7825936550804906 8.1734908806863054 10.703282669671836 10.585217301576824 10.113302673639005 9.4309848030892969 6.3614751742317441 7.8936840075385621 10.593055836478793 7.1953373464335844 10.185043397920472 10.471431422668699 8.913146539151807 7.9663438655209271 6.0579542883768145 6.2904574107056295 8.0050333446371109 6.417875419731609 7.613917396619577 10.367966574201658 9.46374151045109 10.578419844675169 7.2487885269309125 7.9893231330409886 8.5616119099628634 6.7895346475947056 10.741174374503975 10.285738621092536 10.430494548880466 8.4967863816385751 10.672226782034295 8.399602637234107 9.1233326313435779 6.6868592002084064 7.2917924396766809 10.723936763469254 6.7631918277907843 6.9542571126335568 9.2745350840181793 9.1360154532143234 6.888266602398275 5.3872435757424384 9.3343970206381623 9.3034207949921939 11.56262378806705 10.819582265199772 6.0447683191302932 5.878855602725328 9.032743635617944 8.4520144653912421 6.3949276525454728 9.8832440280590692 8.0292373817409946 7.0309458895373353 8.9210970814574466 9.1161066126234367 7.8929002060614657 7.3937552813124716 7.7172177519234308 8.7810640127644799 7.9603236291488395 6.0100409326809174 6.7755943753797983 8.5418272657079104 8.7307065206370034 6.2817058419546861 9.9194150340855014 10.755979756077155 10.472190498332305 10.385052219700158 7.0316529156383742 5.879694646264972 7.1227053552678186 6.2225762680713688 11.34555596693313 9.9422754797433885 6.9109501698786566 9.2893178971596093 7.5063170170522149 8.937743936942443 7.2643102157202932 7.926999632266674 8.5961337534888447 7.6686078358960952 9.4143581868518975 9.9729016686204481 10.183427229849748 11.189932572428278 9.9547603467135506 8.9256405149628666 9.2448770552464179 6.2772072401787113 8.8064390405316999 8.1147136221484395 7.157190164250415 9.6700347934801432 6.9399320106773583 8.5415345228023956 9.3457974093561873 5.8627785394799368 10.687003177158442 9.6788428750956506 10.048012048968754 7.084645445778885 4.7431914838854663 8.8894185977432674 10.326884257608627 7.7728790242810479 8.7277296056912128 7.5092804699947697 8.8562335561431595 8.1050659404345229 10.797659456791925 11.140124042697861 7.9832695164042695 6.7044143549641069 6.2461067654815627 8.3971701488165067 8.4365903268841382 6.2626360674327737 8.1727573291355231 9.6293861768737905 8.3480879135848998 9.2198054365918818 8.4310904923628254 8.0668980673902784 6.2324480165505225 8.0179667034935989 10.587207940173004 10.500311039860483 10.74819420148998 9.3886873740147259 7.2635398266357232 7.994126281227893 9.5106449444291865 7.0755552392570715 7.2704520552393639 7.1210908893052611 6.3510602215576917 0.40784455052790092 -0.54283247322373751 -0.16250466654320006 0.70471666728028692 1.5290119690146708E-3 -6.6507549398076016E-5 -0.45387353352405002 -7.2969904477447556E-2 0.2706979764430093 -0.1481510330829815 -0.11177318394486224 3.9717643486564924E-2 0.25417176250742846 -0.54868414792307563 -0.22640129019499805 -0.48259125618318177 0.15549749570361471 6.2252164308221669E-2 0.3282840167818124 0.26883587721893898 -0.27167061175699891 7.888872872736874E-2 -0.79827588511939407 0.14214863482991003 -0.15548336518918915 0.17262449092595411 -0.41549733017803653 0.37905227523244367 -0.19477392722961406 -0.3969240974443905 0.25992395369924548 8.5473892507772709E-2 -0.1670552104573807 7.312753343396533E-2 8.7208131955557766E-2 0.44643774371423639 -0.11635886437227561 -0.48578571024578354 -2.5990928284407744E-2 0.25856386191510383 0.45959425184392932 0.2123479067654197 -0.21719554037918076 0.23590411595211158 -0.28444371175972039 -0.50161729398451049 -0.16455843733765496 -0.22026084979815919 0.13467558547477743 0.23258219414074288 9.4863663222713113E-2 0.26775447083487869 1.9051355976275164E-2 0.47134345043225134 -7.1122861885415833E-2 -6.3135843443891004E-2 -0.2043207239981315 0.95595572152516284 3.5441015195993408E-2 -0.15408930707146618 -0.12009076478639757 -1.6090068011292091E-2 0.18028403993942077 0.21384412830956245 0.13897368502954366 0.44970623710019386 0.19749022553638595 -0.60637269135134031 -9.4778557216746828E-2 0.2082951083521829 -0.12389535748305203 0.29980237486767813 -4.3963045575813986E-2 0.3301914585618182 0.20521411816702728 0.22208984761479234 -0.22336484687618707 -0.18579029394527757 8.992089877325915E-3 -0.38939206225361073 -0.34742086152570034 0.26679458296903225 -0.23254597383460707 -0.29024490973217454 -0.43012581826163576 0.25276839745170498 0.30003239099754841 0.53299059957184181 -0.11549689424761389 -8.9150476454901706E-2 -0.10551041186229326 0.13537897544440858 0.13305077233064977 0.25071796190040652 9.7748876706410304E-2 0.36732843355919531 -0.30095767126857598 -0.29158997623424598 -0.33483224723295835 -0.20539973095347253 -0.12313497703659215 6.7468195869053282E-2 0.14773775827371094 -0.33617950091094345 0.25026562480995496 -0.27323030957928895 8.9185758144570526E-2 0.33870820720063821 0.15030738288540546 -0.40304904309775014 0.47027233942520019 -0.36821524363059799 0.47581536899223642 0.26365298993807706 -0.35376996709978464 2.3547587662120062E-2 0.16554668759545899 -0.7623289544951628 -0.17243329198076429 -0.35793178877606141 -0.23582792114831341 0.12979600531438029 -0.59977203426597092 0.22070994798706778 0.33697912114196926 -0.41375441150628633 3.1151253444757443E-2 0.14703933434420324 0.24144710704154604 0.24422065747338162 -0.29261120674261742 0.48760820406256311 0.50208283385255248 -0.68937288507316674 0.35152536204853446 0.15763854791495036 -7.0442225625999777E-2 -4.8079939466696975E-2 0.34103845582346404 6.5156132858059324E-2 0.17403084559532167 2.6691021956819494E-2 -5.1933197922517937E-3 3.8184727653630901E-2 -0.36819551963553754 -0.3280701972888157 7.5952464258013386E-3 0.44275869519486766 -0.27479679499577225 -0.46028794813455265 -0.32581910398760566 0.2991196147679589 -0.19572404539564148 0.34067036696086506 6.6431581659919692E-2 0.30803836123023565 0.29924076522325804 -0.45016323484933185 0.12062352822809463 0.10246826418642807 -0.13907835513730787 -0.34426757476238146 -0.19405078501904788 0.19856763877674233 0.15489133812783029 4.4294023651141656E-2 -0.11816724459970113 -0.25111588050291644 -0.16691596428366495 0.33105776803600029 -1.2924286137393604E-2 0.16844796224789405 0.22615147954587755 7.1348612337216899E-2 7.7943182542945522E-3 -0.12548459776127596 0.33293860172954837 -0.59170825522088899 -0.49390976328647956 -1.6500698078016907E-2 0.35799494250225949 -0.18097579199479147 -0.28962316529430521 -5.1539490784188291E-2 -7.9167183866154067E-2 0.31388169304699987 0.40066476535591944 -0.610520185024788 6.2367968912100835E-2 0.13396271532446891 0.29190333963216197 -6.2234382901104057E-3 -0.34373345420351176 0.31223005342271026 0.17633241900669205 -0.64019179372311563 0.43752564305704156 0.65017475191810514 -0.2155854387158056ln(ppgdp)

Residuals

ln(ferility)

ln(ferility) 6.2126060957515188 8.2099068719895989 8.405814603432848 8.371450399362784 9.5288013757955436 9.1228306890345792 8.0165488949239982 10.036772039682001 10.952890339124952 10.717940445722775 8.6372137220128131 10.019562463511157 9.8083028648573372 6.5078745491678731 9.5817177041734567 8.6485722694726181 10.687726938832723 8.4108989065983195 6.6081355689573131 11.436311123726746 7.6242282848455787 7.5897909547873637 8.406864800720653 8.9096270943145814 9.2794559026068608 10.393526625111543 8.7585852217871807 6.2532517220143964 5.1738872881698592 6.6811055883386397 7.0955617660066617 10.74421171055257 8.0845624152353039 10.951646544796773 6.1110237821656215 6.5894765325528883 9.3832595311074911 8.3788502417944919 8.7359752452129662 6.6020450040109653 7.8879968593481156 9.4101825424881262 8.9494689926010018 7.0510760984263587 9.5338359172170968 8.6489930858626121 10.252886591155431 9.8436738518342715 5.3013128755278354 10.930070220601412 7.1566445467147624 8.8566324506408556 8.5555288976818105 6.5597568705223015 8.3120368951164139 7.8837101715776026 8.1390319178354176 9.7322483588722797 6.0616899919974792 9.5564375682769942 5.7825936550804906 8.1734908806863054 10.703282669671836 10.585217301576824 10.113302673639005 9.4309848030892969 6.3614751742317441 7.8936840075385621 10.593055836478793 7.1953373464335844 10.185043397920472 10.471431422668699 8.913146539151807 7.9663438655209271 6.0579542883768145 6.2904574107056295 8.0050333446371109 6.417875419731609 7.613917396619577 10.367966574201658 9.46374151045109 10.578419844675169 7.2487885269309125 7.9893231330409886 8.5616119099628634 6.7895346475947056 10.741174374503975 10.285738621092536 10.430494548880466 8.4967863816385751 10.672226782034295 8.399602637234107 9.1233326313435779 6.6868592002084064 7.2917924396766809 10.723936763469254 6.7631918277907843 6.9542571126335568 9.2745350840181793 9.1360154532143234 6.888266602398275 5.3872435757424384 9.3343970206381623 9.3034207949921939 11.56262378806705 10.819582265199772 6.0447683191302932 5.878855602725328 9.032743635617944 8.4520144653912421 6.3949276525454728 9.8832440280590692 8.0292373817409946 7.0309458895373353 8.9210970814574466 9.1161066126234367 7.8929002060614657 7.3937552813124716 7.7172177519234308 8.7810640127644799 7.9603236291488395 6.0100409326809174 6.7755943753797983 8.5418272657079104 8.7307065206370034 6.2817058419546861 9.9194150340855014 10.755979756077155 10.472190498332305 10.385052219700158 7.0316529156383742 5.879694646264972 7.1227053552678186 6.2225762680713688 11.34555596693313 9.9422754797433885 6.9109501698786566 9.2893178971596093 7.5063170170522149 8.937743936942443 7.2643102157202932 7.926999632266674 8.5961337534888447 7.6686078358960952 9.4143581868518975 9.9729016686204481 10.183427229849748 11.189932572428278 9.9547603467135506 8.9256405149628666 9.2448770552464179 6.2772072401787113 8.8064390405316999 8.1147136221484395 7.157190164250415 9.6700347934801432 6.9399320106773583 8.5415345228023956 9.3457974093561873 5.8627785394799368 10.687003177158442 9.6788428750956506 10.048012048968754 7.084645445778885 4.7431914838854663 8.8894185977432674 10.326884257608627 7.7728790242810479 8.7277296056912128 7.5092804699947697 8.8562335561431595 8.1050659404345229 10.797659456791925 11.140124042697861 7.9832695164042695 6.7044143549641069 6.2461067654815627 8.3971701488165067 8.4365903268841382 6.2626360674327737 8.1727573291355231 9.6293861768737905 8.3480879135848998 9.2198054365918818 8.4310904923628254 8.0668980673902784 6.2324480165505225 8.0179667034935989 10.587207940173004 10.500311039860483 10.74819420148998 9.3886873740147259 7.2635398266357232 7.994126281227893 9.5106449444291865 7.0755552392570715 7.2704520552393639 7.1210908893052611 6.3510602215576917 1.7864118629014598 0.42199441005937488 0.76173997202555699 1.6360798433805215 0.69314718055994529 0.77564840207168906 0.55100741339882253 0.51342224961325666 0.66731642052542384 0.2971372312225361 0.76453717664661835 0.62967475760437175 0.88789125735245711 0.76871836740701938 0.45425527227759638 0.39136618372866283 0.60704448150653356 0.98544359056247166 1.6249174832824866 0.56531380905006046 0.81447946572747032 1.1721724917761382 0.12575120530556025 0.96202862354800878 0.58778666490211906 0.68511500886268106 0.43567095016523022 1.7491998548092591 1.3989637642205535 0.88459364513090055 1.4555871876158399 0.52532006991644331 0.8237367502635472 0.47000362924573563 1.4868181988861897 1.7469364256197339 0.60540826625193855 0.44404459007563946 0.82986100387576744 1.5564589876432138 1.4911047254722358 0.92853794133402046 0.5944312076207876 1.4407825464039603 0.40613155265132483 0.37225297390205087 0.37706563358646639 0.40613155265132483 1.7020170937271937 0.63392782089997413 1.2778736121654701 1.0986122886681098 0.91228271047661635 1.7779985539780179 0.87254780892623618 0.96926261664026081 0.7751878908961547 1.6054298910365616 1.4452705662201879 0.53180403015118238 1.34755353280346 0.95628038009031346 0.62860865942237409 0.68662596356967986 0.70951253464620956 1.161587087829498 1.5452193401074492 0.42395969074432877 0.37637952721306783 1.383289852099592 0.43178241642553783 0.79615493063417442 0.7751878908961547 1.3454723665996355 1.6158175193981394 1.5845302767279155 0.78390154382840938 1.1502555218199482 1.097278065654973 0.12839321476839899 0.35767444427181588 0.74098450997410537 0.9313763692921958 0.72027584794819799 0.46184544154427198 1.5118250835670999 0.74050775191978291 1.0678093795130645 0.38933572617828072 0.81624937769392869 0.3492474281099357 1.0609104214840981 0.9086617047096639 1.5310438450060884 1.2527629684953681 0.81137456192459512 0.96355592434126924 0.93334448643998269 0.40945712937770185 0.56758395758459956 1.1154694057345327 1.6170091779304185 0.87962674750256364 0.40212620684264982 0.52057791520866903 0.15100287353652742 1.5025206300880229 1.7864118629014598 0.94468380637537297 0.51162530393655492 1.8110717802604279 0.24998020526776946 1.4780678985817615 1.4727013888606293 0.46373401623214022 0.80065538827523053 1.1960414339996557 0.37156355643248301 0.89445403726498074 0.48858001481867092 0.78070007756780679 1.5503246479415937 0.66217237626051473 1.1167795926235586 1.1939224684724346 0.95049890320389219 0.64185388617239469 0.58444776363660444 0.73764242044649664 0.75846664668058783 0.91629073187415511 1.9351380520734023 1.6921232790527083 0.68712910823438234 0.66680320522034331 0.76360564420850674 1.163463260987726 0.69314718055994529 1.451613827240533 0.87921172363273425 1.3347378742054885 1.0501220795076758 0.87962674750256364 1.1151415906193203 0.34712953109520095 0.27155269052189734 0.56360780920496012 0.79027389129066816 0.32858406377220672 0.3562748639173926 0.42461392694692518 1.6643048138749406 0.64553132661828205 1.3252165116113002 1.2493285060467332 0.97040005752118697 1.5271426697072703 0.44596705141749426 0.85015092936961001 1.553502280103797 0.31261855774181252 0.31626952930369356 0.39001300354924279 1.3964921860963366 1.83784757342081 0.86836019811660503 0.4081282255276481 0.80424122806553211 0.69064405034182685 1.441019260809137 0.81801616260581456 1.1549926221042173 0.65492596773974754 0.42918163472548043 1.0195690813276568 1.1512047387872804 1.7045662575256777 0.33432708027482477 0.42395969074432877 1.3517029163502716 1.3305173456508921 0.48980625654191517 0.64657954474361057 0.7040871205982796 0.8398415597107487 1.3083328196501789 1.7751218280750316 0.39406706315579509 0.53473744381230359 0.62433286455958559 0.73092454489397518 0.71441931583548512 0.81713316034093642 1.3217558399823195 0.87171168847618763 0.55961578793542266 1.5969603909229877 1.8405496333974869 1.1343011310766167

Variable Transformation; file UN11

29

A linear regression model with more than one independent variable is called a multiple linear regression model.

Multiple Linear Regression

Note: The error term ε is assumed to be normally distributed with

a zero mean and a constant unknown standard deviation σ.

30

We estimate the regression coefficients β0, β1, β2,…, βk by finding b0, b1, b2,… bk, then we use the estimated regression equation:

The estimated regression coefficient bj (j = 1,2,…,k) represents the expected change in the dependent variable Y when the associated independent variable Xj is increased by one unit while the values of all other independent variables are held constant.

Estimated Multiple Regression Equation

31

ANOVA Table for Multiple Regression

32

Testing for Significance

33

Example: Adding House Age to Predict Market Value

Although House Age is found insignificant, both adjusted R Square and Standard Error improve.

34

 SUMMARY OUTPUT Regression Statistics Multiple R 0.7455 R Square 0.5558 Adjusted R Square 0.5330 Standard Error 7211.8485 Observations 42 ANOVA df SS MS F Significance F Regression 2 2537650171 1268825085 24.3954 0.0000 Residual 39 2028419591 52010758.75 Total 41 4566069762 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 47331.38154 13884.34664 3.408974347 0.0015 19247.6396 75415.1234 House Age -825.1612203 607.3128421 -1.358708664 0.1820 -2053.5674 403.2450 Square Feet 40.91106845 6.696523994 6.109299165 0.0000 27.3661 54.4561

Predict student graduation rates using several indicators:

Example 8.12: Interpreting Regression Results for the Colleges and Universities Data

35

Regression model

The value of R2 indicates that 53.44% of the variation in Graduation% is explained by the four independent variables.

All independent variables are statistically significant at α = 0.05.

Example 8.12 Continued

36

Model Building Issues

37

Construct a model with all available independent variables. Check for significance of the independent variables by examining the p-values.

Identify the independent variable having the largest p-value that exceeds the chosen level of significance.

Remove the variable identified in step 2 from the model and evaluate adjusted R2 and Standard Error

(Don’t remove all variables with p-values that exceed α at the same time, but remove only one at a time.)

In general, continue until all variables are significant and/or adjusted R2 and Standard Error cannot be improved.

Systematic Model Building Approach

38

Banking Data (Predicting Customer Average Bank Balance)

Example 8.13: Identifying the Best Regression Model

Home Value has the largest p-value; drop and re-run the regression.

39

Banking Data regression after removing Home Value

Example 8.13 Continued

Adjusted R2 and Standard Error improve. All X variables are significant.

40

Income and Wealth are highly correlated!

Remove one of them.

Multicollinearity

41

Colleges and Universities correlation matrix; none exceed the recommended threshold of ±0.7

Banking Data correlation matrix; large correlations exist

Example 8.14: Identifying Potential Multicollinearity

42

If we remove Wealth from the model, adjusted R2 = 0.9201 and s = 2458, but we discover that Education is no longer significant.

Dropping Education and leaving only Age and Income in the model results in adjusted R2 = 0.9202 and s = 2457.

However, if we remove Income from the model instead of Wealth, adjusted R2 = 0.9345, s = 2226, and all remaining variables (Age, Education, and Wealth) are significant:

Example 8.14 Continued

43

The regression analysis tool in XLMiner has some advanced options not available in Regression tool of Data Analysis of Excel.

Best-subsets regression evaluates either all possible regression models for a set of independent variables or the best subsets of models for a fixed number of independent variables.

Advanced Techniques for Regression Modeling using XLMiner

44

In XLMiner regression models are evaluated by minimizing Mallow’s statistic Cp.

Backward Elimination begins with all independent variables in the model and deletes one at a time until the best model is identified.

Forward Selection begins with a model having no independent variables and successively adds one at a time until no additional variable makes a significant contribution.

Stepwise Selection is similar to Forward Selection except that at each step, the procedure considers dropping variables that are not statistically significant.

Sequential Replacement replaces variables sequentially, retaining those that improve performance. These options might terminate with a different model.

Exhaustive Search looks at all combinations of variables to find the one with the best fit, but it can be time consuming for large numbers of variables.

Best-Subsets Procedures

45

Click the Predict button in the Data Mining group and choose Multiple Linear Regression.

Enter the range of the data (including headers)

Move the appropriate variables to the boxes on the right.

Example 8.19: Using XLMiner for Regression on the file: Banking Data

46

Select the output options and check the Summary report box. Before clicking Finish, click on the Best subsets button.

Select the best subsets option:

Example 8.19 Continued

47

Regression output (all variables):

Best subsets results:

Example 8.19 Continued

The strongly correlated Income and Wealth are kept together!

If you click “Choose Subset,” XLMiner will create a new worksheet

with the results for this model.

48

Identifying the best regression model often requires experimentation and trial and error.

The independent variables selected should make sense in attempting to explain the dependent variable

Logic should guide your model development. In many applications, behavioral, economic, or physical theory might suggest that certain variables should belong in a model.

Additional variables increase R2 and, therefore, help to explain a larger proportion of the variation.

Even though a variable with a large p-value is not statistically significant, it could simply be the result of sampling error and a modeler might wish to keep it.

Good models are as simple as possible (the principle of parsimony).

Practical Issues in Regression Modeling

49

Regression analysis requires numerical data.

Categorical data can be included as independent variables, but must be coded numeric using dummy variables.

For categorical variables with 2 levels, one dummy variable (coded as 0 or 1), is needed.

For categorical variables with m levels, m – 1 dummy variables are needed.

Regression with Categorical Variables

50

Employee Salaries provides data for 35 employees

Predict Salary using Age and MBA (coded as yes=1, no=0)

Example 8.15: A Model with Categorical Variables

51

Example 8.15 Continued

52

Interactions

53

Define an interaction between Age and MBA and re-run the regression.

Example 8.16: Incorporating Interaction Terms in a Regression Model

The MBA variable becomes insignificant; drop it and re-run.

54

Example 8.16 Continued

55

Example 8.17: A Regression Model with Multiple Levels of Categorical Variables

The Excel file Surface Finish provides measurements of the surface finish of 35 parts produced on a lathe, along with the revolutions per minute (RPM) of the spindle and one of four types of cutting tools used.

56

Because we have a continuous independent variable RPM, and a categorical independent variable Cutting Tool with m = 4 levels, we define a regression model of the form:

Example 8.17 Continued

57

Note. There are m – 1 dummies defined.

Add 3 columns to the data, one for each of the three tool type variables

Dummy variables can be created in XLMiner by using Transform > Transform Categorical Data > Create Dummies

Example 8.17 Continued

58

Regression results:

Example 8.17 Continued

59

Curvilinear models may be appropriate when scatter charts or residual plots show nonlinear relationships.

A second order polynomial might be used

Here β1 represents the linear effect of X on Y and β2 represents the curvilinear effect.

This model is linear in the β parameters so we can use linear regression methods.

Regression Models with Nonlinear Terms

60

The U-shape of the residual plot (a second-order polynomial trendline was fit to the residual data) suggests that a linear relationship is not appropriate.

Example 8.18: Modeling Beverage Sales Using Curvilinear Regression

61

Example 8.18 Continued

62

Regression Statistics

Multiple R0.439989

R Square0.19359

Standard Error1.206005

Observations199

ANOVA

dfSSMSFSignificance F

Regression168.7847768.7847747.292727.9E-11

Residual197286.52621.454447

Total198355.3109

CoefficientsStandard Errort StatP-valueLower 95%Upper 95%

Intercept3.1779120.10477330.331463.69E-762.9712913.384532

ppgdp-3.2E-054.65E-06-6.876977.9E-11-4.1E-05-2.3E-05

## UNdata

 region group fertility ppgdp lifeExpF pctUrban Afghanistan Asia other 5.968 499 49.49 23 Albania Europe other 1.525 3677.2 80.4 53 Algeria Africa africa 2.142 4473 75 67 Angola Africa africa 5.135 4321.9 53.17 59 Anguilla Caribbean other 2 13750.1 81.1 100 Argentina Latin Amer other 2.172 9162.1 79.89 93 Armenia Asia other 1.735 3030.7 77.33 64 Aruba Caribbean other 1.671 22851.5 77.75 47 Australia Oceania oecd 1.949 57118.9 84.27 89 Austria Europe oecd 1.346 45158.8 83.55 68 Azerbaijan Asia other 2.148 5637.6 73.66 52 Bahamas Caribbean other 1.877 22461.6 78.85 84 Bahrain Asia other 2.43 18184.1 76.06 89 Bangladesh Asia other 2.157 670.4 70.23 29 Barbados Caribbean other 1.575 14497.3 80.26 45 Belarus Europe other 1.479 5702 76.37 75 Belgium Europe oecd 1.835 43814.8 82.81 97 Belize Latin Amer other 2.679 4495.8 77.81 53 Benin Africa africa 5.078 741.1 58.66 42 Bermuda Caribbean other 1.76 92624.7 82.3 100 Bhutan Asia other 2.258 2047.2 69.84 35 Bolivia Latin Amer other 3.229 1977.9 69.4 67 Bosnia and Herzegovina Europe other 1.134 4477.7 78.4 49 Botswana Africa africa 2.617 7402.9 51.34 62 Brazil Latin Amer other 1.8 10715.6 77.41 87 Brunei Darussalam Asia other 1.984 32647.6 80.64 76 Bulgaria Europe other 1.546 6365.1 77.12 72 Burkina Faso Africa africa 5.75 519.7 57.02 27 Burundi Africa africa 4.051 176.6 52.58 11 Cambodia Asia other 2.422 797.2 65.1 20 Cameroon Africa africa 4.287 1206.6 53.56 59 Canada North America oecd 1.691 46360.9 83.49 81 Cape Verde Africa africa 2.279 3244 77.7 62 Cayman Islands Caribbean other 1.6 57047.9 83.8 100 Central African Republic Africa africa 4.423 450.8 51.3 39 Chad Africa africa 5.737 727.4 51.61 28 Chile Latin Amer oecd 1.832 11887.7 82.35 89 China Asia other 1.559 4354 75.61 48 Colombia Latin Amer other 2.293 6222.8 77.69 75 Comoros Africa africa 4.742 736.6 63.18 28 Congo Africa africa 4.442 2665.1 59.33 63 Cook Islands Oceania other 2.5308062841 12212.1 76.2454672362 76 Costa Rica Latin Amer other 1.812 7703.8 81.99 65 Cote dIvoire Africa africa 4.224 1154.1 57.71 51 Croatia Europe other 1.501 13819.5 80.37 58 Cuba Caribbean other 1.451 5704.4 81.33 75 Cyprus Asia other 1.458 28364.3 82.14 71 Czech Republic Europe oecd 1.501 18838.8 81 74 Democratic Republic of the Congo Africa africa 5.485 200.6 50.56 36 Denmark Europe oecd 1.885 55830.2 81.37 87 Djibouti Africa africa 3.589 1282.6 60.04 76 Dominica Caribbean other 3 7020.8 78.2 67 Dominican Republic Caribbean other 2.49 5195.4 76.57 70 East Timor Asia other 5.918 706.1 64.2 29 Ecuador Latin Amer other 2.393 4072.6 78.91 68 Egypt Africa africa 2.636 2653.7 75.52 44 El Salvador Latin Amer other 2.171 3425.6 77.09 65 Equatorial Guinea Africa africa 4.98 16852.4 52.91 40 Eritrea Africa africa 4.243 429.1 64.41 22 Estonia Europe oecd 1.702 14135.4 79.95 70 Ethiopia Africa africa 3.848 324.6 61.59 17 Fiji Oceania other 2.602 3545.7 72.27 52 Finland Europe oecd 1.875 44501.7 83.28 85 France Europe oecd 1.987 39545.9 84.9 86 French Polynesia Oceania other 2.033 24669 78.07 51 Gabon Africa africa 3.195 12468.8 64.32 86 Gambia Africa africa 4.689 579.1 60.3 59 Georgia Asia other 1.528 2680.3 77.31 53 Germany Europe oecd 1.457 39857.1 82.99 74 Ghana Africa africa 3.988 1333.2 65.8 52 Greece Europe oecd 1.54 26503.8 82.58 62 Greenland NorthAtlantic other 2.217 35292.7 71.6 84 Grenada Caribbean other 2.171 7429 77.72 40 Guatemala Latin Amer other 3.84 2882.3 75.1 50 Guinea Africa africa 5.032 427.5 56.39 36 Guinea-Bissau Africa africa 4.877 539.4 50.4 30 Guyana Latin Amer other 2.19 2996 73.45 29 Haiti Caribbean other 3.159 612.7 63.87 54 Honduras Latin Amer other 2.996 2026.2 75.92 52 Hong Kong Asia other 1.137 31823.7 86.35 100 Hungary Europe oecd 1.43 12884 78.47 68 Iceland Europe other 2.098 39278 83.77 94 India Asia other 2.538 1406.4 67.62 30 Indonesia Asia other 2.055 2949.3 71.8 45 Iran Asia other 1.587 5227.1 75.28 71 Iraq Asia other 4.535 888.5 72.6 66 Ireland Europe oecd 2.097 46220.3 83.17 62 Israel Asia oecd 2.909 29311.6 84.19 92 Italy Europe oecd 1.476 33877.1 84.62 69 Jamaica Caribbean other 2.262 4899 75.98 52 Japan Asia oecd 1.418 43140.9 87.12 67 Jordan Asia other 2.889 4445.3 75.17 79 Kazakhstan Asia other 2.481 9166.7 72.84 59 Kenya Africa africa 4.623 801.8 59.16 23 Kiribati Oceania other 3.5 1468.2 63.1 44 Kuwait Asia other 2.251 45430.4 75.89 98 Kyrgyzstan Asia other 2.621 865.4 72.36 35 Laos Asia other 2.543 1047.6 69.42 34 Latvia Europe other 1.506 10663 78.51 68 Lebanon Asia other 1.764 9283.7 75.07 87 Lesotho Africa africa 3.051 980.7 48.11 28 Liberia Africa africa 5.038 218.6 58.59 48 Libya Africa africa 2.41 11320.8 77.86 78 Lithuania Europe other 1.495 10975.5 78.28 67 Luxembourg Europe oecd 1.683 105095.4 82.67 85 Macao Asia other 1.163 49990.2 83.8 100 Madagascar Africa africa 4.493 421.9 68.61 31 Malawi Africa africa 5.968 357.4 55.17 20 Malaysia Asia other 2.572 8372.8 76.86 73 Maldives Asia other 1.668 4684.5 78.7 41 Mali Africa africa 6.117 598.8 53.14 37 Malta Europe other 1.284 19599.2 82.29 95 Marshall Islands Oceania other 4.3844662585 3069.4 70.6 72 Mauritania Africa africa 4.361 1131.1 60.95 42 Mauritius Africa africa 1.59 7488.3 76.89 42 Mexico Latin Amer oecd 2.227 9100.7 79.64 78 Micronesia Oceania other 3.307 2678.2 70.17 23 Moldova Europe other 1.45 1625.8 73.48 48 Mongolia Asia other 2.446 2246.7 72.83 63 Montenegro Europe other 1.63 6509.8 77.37 61 Morocco Africa africa 2.183 2865 74.86 59 Mozambique Africa africa 4.713 407.5 51.81 39 Myanmar Asia other 1.939 876.2 67.87 34 Namibia Africa africa 3.055 5124.7 63.04 39 Nauru Oceania other 3.3 6190.1 57.1 100 Nepal Asia other 2.587 534.7 70.05 19 Neth Antilles Caribbean other 1.9 20321.1 79.86 93 Netherlands Europe oecd 1.794 46909.7 82.79 83 New Caledonia Oceania other 2.091 35319.5 80.49 57 New Zealand Oceania oecd 2.135 32372.1 82.77 86 Nicaragua Latin Amer other 2.5 1131.9 77.45 58 Niger Africa africa 6.925 357.7 55.77 17 Nigeria Africa africa 5.431 1239.8 53.38 51 North Korea Asia other 1.988 504 72.12 60 Norway Europe oecd 1.948 84588.7 83.47 80 Oman Asia other 2.146 20791 76.44 73 Pakistan Asia other 3.201 1003.2 66.88 36 Palau Oceania other 2 10821.8 72.1 84 Palestinian Territory Asia other 4.27 1819.5 74.81 74 Panama Latin Amer other 2.409 7614 79.07 75 Papua New Guinea Oceania other 3.799 1428.4 65.52 13 Paraguay Latin Amer other 2.858 2771.1 74.91 62 Peru Latin Amer other 2.41 5410.7 76.9 77 Philippines Asia other 3.05 2140.1 72.57 49 Poland Europe oecd 1.415 12263.2 80.56 61 Portugal Europe oecd 1.312 21437.6 82.76 61 Puerto Rico Caribbean other 1.757 26461 83.2 99 Qatar Asia other 2.204 72397.9 78.24 96 Republic of Korea Asia other 1.389 21052.2 83.95 83 Romania Europe other 1.428 7522.4 77.95 58 Russian Federation Europe other 1.529 10351.4 75.01 73 Rwanda Africa africa 5.282 532.3 57.13 19 Saint Lucia Caribbean other 1.907 6677.1 77.54 28 Samoa Oceania other 3.763 3343.3 76.02 20 Sao Tome and Principe Africa africa 3.488 1283.3 66.48 63 Saudi Arabia Asia other 2.639 15835.9 75.57 82 Senegal Africa africa 4.605 1032.7 60.92 43 Serbia Europe other 1.562 5123.2 77.05 56 Seychelles Africa africa 2.34 11450.6 78 56 Sierra Leone Africa africa 4.728 351.7 48.87 39 Singapore Asia other 1.367 43783.1 83.71 100 Slovakia Europe oecd 1.372 15976 79.53 55 Slovenia Europe oecd 1.477 23109.8 82.84 49 Solomon Islands Oceania other 4.041 1193.5 70 19 Somalia Africa africa 6.283 114.8 53.38 38 South Africa Africa africa 2.383 7254.8 54.09 62 Spain Europe other 1.504 30542.8 84.76 78 Sri Lanka Asia other 2.235 2375.3 78.4 14 St Vincent and Grenadines Caribbean other 1.995 6171.7 74.73 50 Sudan Africa africa 4.225 1824.9 63.82 41 Suriname Latin Amer other 2.266 7018 74.18 70 Swaziland Africa africa 3.174 3311.2 48.54 21 Sweden Europe oecd 1.925 48906.2 83.65 85 Switzerland Europe oecd 1.536 68880.2 84.71 74 Syria Asia other 2.772 2931.5 77.72 56 Tajikistan Asia other 3.162 816 71.23 26 Tanzania Africa africa 5.499 516 60.31 27 TFYR Macedonia Europe other 1.397 4434.5 77.14 59 Thailand Asia other 1.528 4612.8 77.76 34 Togo Africa africa 3.864 524.6 59.4 44 Tonga Oceania other 3.783 3543.1 75.38 24 Trinidad and Tobago Caribbean other 1.632 15205.1 73.82 14 Tunisia Africa africa 1.909 4222.1 77.05 68 Turkey Asia oecd 2.022 10095.1 76.61 70 Turkmenistan Asia other 2.316 4587.5 69.4 50 Tuvalu Oceania other 3.7 3187.2 65.1 51 Uganda Africa africa 5.901 509 55.44 13 Ukraine Europe other 1.483 3035 74.58 69 United Arab Emirates Asia other 1.707 39624.7 78.02 84 United Kingdom Europe oecd 1.867 36326.8 82.42 80 United States North America oecd 2.077 46545.9 81.31 83 Uruguay Latin Amer other 2.043 11952.4 80.66 93 Uzbekistan Asia other 2.264 1427.3 71.9 36 Vanuatu Oceania other 3.75 2963.5 73.58 26 Venezuela Latin Amer other 2.391 13502.7 77.73 94 Viet Nam Asia other 1.75 1182.7 77.44 31 Yemen Asia other 4.938 1437.2 67.66 32 Zambia Africa africa 6.3 1237.8 50.04 36 Zimbabwe Africa africa 3.109 573.1 52.72 39

## Ferility-ppgdp

 ppgdp fertility SUMMARY OUTPUT Afghanistan 499 5.968 Albania 3677.2 1.525 Regression Statistics Algeria 4473 2.142 Multiple R 0.439989055 Angola 4321.9 5.135 R Square 0.1935903686 Anguilla 13750.1 2 Adjusted R Square 0.1894969186 Argentina 9162.1 2.172 Standard Error 1.2060047574 Armenia 3030.7 1.735 Observations 199 Aruba 22851.5 1.671 Australia 57118.9 1.949 ANOVA Austria 45158.8 1.346 df SS MS F Significance F Azerbaijan 5637.6 2.148 Regression 1 68.7847730399 68.7847730399 47.2927171482 0.0000000001 Bahamas 22461.6 1.877 Residual 197 286.5261525659 1.454447475 Bahrain 18184.1 2.43 Total 198 355.3109256058 Bangladesh 670.4 2.157 Barbados 14497.3 1.575 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Belarus 5702 1.479 Intercept 3.1779116422 0.1047727783 30.3314629275 3.69486423775359E-76 2.9712914427 3.3845318417 2.9712914427 3.3845318417 Belgium 43814.8 1.835 ppgdp -0.0000320112 0.0000046548 -6.8769700558 0.0000000001 -0.0000411909 -0.0000228315 -0.0000411909 -0.0000228315 Belize 4495.8 2.679 Benin 741.1 5.078 Bermuda 92624.7 1.76 Bhutan 2047.2 2.258 RESIDUAL OUTPUT PROBABILITY OUTPUT Bolivia 1977.9 3.229 Bosnia and Herzegovina 4477.7 1.134 Observation Predicted fertility Residuals Percentile fertility Botswana 7402.9 2.617 1 3.1619380468 2.8060619532 0.2512562814 1.134 Brazil 10715.6 1.8 2 3.0602000087 -1.5352000087 0.7537688442 1.137 Brunei Darussalam 32647.6 1.984 3 3.0347254851 -0.8927254851 1.256281407 1.163 Bulgaria 6365.1 1.546 4 3.0395623795 2.0954376205 1.7587939698 1.284 Burkina Faso 519.7 5.75 5 2.7377542583 -0.7377542583 2.2613065327 1.312 Burundi 176.6 4.051 6 2.8846217049 -0.7126217049 2.7638190955 1.346 Cambodia 797.2 2.422 7 3.0808952581 -1.3458952581 3.2663316583 1.367 Cameroon 1206.6 4.287 8 2.4464074017 -0.7754074017 3.7688442211 1.372 Canada 46360.9 1.691 9 1.3494663513 0.5995336487 4.2713567839 1.389 Cape Verde 3244 2.279 10 1.7323236634 -0.3863236634 4.7738693467 1.397 Cayman Islands 57047.9 1.6 11 2.9974452261 -0.8494452261 5.2763819095 1.415 Central African Republic 450.8 4.423 12 2.4588885737 -0.5818885737 5.7788944724 1.418 Chad 727.4 5.737 13 2.5958165386 -0.1658165386 6.2814070352 1.428 Chile 11887.7 1.832 14 3.1564513248 -0.9994513248 6.783919598 1.43 China 4354 1.559 15 2.7138354797 -1.1388354797 7.2864321608 1.45 Colombia 6222.8 2.293 16 2.995383704 -1.516383704 7.7889447236 1.451 Comoros 736.6 4.742 17 1.7753467341 0.0596532659 8.2914572864 1.457 Congo 2665.1 4.442 18 3.0339956295 -0.3549956295 8.7939698492 1.458 Cook Islands 12212.1 2.5308062841 19 3.154188132 1.923811868 9.2964824121 1.476 Costa Rica 7703.8 1.812 20 0.2128826145 1.5471173855 9.7989949749 1.477 Cote dIvoire 1154.1 4.224 21 3.1123782863 -0.8543782863 10.3015075377 1.479 Croatia 13819.5 1.501 22 3.1145966634 0.1144033366 10.8040201005 1.483 Cuba 5704.4 1.451 23 3.0345750324 -1.9005750324 11.3065326633 1.495 Cyprus 28364.3 1.458 24 2.9409358313 -0.3239358313 11.8090452261 1.501 Czech Republic 18838.8 1.501 25 2.8348922851 -1.0348922851 12.3115577889 1.501 Democratic Republic of the Congo 200.6 5.485 26 2.1328223551 -0.1488223551 12.8140703518 1.504 Denmark 55830.2 1.885 27 2.9741570685 -1.4281570685 13.3165829146 1.506 Djibouti 1282.6 3.589 28 3.1612754146 2.5887245854 13.8190954774 1.525 Dominica 7020.8 3 29 3.1722584619 0.8787415381 14.3216080402 1.528 Dominican Republic 5195.4 2.49 30 3.152392303 -0.730392303 14.824120603 1.528 East Timor 706.1 5.918 31 3.1392869122 1.1477130878 15.3266331658 1.529 Ecuador 4072.6 2.393 32 1.6938429839 -0.0028429839 15.8291457286 1.536 Egypt 2653.7 2.636 33 3.0740672663 -0.7950672663 16.3316582915 1.54 El Salvador 3425.6 2.171 34 1.3517391475 0.2482608525 16.8341708543 1.546 Equatorial Guinea 16852.4 4.98 35 3.1634809872 1.2595190128 17.3366834171 1.559 Eritrea 429.1 4.243 36 3.1546266856 2.5823733144 17.8391959799 1.562 Estonia 14135.4 1.702 37 2.797371942 -0.965371942 18.3417085427 1.575 Ethiopia 324.6 3.848 38 3.0385348195 -1.4795348195 18.8442211055 1.587 Fiji 3545.7 2.602 39 2.9787122641 -0.6857122641 19.3467336683 1.59 Finland 44501.7 1.875 40 3.1543321825 1.5876678175 19.8492462312 1.6 France 39545.9 1.987 41 3.0925985577 1.3494014423 20.351758794 1.63 French Polynesia 24669 2.033 42 2.7869875044 -0.2561812203 20.8542713568 1.632 Gabon 12468.8 3.195 43 2.9313036572 -1.1193036572 21.3567839196 1.668 Gambia 579.1 4.689 44 3.1409675009 1.0830324991 21.8592964824 1.671 Georgia 2680.3 1.528 45 2.7355326801 -1.2345326801 22.3618090452 1.683 Germany 39857.1 1.457 46 2.9953068771 -1.5443068771 22.864321608 1.691 Ghana 1333.2 3.988 47 2.269935985 -0.811935985 23.3668341709 1.702 Greece 26503.8 1.54 48 2.5748587972 -1.0738587972 23.8693467337 1.707 Greenland 35292.7 2.217 49 3.1714901928 2.3135098072 24.3718592965 1.735 Grenada 7429 2.171 50 1.3907192019 0.4942807981 24.8743718593 1.75 Guatemala 2882.3 3.84 51 3.13685406 0.45214594 25.3768844221 1.757 Guinea 427.5 5.032 52 2.9531673159 0.0468326841 25.8793969849 1.76 Guinea-Bissau 539.4 4.877 53 3.0116005847 -0.5216005847 26.3819095477 1.764 Guyana 2996 2.19 54 3.1553085245 2.7626914755 26.8844221106 1.794 Haiti 612.7 3.159 55 3.0475427749 -0.6545427749 27.3869346734 1.8 Honduras 2026.2 2.996 56 3.0929634855 -0.4569634855 27.8894472362 1.812 Hong Kong 31823.7 1.137 57 3.0682540299 -0.8972540299 28.391959799 1.832 Hungary 12884 1.43 58 2.6384458713 2.3415541287 28.8944723618 1.835 Iceland 39278 2.098 59 3.1641756306 1.0788243694 29.3969849246 1.867 India 1406.4 2.538 60 2.7254203378 -1.0234203378 29.8994974874 1.875 Indonesia 2949.3 2.055 61 3.1675208024 0.6804791976 30.4020100503 1.877 Iran 5227.1 1.587 62 3.0644094832 -0.4624094832 30.9045226131 1.885 Iraq 888.5 4.535 63 1.7533582317 0.1216417683 31.4070351759 1.9 Ireland 46220.3 2.097 64 1.9119994025 0.0750005975 31.9095477387 1.907 Israel 29311.6 2.909 65 2.3882270215 -0.3552270215 32.4120603015 1.909 Italy 33877.1 1.476 66 2.7787702259 0.4162297741 32.9145728643 1.925 Jamaica 4899 2.262 67 3.1593739486 1.5296260514 33.4170854271 1.939 Japan 43140.9 1.418 68 3.0921119872 -1.5641119872 33.9195979899 1.948 Jordan 4445.3 2.889 69 1.9020375129 -0.4450375129 34.4221105528 1.949 Kazakhstan 9166.7 2.481 70 3.1352342926 0.8527657074 34.9246231156 1.984 Kenya 801.8 4.623 71 2.3294928474 -0.7894928474 35.4271356784 1.987 Kiribati 1468.2 3.5 72 2.0481494949 0.1688505051 35.9296482412 1.988 Kuwait 45430.4 2.251 73 2.9401003387 -0.7691003387 36.432160804 1.995 Kyrgyzstan 865.4 2.621 74 3.0856457221 0.7543542779 36.9346733668 2 Laos 1047.6 2.543 75 3.1642268485 1.8677731515 37.4371859296 2 Latvia 10663 1.506 76 3.1606447937 1.7163552063 37.9396984925 2.022 Lebanon 9283.7 1.764 77 3.0820060472 -0.8920060472 38.4422110553 2.033 Lesotho 980.7 3.051 78 3.1582983718 0.0007016282 38.9447236181 2.043 Liberia 218.6 5.038 79 3.1130505218 -0.1170505218 39.4472361809 2.055 Libya 11320.8 2.41 80 2.1591963938 -1.0221963938 39.9497487437 2.077 Lithuania 10975.5 1.495 81 2.7654791702 -1.3354791702 40.4522613065 2.091 Luxembourg 105095.4 1.683 82 1.9205752065 0.1774247935 40.9547738693 2.097 Macao 49990.2 1.163 83 3.1328910718 -0.5948910718 41.4572864322 2.098 Madagascar 421.9 4.493 84 3.0835009708 -1.0285009708 41.959798995 2.135 Malawi 357.4 5.968 85 3.0105858292 -1.4235858292 42.4623115578 2.142 Malaysia 8372.8 2.572 86 3.1494696792 1.3855303208 42.9648241206 2.146 Maldives 4684.5 1.668 87 1.6983437605 0.3986562395 43.4673366834 2.148 Mali 598.8 6.117 88 2.2396117627 0.6693882373 43.9698492462 2.157 Malta 19599.2 1.284 89 2.0934645684 -0.6174645684 44.472361809 2.171 Marshall Islands 3069.4 4.3844662585 90 3.0210887083 -0.7590887083 44.9748743719 2.171 Mauritania 1131.1 4.361 91 1.7969190907 -0.3789190907 45.4773869347 2.172 Mauritius 7488.3 1.59 92 3.0356121958 -0.1466121958 45.9798994975 2.183 Mexico 9100.7 2.227 93 2.8844744533 -0.4034744533 46.4824120603 2.19 Micronesia 2678.2 3.307 94 3.1522450514 1.4707549486 46.9849246231 2.204 Moldova 1625.8 1.45 95 3.1309127788 0.3690872212 47.4874371859 2.217 Mongolia 2246.7 2.446 96 1.7236294179 0.5273705821 47.9899497487 2.227 Montenegro 6509.8 1.63 97 3.1502091382 -0.5292091382 48.4924623116 2.235 Morocco 2865 2.183 98 3.1443766951 -0.6013766951 48.9949748744 2.251 Mozambique 407.5 4.713 99 2.8365760749 -1.3305760749 49.4974874372 2.258 Myanmar 876.2 1.939 100 2.8807291414 -1.1167291414 50 2.262 Namibia 5124.7 3.055 101 3.1465182453 -0.0955182453 50.5025125628 2.264 Nauru 6190.1 3.3 102 3.170913991 1.867086009 51.0050251256 2.266 Nepal 534.7 2.587 103 2.8155190988 -0.4055190988 51.5075376884 2.279 Neth Antilles 20321.1 1.9 104 2.8265725707 -1.3315725707 52.0100502513 2.293 Netherlands 46909.7 1.794 105 -0.1863196231 1.8693196231 52.5125628141 2.316 New Caledonia 35319.5 2.091 106 1.5776646875 -0.4146646875 53.0150753769 2.34 New Zealand 32372.1 2.135 107 3.1644061113 1.3285938887 53.5175879397 2.383 Nicaragua 1131.9 2.5 108 3.1664708346 2.8015291654 54.0201005025 2.391 Niger 357.7 6.925 109 2.9098881555 -0.3378881555 54.5226130653 2.393 Nigeria 1239.8 5.431 110 3.0279551135 -1.3599551135 55.0251256281 2.409 North Korea 504 1.988 111 3.1587433277 2.9582566723 55.527638191 2.41 Norway 84588.7 1.948 112 2.5505174707 -1.2665174707 56.0301507538 2.41 Oman 20791 2.146 113 3.0796564241 1.3048098344 56.5326633166 2.422 Pakistan 1003.2 3.201 114 3.1417037588 1.2192962412 57.0351758794 2.43 Palau 10821.8 2 115 2.9382020737 -1.3482020737 57.5376884422 2.446 Palestinian Territory 1819.5 4.27 116 2.8865871934 -0.6595871934 58.040201005 2.481 Panama 7614 2.409 117 3.0921792108 0.2148207892 58.5427135678 2.49 Papua New Guinea 1428.4 3.799 118 3.1258678116 -1.6758678116 59.0452261307 2.5 Paraguay 2771.1 2.858 119 3.1059920493 -0.6599920493 59.5477386935 2.5308062841 Peru 5410.7 2.41 120 2.9695250459 -1.3395250459 60.0502512563 2.538 Philippines 2140.1 3.05 121 3.0861995161 -0.9031995161 60.5527638191 2.543 Poland 12263.2 1.415 122 3.1648670728 1.5481329272 61.0552763819 2.572 Portugal 21437.6 1.312 123 3.1498634171 -1.2108634171 61.5577889447 2.587 Puerto Rico 26461 1.757 124 3.0138637774 0.0411362226 62.0603015075 2.602 Qatar 72397.9 2.204 125 2.9797590308 0.3202409692 62.5628140704 2.617 Republic of Korea 21052.2 1.389 126 3.1607952464 -0.5737952464 63.0653266332 2.621 Romania 7522.4 1.428 127 2.5274085758 -0.6274085758 63.567839196 2.636 Russian Federation 10351.4 1.529 128 1.6762752301 0.1177247699 64.0703517588 2.639 Rwanda 532.3 5.282 129 2.0472915944 0.0437084056 64.5728643216 2.679 Saint Lucia 6677.1 1.907 130 2.1416414444 -0.0066414444 65.0753768844 2.772 Samoa 3343.3 3.763 131 3.1416781499 -0.6416781499 65.5778894472 2.858 Sao Tome and Principe 1283.3 3.488 132 3.1664612312 3.7585387688 66.0804020101 2.889 Saudi Arabia 15835.9 2.639 133 3.13822414 2.29277586 66.5829145729 2.909 Senegal 1032.7 4.605 134 3.1617779907 -1.1737779907 67.0854271357 2.996 Serbia 5123.2 1.562 135 0.4701247245 1.4778752755 67.5879396985 3 Seychelles 11450.6 2.34 136 2.5123665067 -0.3663665067 68.0904522613 3.05 Sierra Leone 351.7 4.728 137 3.145797993 0.055202007 68.5929648241 3.051 Singapore 43783.1 1.367 138 2.8314926942 -0.8314926942 69.0954773869 3.055 Slovakia 15976 1.372 139 3.1196672396 1.1503327604 69.5979899497 3.109 Slovenia 23109.8 1.477 140 2.9341782642 -0.5251782642 70.1005025126 3.159 Solomon Islands 1193.5 4.041 141 3.1321868251 0.6668131749 70.6030150754 3.162 Somalia 114.8 6.283 142 3.089205369 -0.231205369 71.1055276382 3.174 South Africa 7254.8 2.383 143 3.0047085704 -0.5947085704 71.608040201 3.195 Spain 30542.8 1.504 144 3.1094044446 -0.0594044446 72.1105527638 3.201 Sri Lanka 2375.3 2.235 145 2.7853517314 -1.3703517314 72.6130653266 3.229 St Vincent and Grenadines 6171.7 1.995 146 2.4916680561 -1.1796680561 73.1155778894 3.3 Sudan 1824.9 4.225 147 2.3308629273 -0.5738629273 73.6180904523 3.307 Suriname 7018 2.266 148 0.8603670235 1.3436329765 74.1206030151 3.488 Swaziland 3311.2 3.174 149 2.5040051777 -1.1150051777 74.6231155779 3.5 Sweden 48906.2 1.925 150 2.9371104913 -1.5091104913 75.1256281407 3.589 Switzerland 68880.2 1.536 151 2.8465507689 -1.3175507689 75.6281407035 3.7 Syria 2931.5 2.772 152 3.1608720734 2.1211279266 76.1306532663 3.75 Tajikistan 816 3.162 153 2.9641695699 -1.0571695699 76.6331658291 3.763 Tanzania 516 5.499 154 3.0708885528 0.6921114472 77.135678392 3.783 TFYR Macedonia 4434.5 1.397 155 3.1368316522 0.3511683478 77.6381909548 3.799 Thailand 4612.8 1.528 156 2.6709852696 -0.0319852696 78.1407035176 3.84 Togo 524.6 3.864 157 3.1448536622 1.4601463378 78.6432160804 3.848 Tonga 3543.1 3.783 158 3.0139117943 -1.4519117943 79.1457286432 3.864 Trinidad and Tobago 15205.1 1.632 159 2.8113640433 -0.4713640433 79.648241206 3.988 Tunisia 4222.1 1.909 160 3.1666532985 1.5613467015 80.1507537688 4.041 Turkey 10095.1 2.022 161 1.7763614895 -0.4093614895 80.6532663317 4.051 Turkmenistan 4587.5 2.316 162 2.6665004987 -1.2945004987 81.1557788945 4.224 Tuvalu 3187.2 3.7 163 2.4381389053 -0.9611389053 81.6582914573 4.225 Uganda 509 5.901 164 3.1397062591 0.9012937409 82.1608040201 4.243 Ukraine 3035 1.483 165 3.1742367549 3.1087632451 82.6633165829 4.27 United Arab Emirates 39624.7 1.707 166 2.945676692 -0.562676692 83.1658291457 4.287 United Kingdom 36326.8 1.867 167 2.2001995569 -0.6961995569 83.6683417085 4.361 United States 46545.9 2.077 168 3.1018754073 -0.8668754073 84.1708542714 4.3844662585 Uruguay 11952.4 2.043 169 2.9803480371 -0.9853480371 84.6733668342 4.423 Uzbekistan 1427.3 2.264 170 3.1194943791 1.1055056209 85.175879397 4.442 Vanuatu 2963.5 3.75 171 2.9532569473 -0.6872569473 85.6783919598 4.493 Venezuela 13502.7 2.391 172 3.0719161127 0.1020838873 86.1809045226 4.535 Viet Nam 1182.7 1.75 173 1.6123648427 0.3126351573 86.6834170854 4.605 Yemen 1437.2 4.938 174 0.9729728685 0.5630271315 87.1859296482 4.623 Zambia 1237.8 6.3 175 3.0840707704 -0.3120707704 87.6884422111 4.689 Zimbabwe 573.1 3.109 176 3.1517904921 0.0102095079 88.1909547739 4.713 177 3.1613938561 2.3376061439 88.6934673367 4.728 178 3.0359579169 -1.6389579169 89.1959798995 4.742 179 3.0302503175 -1.5022503175 89.6984924623 4.877 180 3.1611185597 0.7028814403 90.2010050251 4.938 181 3.0644927124 0.7185072876 90.7035175879 4.98 182 2.691177943 -1.059177943 91.2060301508 5.032 183 3.0427570986 -1.1337570986 91.7085427136 5.038 184 2.8547552429 -0.8327552429 92.2110552764 5.078 185 3.0310602012 -0.7150602012 92.7135678392 5.135 186 3.0758855032 0.6241144968 93.216080402 5.282 187 3.1616179346 2.7393820654 93.7185929648 5.431 188 3.0807576099 -1.5977576099 94.2211055276 5.485 189 1.9094769189 -0.2024769189 94.7236180905 5.499 190 2.0150466992 -0.1480466992 95.2261306533 5.737 191 1.6879209095 0.3890790905 95.7286432161 5.75 192 2.7953008165 -0.7523008165 96.2311557789 5.901 193 3.1322220375 -0.8682220375 96.7336683417 5.918 194 3.0830464116 0.6669535884 97.2361809045 5.968 195 2.7456738325 -0.3546738325 97.7386934673 5.968 196 3.1400519802 -1.3900519802 98.2412060302 6.117 197 3.1319051265 1.8060948735 98.743718593 6.283 198 3.1382881624 3.1617118376 99.2462311558 6.3 199 3.1595660159 -0.0505660159 99.7487437186 6.925

ppgdp Residual Plot

499 3677.2 4473 4321.8999999999996 13750.1 9162.1 3030.7 22851.5 57118.9 45158.8 5637.6 22461.599999999999 18184.099999999999 670.4 14497.3 5702 43814.8 4495.8 741.1 92624.7 2047.2 1977.9 4477.7 7402.9 10715.6 32647.599999999999 6365.1 519.70000000000005 176.6 797.2 1206.5999999999999 46360.9 3244 57047.9 450.8 727.4 11887.7 4354 6222.8 736.6 2665.1 12212.1 7703.8 1154.0999999999999 13819.5 5704.4 28364.3 18838.8 200.6 55830.2 1282.5999999999999 7020.8 5195.3999999999996 706.1 4072.6 2653.7 3425.6 16852.400000000001 429.1 14135.4 324.60000000000002 3545.7 44501.7 39545.9 24669 12468.8 579.1 2680.3 39857.1 1333.2 26503.8 35292.699999999997 7429 2882.3 427.5 539.4 2996 612.70000000000005 2026.2 31823.7 12884 39278 1406.4 2949.3 5227.1000000000004 888.5 46220.3 29311.599999999999 33877.1 4899 43140.9 4445.3 9166.7000000000007 801.8 1468.2 45430.400000000001 865.4 1047.5999999999999 10663 9283.7000000000007 980.7 218.6 11320.8 10975.5 105095.4 49990.2 421.9 357.4 8372.7999999999993 4684.5 598.79999999999995 19599.2 3069.4 1131.0999999999999 7488.3 9100.7000000000007 2678.2 1625.8 2246.6999999999998 6509.8 2865 407.5 876.2 5124.7 6190.1 534.70000000000005 20321.099999999999 46909.7 35319.5 32372.1 1131.9000000000001 357.7 1239.8 504 84588.7 20791 1003.2 10821.8 1819.5 7614 1428.4 2771.1 5410.7 2140.1 12263.2 21437.599999999999 26461 72397.899999999994 21052.2 7522.4 10351.4 532.29999999999995 6677.1 3343.3 1283.3 15835.9 1032.7 5123.2 11450.6 351.7 43783.1 15976 23109.8 1193.5 114.8 7254.8 30542.799999999999 2375.3000000000002 6171.7 1824.9 7018 3311.2 48906.2 68880.2 2931.5 816 516 4434.5 4612.8 524.6 3543.1 15205.1 4222.1000000000004 10095.1 4587.5 3187.2 509 3035 39624.699999999997 36326.800000000003 46545.9 11952.4 1427.3 2963.5 13502.7 1182.7 1437.2 1237.8 573.1 2.8060619532387685 -1.5352000086793103 -0.89272548514221617 2.0954376205294913 -0.73775425831892294 -0.71262170489870202 -1.3458952580720365 -0.77540740167088429 0.59953364866214143 -0.38632366342129698 -0.84944522614334694 -0.58188857373310232 -0.16581653858598022 -0.99945132480312893 -1.1388354797477789 -1.5163837040073971 5.965326591540232E-2 -0.35499562947917829 1.9238118679765552 1.5471173855349225 -0.85437828634387891 0.11440333657504498 -1.9005750324397477 -0.32393583132048676 -1.0348922850509064 -0.14882235514948672 -1.4281570684740383 2.5887245853538952 0.87874153807370314 -0.73039230295781143 1.1477130877635835 -2.8429839240102783E-3 -0.79506726627703506 0.24826085251846997 1.2595190127581355 2.5823733143544665 -0.96537194195235387 -1.4795348195238625 -0.68571226412536834 1.5876678175167451 1.3494014423487206 -0.25618122026659584 -1.1193036572411807 1.0830324990657987 -1.2345326801165175 -1.5443068770954986 -0.81193598503945341 -1.073858797244267 2.3135098071926907 0.49428079809384085 0.45214593997371066 4.6832684080966303E-2 -0.5216005846606917 2.7626914755113652 -0.65454277494399138 -0.45696348548279841 -0.89725402994336312 2.3415541286742005 1.0788243694297179 -1.0234203378378446 0.68047919764079268 -0.46240948322709619 0.12164176832509033 7.500059749682797E-2 -0.35522702151422614 0.41622977409113115 1.5296260514233895 -1.5641119872092539 -0.44503751292696747 0.85276570736624269 -0.78949284736763081 0.16885050512692468 -0.76910033865358818 0.75435427787555742 1.8677731514884517 1.7163552062557308 -0.89200604717323939 7.0162818997188126E-4 -0.11705052182299269 -1.0221963937800616 -1.335479170150385 0.17742479345612971 -0.59489107182084533 -1.0285009708339357 -1.4235858291993628 1.3855303208156702 0.39865623948725459 0.66938823731124941 -0.617464568408022 -0.75908870828018804 -0.37891909072150143 -0.14661219575038098 -0.40347445331756315 1.4707549486233278 0.3690872211605476 0.5273705821085779 -0.52920913821135551 -0.6013766951497086 -1.3305760748700208 -1.1167291413624987 -9.5518245318886308E-2 1.8670860090319312 -0.40551909876710468 -1.3315725707165376 1.8693196231248199 -0.41466468752645325 1.3285938886940216 2.801529165436742 -0.33788815554940399 -1.3599551135311387 2.9582566723252248 -1.2665174706576792 1.3048098344105714 1.219296241160102 -1.3482020737054226 -0.65958719339477856 0.21482078924283465 -1.6758678116247678 -0.65999204929229505 -1.3395250459108095 -0.90319951611437954 1.5481329272226287 -1.2108634171078112 4.1136222559623903E-2 0.32024096920001099 -0.57379524644673729 -0.62740857578280096 0.11772476993017067 4.3708405643127612E-2 -6.6414444111977389E-3 -0.64167814986926475 3.7585387688007295 2.2927758600448498 -1.1737779906947758 1.4778752755272708 -0.36636650665729142 5.520200698016442E-2 -0.83149269419938676 1.1503327603897269 -0.52517826419472602 0.66681317487155978 -0.23120536904241806 -0.59470857043910819 -5.9404444629131525E-2 -1.3703517313615285 -1.179668056143236 -0.57386292729649191 1.343632976537565 -1.1150051777456438 -1.5091104913321947 -1.3175507689315422 2.1211279266413636 -1.0571695699272006 0.69211144720277584 0.35116834782301476 -3.1985269636250369E-2 1.4601463377722537 -1.4519117942603128 -0.47136404328191395 1.5613467015209825 -0.40936148954592722 -1.2945004986541606 -0.96113890527778145 0.90129374086947012 3.1087632450923106 -0.56267669200890547 -0.69619955688469126 -0.86687540726305379 -0.98534803712454577 1.1055056209414991 -0.68725694731624909 0.10208388725612982 0.31263515726594426 0.56302713154329975 -0.31207077043051834 1.0209507852061872E-2 2.3376061438647175 -1.6389579168539254 -1.5022503175241138 0.70288144029902178 0.7185072876183467 -1.0591779429803052 -1.1337570985569647 -0.83275524289806269 -0.71506020122038016 0.62411449680802811 2.7393820653716801 -1.5977576098548845 -0.20247691889582975 -0.14804669920870106 0.38907909053485179 -0.75230081645241675 -0.86822203746306048 0.66695358839479857 -0.35467383248715256 -1.3900519802340745 1.8060948735485218 3.1617118376182671 -5.0566015856357449E-2ppgdp

Residuals

Normal Probability Plot

0.25125628140703515 0.75376884422110546 1.2562814070351758 1.7587939698492461 2.2613065326633164 2.7638190954773867 3.266331658291457 3.7688442211055273 4.2713567839195976 4.7738693467336679 5.2763819095477382 5.7788944723618085 6.2814070351758788 6.7839195979899491 7.2864321608040195 7.7889447236180898 8.2914572864321592 8.7939698492462313 9.2964824120602998 9.7989949748743719 10.30150753768844 10.804020100502512 11.306532663316581 11.809045226130653 12.311557788944722 12.814070351758794 13.316582914572862 13.819095477386934 14.321608040201003 14.824120603015075 15.326633165829143 15.829145728643216 16.331658291457284 16.834170854271353 17.336683417085425 17.839195979899497 18.341708542713565 18.844221105527634 19.346733668341706 19.849246231155778 20.351758793969847 20.854271356783915 21.356783919597987 21.859296482412059 22.361809045226128 22.864321608040196 23.366834170854268 23.86934673366834 24.371859296482409 24.874371859296478 25.37688442211055 25.879396984924622 26.38190954773869 26.884422110552759 27.386934673366831 27.889447236180903 28.391959798994971 28.89447236180904 29.396984924623112 29.899497487437184 30.402010050251253 30.904522613065321 31.407035175879393 31.909547738693465 32.412060301507537 32.914572864321606 33.417085427135675 33.91959798994975 34.422110552763819 34.924623115577887 35.427135678391963 35.929648241206031 36.4321608040201 36.934673366834168 37.437185929648237 37.939698492462313 38.442211055276381 38.94472361809045 39.447236180904525 39.949748743718594 40.452261306532662 40.954773869346731 41.457286432160799 41.959798994974875 42.462311557788944 42.964824120603012 43.467336683417088 43.969849246231156 44.472361809045225 44.974874371859293 45.477386934673362 45.979899497487438 46.482412060301506 46.984924623115575 47.48743718592965 47.989949748743719 48.492462311557787 48.994974874371856 49.497487437185924 50 50.502512562814069 51.005025125628137 51.507537688442213 52.010050251256281 52.51256281407035 53.015075376884418 53.517587939698487 54.020100502512562 54.522613065326631 55.0251256281407 55.527638190954775 56.030150753768844 56.532663316582912 57.035175879396981 57.537688442211049 58.040201005025125 58.542713567839193 59.045226130653262 59.547738693467338 60.050251256281406 60.552763819095475 61.055276381909543 61.557788944723612 62.060301507537687 62.562814070351756 63.065326633165824 63.5678391959799 64.070351758793961 64.572864321608037 65.075376884422113 65.577889447236174 66.08040201005025 66.582914572864311 67.085427135678387 67.587939698492463 68.090452261306524 68.5929648241206 69.095477386934675 69.597989949748737 70.100502512562812 70.603015075376888 71.105527638190949 71.608040201005025 72.110552763819086 72.613065326633162 73.115577889447238 73.618090452261299 74.120603015075375 74.623115577889436 75.125628140703512 75.628140703517587 76.130653266331649 76.633165829145725 77.1356783919598 77.638190954773862 78.140703517587937 78.643216080402013 79.145728643216074 79.64824120603015 80.150753768844211 80.653266331658287 81.155778894472363 81.658291457286424 82.1608040201005 82.663316582914561 83.165829145728637 83.668341708542712 84.170854271356774 84.673366834170849 85.175879396984925 85.678391959798986 86.180904522613062 86.683417085427138 87.185929648241199 87.688442211055275 88.190954773869336 88.693467336683412 89.195979899497488 89.698492462311549 90.201005025125625 90.703517587939686 91.206030150753762 91.708542713567837 92.211055276381899 92.713567839195974 93.21608040201005 93.718592964824111 94.221105527638187 94.723618090452263 95.226130653266324 95.7286432160804 96.231155778894461 96.733668341708537 97.236180904522612 97.738693467336674 98.241206030150749 98.743718592964811 99.246231155778887 99.748743718592962 1.1339999999999999 1.137 1.163 1.284 1.3120000000000001 1.3460000000000001 1.367 1.3720000000000001 1.389 1.397 1.415 1.4179999999999999 1.4279999999999999 1.43 1.45 1.4510000000000001 1.4570000000000001 1.458 1.476 1.4770000000000001 1.4790000000000001 1.4830000000000001 1.4950000000000001 1.5009999999999999 1.5009999999999999 1.504 1.506 1.5249999999999999 1.528 1.528 1.5289999999999999 1.536 1.54 1.546 1.5589999999999999 1.5620000000000001 1.575 1.587 1.59 1.6 1.63 1.6319999999999999 1.6679999999999999 1.671 1.6830000000000001 1.6910000000000001 1.702 1.7070000000000001 1.7350000000000001 1.75 1.7569999999999999 1.76 1.764 1.794 1.8 1.8120000000000001 1.8320000000000001 1.835 1.867 1.875 1.877 1.885 1.9 1.907 1.909 1.925 1.9390000000000001 1.948 1.9490000000000001 1.984 1.9870000000000001 1.988 1.9950000000000001 2 2 2.0219999999999998 2.0329999999999999 2.0430000000000001 2.0550000000000002 2.077 2.0910000000000002 2.097 2.0979999999999999 2.1349999999999998 2.1419999999999999 2.1459999999999999 2.1480000000000001 2.157 2.1709999999999998 2.1709999999999998 2.1720000000000002 2.1829999999999998 2.19 2.2040000000000002 2.2170000000000001 2.2269999999999999 2.2349999999999999 2.2509999999999999 2.258 2.262 2.2639999999999998 2.266 2.2789999999999999 2.2930000000000001 2.3159999999999998 2.34 2.383 2.391 2.3929999999999998 2.4089999999999998 2.41 2.41 2.4220000000000002 2.4300000000000002 2.4460000000000002 2.4809999999999999 2.4900000000000002 2.5 2.5308062840941101 2.5379999999999998 2.5430000000000001 2.5720000000000001 2.5870000000000002 2.6019999999999999 2.617 2.621 2.6360000000000001 2.6389999999999998 2.6789999999999998 2.7719999999999998 2.8580000000000001 2.8889999999999998 2.9089999999999998 2.996 3 3.05 3.0510000000000002 3.0550000000000002 3.109 3.1589999999999998 3.1619999999999999 3.1739999999999999 3.1949999999999998 3.2010000000000001 3.2290000000000001 3.3 3.3069999999999999 3.488 3.5 3.589 3.7 3.75 3.7629999999999999 3.7829999999999999 3.7989999999999999 3.84 3.8479999999999999 3.8639999999999999 3.988 4.0410000000000004 4.0510000000000002 4.2240000000000002 4.2249999999999996 4.2430000000000003 4.2699999999999996 4.2869999999999999 4.3609999999999998 4.3844662585282403 4.423 4.4420000000000002 4.4930000000000003 4.5350000000000001 4.6050000000000004 4.6230000000000002 4.6890000000000001 4.7130000000000001 4.7279999999999998 4.742 4.8769999999999998 4.9379999999999997 4.9800000000000004 5.032 5.0380000000000003 5.0780000000000003 5.1349999999999998 5.282 5.431 5.4850000000000003 5.4989999999999997 5.7370000000000001 5.75 5.9009999999999998 5.9180000000000001 5.968 5.968 6.117 6.2830000000000004 6.3 6.9249999999999998Sample Percentile

fertility

ppgdp Residual Plot

499 3677.2 4473 4321.8999999999996 13750.1 9162.1 3030.7 22851.5 57118.9 45158.8 5637.6 22461.599999999999 18184.099999999999 670.4 14497.3 5702 43814.8 4495.8 741.1 92624.7 2047.2 1977.9 4477.7 7402.9 10715.6 32647.599999999999 6365.1 519.70000000000005 176.6 797.2 1206.5999999999999 46360.9 3244 57047.9 450.8 727.4 11887.7 4354 6222.8 736.6 2665.1 12212.1 7703.8 1154.0999999999999 13819.5 5704.4 28364.3 18838.8 200.6 55830.2 1282.5999999999999 7020.8 5195.3999999999996 706.1 4072.6 2653.7 3425.6 16852.400000000001 429.1 14135.4 324.60000000000002 3545.7 44501.7 39545.9 24669 12468.8 579.1 2680.3 39857.1 1333.2 26503.8 35292.699999999997 7429 2882.3 427.5 539.4 2996 612.70000000000005 2026.2 31823.7 12884 39278 1406.4 2949.3 5227.1000000000004 888.5 46220.3 29311.599999999999 33877.1 4899 43140.9 4445.3 9166.7000000000007 801.8 1468.2 45430.400000000001 865.4 1047.5999999999999 10663 9283.7000000000007 980.7 218.6 11320.8 10975.5 105095.4 49990.2 421.9 357.4 8372.7999999999993 4684.5 598.79999999999995 19599.2 3069.4 1131.0999999999999 7488.3 9100.7000000000007 2678.2 1625.8 2246.6999999999998 6509.8 2865 407.5 876.2 5124.7 6190.1 534.70000000000005 20321.099999999999 46909.7 35319.5 32372.1 1131.9000000000001 357.7 1239.8 504 84588.7 20791 1003.2 10821.8 1819.5 7614 1428.4 2771.1 5410.7 2140.1 12263.2 21437.599999999999 26461 72397.899999999994 21052.2 7522.4 10351.4 532.29999999999995 6677.1 3343.3 1283.3 15835.9 1032.7 5123.2 11450.6 351.7 43783.1 15976 23109.8 1193.5 114.8 7254.8 30542.799999999999 2375.3000000000002 6171.7 1824.9 7018 3311.2 48906.2 68880.2 2931.5 816 516 4434.5 4612.8 524.6 3543.1 15205.1 4222.1000000000004 10095.1 4587.5 3187.2 509 3035 39624.699999999997 36326.800000000003 46545.9 11952.4 1427.3 2963.5 13502.7 1182.7 1437.2 1237.8 573.1 2.8060619532387685 -1.5352000086793103 -0.89272548514221617 2.0954376205294913 -0.73775425831892294 -0.71262170489870202 -1.3458952580720365 -0.77540740167088429 0.59953364866214143 -0.38632366342129698 -0.84944522614334694 -0.58188857373310232 -0.16581653858598022 -0.99945132480312893 -1.1388354797477789 -1.5163837040073971 5.965326591540232E-2 -0.35499562947917829 1.9238118679765552 1.5471173855349225 -0.85437828634387891 0.11440333657504498 -1.9005750324397477 -0.32393583132048676 -1.0348922850509064 -0.14882235514948672 -1.4281570684740383 2.5887245853538952 0.87874153807370314 -0.73039230295781143 1.1477130877635835 -2.8429839240102783E-3 -0.79506726627703506 0.24826085251846997 1.2595190127581355 2.5823733143544665 -0.96537194195235387 -1.4795348195238625 -0.68571226412536834 1.5876678175167451 1.3494014423487206 -0.25618122026659584 -1.1193036572411807 1.0830324990657987 -1.2345326801165175 -1.5443068770954986 -0.81193598503945341 -1.073858797244267 2.3135098071926907 0.49428079809384085 0.45214593997371066 4.6832684080966303E-2 -0.5216005846606917 2.7626914755113652 -0.65454277494399138 -0.45696348548279841 -0.89725402994336312 2.3415541286742005 1.0788243694297179 -1.0234203378378446 0.68047919764079268 -0.46240948322709619 0.12164176832509033 7.500059749682797E-2 -0.35522702151422614 0.41622977409113115 1.5296260514233895 -1.5641119872092539 -0.44503751292696747 0.85276570736624269 -0.78949284736763081 0.16885050512692468 -0.76910033865358818 0.75435427787555742 1.8677731514884517 1.7163552062557308 -0.89200604717323939 7.0162818997188126E-4 -0.11705052182299269 -1.0221963937800616 -1.335479170150385 0.17742479345612971 -0.59489107182084533 -1.0285009708339357 -1.4235858291993628 1.3855303208156702 0.39865623948725459 0.66938823731124941 -0.617464568408022 -0.75908870828018804 -0.37891909072150143 -0.14661219575038098 -0.40347445331756315 1.4707549486233278 0.3690872211605476 0.5273705821085779 -0.52920913821135551 -0.6013766951497086 -1.3305760748700208 -1.1167291413624987 -9.5518245318886308E-2 1.8670860090319312 -0.40551909876710468 -1.3315725707165376 1.8693196231248199 -0.41466468752645325 1.3285938886940216 2.801529165436742 -0.33788815554940399 -1.3599551135311387 2.9582566723252248 -1.2665174706576792 1.3048098344105714 1.219296241160102 -1.3482020737054226 -0.65958719339477856 0.21482078924283465 -1.6758678116247678 -0.65999204929229505 -1.3395250459108095 -0.90319951611437954 1.5481329272226287 -1.2108634171078112 4.1136222559623903E-2 0.32024096920001099 -0.57379524644673729 -0.62740857578280096 0.11772476993017067 4.3708405643127612E-2 -6.6414444111977389E-3 -0.64167814986926475 3.7585387688007295 2.2927758600448498 -1.1737779906947758 1.4778752755272708 -0.36636650665729142 5.520200698016442E-2 -0.83149269419938676 1.1503327603897269 -0.52517826419472602 0.66681317487155978 -0.23120536904241806 -0.59470857043910819 -5.9404444629131525E-2 -1.3703517313615285 -1.179668056143236 -0.57386292729649191 1.343632976537565 -1.1150051777456438 -1.5091104913321947 -1.3175507689315422 2.1211279266413636 -1.0571695699272006 0.69211144720277584 0.35116834782301476 -3.1985269636250369E-2 1.4601463377722537 -1.4519117942603128 -0.47136404328191395 1.5613467015209825 -0.40936148954592722 -1.2945004986541606 -0.96113890527778145 0.90129374086947012 3.1087632450923106 -0.56267669200890547 -0.69619955688469126 -0.86687540726305379 -0.98534803712454577 1.1055056209414991 -0.68725694731624909 0.10208388725612982 0.31263515726594426 0.56302713154329975 -0.31207077043051834 1.0209507852061872E-2 2.3376061438647175 -1.6389579168539254 -1.5022503175241138 0.70288144029902178 0.7185072876183467 -1.0591779429803052 -1.1337570985569647 -0.83275524289806269 -0.71506020122038016 0.62411449680802811 2.7393820653716801 -1.5977576098548845 -0.20247691889582975 -0.14804669920870106 0.38907909053485179 -0.75230081645241675 -0.86822203746306048 0.66695358839479857 -0.35467383248715256 -1.3900519802340745 1.8060948735485218 3.1617118376182671 -5.0566015856357449E-2ppgdp

Residuals

Normal Probability Plot

0.25125628140703515 0.75376884422110546 1.2562814070351758 1.7587939698492461 2.2613065326633164 2.7638190954773867 3.266331658291457 3.7688442211055273 4.2713567839195976 4.7738693467336679 5.2763819095477382 5.7788944723618085 6.2814070351758788 6.7839195979899491 7.2864321608040195 7.7889447236180898 8.2914572864321592 8.7939698492462313 9.2964824120602998 9.7989949748743719 10.30150753768844 10.804020100502512 11.306532663316581 11.809045226130653 12.311557788944722 12.814070351758794 13.316582914572862 13.819095477386934 14.321608040201003 14.824120603015075 15.326633165829143 15.829145728643216 16.331658291457284 16.834170854271353 17.336683417085425 17.839195979899497 18.341708542713565 18.844221105527634 19.346733668341706 19.849246231155778 20.351758793969847 20.854271356783915 21.356783919597987 21.859296482412059 22.361809045226128 22.864321608040196 23.366834170854268 23.86934673366834 24.371859296482409 24.874371859296478 25.37688442211055 25.879396984924622 26.38190954773869 26.884422110552759 27.386934673366831 27.889447236180903 28.391959798994971 28.89447236180904 29.396984924623112 29.899497487437184 30.402010050251253 30.904522613065321 31.407035175879393 31.909547738693465 32.412060301507537 32.914572864321606 33.417085427135675 33.91959798994975 34.422110552763819 34.924623115577887 35.427135678391963 35.929648241206031 36.4321608040201 36.934673366834168 37.437185929648237 37.939698492462313 38.442211055276381 38.94472361809045 39.447236180904525 39.949748743718594 40.452261306532662 40.954773869346731 41.457286432160799 41.959798994974875 42.462311557788944 42.964824120603012 43.467336683417088 43.969849246231156 44.472361809045225 44.974874371859293 45.477386934673362 45.979899497487438 46.482412060301506 46.984924623115575 47.48743718592965 47.989949748743719 48.492462311557787 48.994974874371856 49.497487437185924 50 50.502512562814069 51.005025125628137 51.507537688442213 52.010050251256281 52.51256281407035 53.015075376884418 53.517587939698487 54.020100502512562 54.522613065326631 55.0251256281407 55.527638190954775 56.030150753768844 56.532663316582912 57.035175879396981 57.537688442211049 58.040201005025125 58.542713567839193 59.045226130653262 59.547738693467338 60.050251256281406 60.552763819095475 61.055276381909543 61.557788944723612 62.060301507537687 62.562814070351756 63.065326633165824 63.5678391959799 64.070351758793961 64.572864321608037 65.075376884422113 65.577889447236174 66.08040201005025 66.582914572864311 67.085427135678387 67.587939698492463 68.090452261306524 68.5929648241206 69.095477386934675 69.597989949748737 70.100502512562812 70.603015075376888 71.105527638190949 71.608040201005025 72.110552763819086 72.613065326633162 73.115577889447238 73.618090452261299 74.120603015075375 74.623115577889436 75.125628140703512 75.628140703517587 76.130653266331649 76.633165829145725 77.1356783919598 77.638190954773862 78.140703517587937 78.643216080402013 79.145728643216074 79.64824120603015 80.150753768844211 80.653266331658287 81.155778894472363 81.658291457286424 82.1608040201005 82.663316582914561 83.165829145728637 83.668341708542712 84.170854271356774 84.673366834170849 85.175879396984925 85.678391959798986 86.180904522613062 86.683417085427138 87.185929648241199 87.688442211055275 88.190954773869336 88.693467336683412 89.195979899497488 89.698492462311549 90.201005025125625 90.703517587939686 91.206030150753762 91.708542713567837 92.211055276381899 92.713567839195974 93.21608040201005 93.718592964824111 94.221105527638187 94.723618090452263 95.226130653266324 95.7286432160804 96.231155778894461 96.733668341708537 97.236180904522612 97.738693467336674 98.241206030150749 98.743718592964811 99.246231155778887 99.748743718592962 1.1339999999999999 1.137 1.163 1.284 1.3120000000000001 1.3460000000000001 1.367 1.3720000000000001 1.389 1.397 1.415 1.4179999999999999 1.4279999999999999 1.43 1.45 1.4510000000000001 1.4570000000000001 1.458 1.476 1.4770000000000001 1.4790000000000001 1.4830000000000001 1.4950000000000001 1.5009999999999999 1.5009999999999999 1.504 1.506 1.5249999999999999 1.528 1.528 1.5289999999999999 1.536 1.54 1.546 1.5589999999999999 1.5620000000000001 1.575 1.587 1.59 1.6 1.63 1.6319999999999999 1.6679999999999999 1.671 1.6830000000000001 1.6910000000000001 1.702 1.7070000000000001 1.7350000000000001 1.75 1.7569999999999999 1.76 1.764 1.794 1.8 1.8120000000000001 1.8320000000000001 1.835 1.867 1.875 1.877 1.885 1.9 1.907 1.909 1.925 1.9390000000000001 1.948 1.9490000000000001 1.984 1.9870000000000001 1.988 1.9950000000000001 2 2 2.0219999999999998 2.0329999999999999 2.0430000000000001 2.0550000000000002 2.077 2.0910000000000002 2.097 2.0979999999999999 2.1349999999999998 2.1419999999999999 2.1459999999999999 2.1480000000000001 2.157 2.1709999999999998 2.1709999999999998 2.1720000000000002 2.1829999999999998 2.19 2.2040000000000002 2.2170000000000001 2.2269999999999999 2.2349999999999999 2.2509999999999999 2.258 2.262 2.2639999999999998 2.266 2.2789999999999999 2.2930000000000001 2.3159999999999998 2.34 2.383 2.391 2.3929999999999998 2.4089999999999998 2.41 2.41 2.4220000000000002 2.4300000000000002 2.4460000000000002 2.4809999999999999 2.4900000000000002 2.5 2.5308062840941101 2.5379999999999998 2.5430000000000001 2.5720000000000001 2.5870000000000002 2.6019999999999999 2.617 2.621 2.6360000000000001 2.6389999999999998 2.6789999999999998 2.7719999999999998 2.8580000000000001 2.8889999999999998 2.9089999999999998 2.996 3 3.05 3.0510000000000002 3.0550000000000002 3.109 3.1589999999999998 3.1619999999999999 3.1739999999999999 3.1949999999999998 3.2010000000000001 3.2290000000000001 3.3 3.3069999999999999 3.488 3.5 3.589 3.7 3.75 3.7629999999999999 3.7829999999999999 3.7989999999999999 3.84 3.8479999999999999 3.8639999999999999 3.988 4.0410000000000004 4.0510000000000002 4.2240000000000002 4.2249999999999996 4.2430000000000003 4.2699999999999996 4.2869999999999999 4.3609999999999998 4.3844662585282403 4.423 4.4420000000000002 4.4930000000000003 4.5350000000000001 4.6050000000000004 4.6230000000000002 4.6890000000000001 4.7130000000000001 4.7279999999999998 4.742 4.8769999999999998 4.9379999999999997 4.9800000000000004 5.032 5.0380000000000003 5.0780000000000003 5.1349999999999998 5.282 5.431 5.4850000000000003 5.4989999999999997 5.7370000000000001 5.75 5.9009999999999998 5.9180000000000001 5.968 5.968 6.117 6.2830000000000004 6.3 6.9249999999999998Sample Percentile

fertility

## MLR_Output

 XLMiner : Multiple Linear Regression Date: 21-Sep-2016 03:55:09 Output Navigator Elapsed Times in Milliseconds Inputs Predictors Regress. Model ANOVA Train. Score – Summary Data read time MLR Time Report Time Total Residuals-Fitted Values Training Lift Chart Train. Score – Detailed Rep. 6 31 38 75 Inputs Data Workbook UN11.xlsx Worksheet Sheet1 Data Range \$A\$1:\$B\$200 # Records 199 Variables # Input Variables 1 Input variables ln(ppgdp) Output variable ln(ferility) Parameters/Options Force constant term to zero No Show fitted values on training data Yes Show ANOVA table Yes Show standardized residuals Yes Show un-standardized residuals No Show variance covariance matrix No Perform Variable Selection No Show studentized residuals No Show deleted residuals No Show Cook’s distance No Show DF fits No Show covariance ratios No Show hat matrix diagonals No Output Options Chosen Summary report of scoring on training data Detailed report of scoring on training data Lift charts on training data Model Predictors Tolerance for Entering the Model 0 Included Excluded Predictor Criteria Predictor Criteria Intercept 2.5472526876 ln(ppgdp) 121.3919348529 Regression Model Input Variables Coefficient Std. Error t-Statistic P-Value CI Lower CI Upper RSS Reduction Residual DF 197 Intercept 2.6655073378 0.1205657647 22.1083268954 2.93530254356826E-55 2.4277421211 2.9032725545 165.6020594861 R² 0.5259850345 ln(ppgdp) -0.2071497864 0.0140107282 -14.7850834534 9.06235683202295E-34 -0.2347800498 -0.1795195229 20.6176721099 Adjusted R² 0.5235788671 Std. Error Estimate 0.3071114681 RSS 18.5805384058 ANOVA Source DF SS MS F-Statistic P-Value Regression 1 20.6177 20.6177 218.5987 0 Error 197 18.5805 0.0943 Total 198 39.1982 20.712 Training Data Scoring – Summary Report Total sum of squared errors RMS Error Average Error 18.5805384058 0.3055642972 4.43531308832663E-16

## lifeExpFOnGroup

 group other africa lifeExpF other 1 0 49.49 SUMMARY OUTPUT other 1 0 80.4 africa 0 1 75 Regression Statistics africa 0 1 53.17 Multiple R 0.7868134043 other 1 0 81.1 R Square 0.6190753331 other 1 0 79.89 Adjusted R Square 0.6151883467 other 1 0 77.33 Standard Error 6.2801061827 other 1 0 77.75 Observations 199 oecd 0 0 84.27 oecd 0 0 83.55 ANOVA other 1 0 73.66 df SS MS F Significance F other 1 0 78.85 Regression 2 12563.0314933582 6281.5157466791 159.2687161617 8.36048455455694E-42 other 1 0 76.06 Residual 196 7730.187798459 39.4397336656 other 1 0 70.23 Total 198 20293.2192918173 other 1 0 80.26 other 1 0 76.37 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% oecd 0 0 82.81 Intercept 82.4464516129 1.1279403677 73.0946900864 3.54078776531392E-144 80.2219939182 84.6709093076 80.2219939182 84.6709093076 other 1 0 77.81 other -7.1197084195 1.2709066366 -5.6020703761 0.000000071 -9.6261157864 -4.6133010527 -9.6261157864 -4.6133010527 africa 0 1 58.66 africa -22.674187462 1.4199983772 -15.9677558973 2.58294591624273E-37 -25.4746247964 -19.8737501276 -25.4746247964 -19.8737501276 other 1 0 82.3 other 1 0 69.84 other 1 0 69.4 other 1 0 78.4 africa 0 1 51.34 other 1 0 77.41 other 1 0 80.64 other 1 0 77.12 africa 0 1 57.02 africa 0 1 52.58 other 1 0 65.1 africa 0 1 53.56 oecd 0 0 83.49 africa 0 1 77.7 other 1 0 83.8 africa 0 1 51.3 africa 0 1 51.61 oecd 0 0 82.35 other 1 0 75.61 other 1 0 77.69 africa 0 1 63.18 africa 0 1 59.33 other 1 0 76.2454672362 other 1 0 81.99 africa 0 1 57.71 other 1 0 80.37 other 1 0 81.33 other 1 0 82.14 oecd 0 0 81 africa 0 1 50.56 oecd 0 0 81.37 africa 0 1 60.04 other 1 0 78.2 other 1 0 76.57 other 1 0 64.2 other 1 0 78.91 africa 0 1 75.52 other 1 0 77.09 africa 0 1 52.91 africa 0 1 64.41 oecd 0 0 79.95 africa 0 1 61.59 other 1 0 72.27 oecd 0 0 83.28 oecd 0 0 84.9 other 1 0 78.07 africa 0 1 64.32 africa 0 1 60.3 other 1 0 77.31 oecd 0 0 82.99 africa 0 1 65.8 oecd 0 0 82.58 other 1 0 71.6 other 1 0 77.72 other 1 0 75.1 africa 0 1 56.39 africa 0 1 50.4 other 1 0 73.45 other 1 0 63.87 other 1 0 75.92 other 1 0 86.35 oecd 0 0 78.47 other 1 0 83.77 other 1 0 67.62 other 1 0 71.8 other 1 0 75.28 other 1 0 72.6 oecd 0 0 83.17 oecd 0 0 84.19 oecd 0 0 84.62 other 1 0 75.98 oecd 0 0 87.12 other 1 0 75.17 other 1 0 72.84 africa 0 1 59.16 other 1 0 63.1 other 1 0 75.89 other 1 0 72.36 other 1 0 69.42 other 1 0 78.51 other 1 0 75.07 africa 0 1 48.11 africa 0 1 58.59 africa 0 1 77.86 other 1 0 78.28 oecd 0 0 82.67 other 1 0 83.8 africa 0 1 68.61 africa 0 1 55.17 other 1 0 76.86 other 1 0 78.7 africa 0 1 53.14 other 1 0 82.29 other 1 0 70.6 africa 0 1 60.95 africa 0 1 76.89 oecd 0 0 79.64 other 1 0 70.17 other 1 0 73.48 other 1 0 72.83 other 1 0 77.37 africa 0 1 74.86 africa 0 1 51.81 other 1 0 67.87 africa 0 1 63.04 other 1 0 57.1 other 1 0 70.05 other 1 0 79.86 oecd 0 0 82.79 other 1 0 80.49 oecd 0 0 82.77 other 1 0 77.45 africa 0 1 55.77 africa 0 1 53.38 other 1 0 72.12 oecd 0 0 83.47 other 1 0 76.44 other 1 0 66.88 other 1 0 72.1 other 1 0 74.81 other 1 0 79.07 other 1 0 65.52 other 1 0 74.91 other 1 0 76.9 other 1 0 72.57 oecd 0 0 80.56 oecd 0 0 82.76 other 1 0 83.2 other 1 0 78.24 other 1 0 83.95 other 1 0 77.95 other 1 0 75.01 africa 0 1 57.13 other 1 0 77.54 other 1 0 76.02 africa 0 1 66.48 other 1 0 75.57 africa 0 1 60.92 other 1 0 77.05 africa 0 1 78 africa 0 1 48.87 other 1 0 83.71 oecd 0 0 79.53 oecd 0 0 82.84 other 1 0 70 africa 0 1 53.38 africa 0 1 54.09 other 1 0 84.76 other 1 0 78.4 other 1 0 74.73 africa 0 1 63.82 other 1 0 74.18 africa 0 1 48.54 oecd 0 0 83.65 oecd 0 0 84.71 other 1 0 77.72 other 1 0 71.23 africa 0 1 60.31 other 1 0 77.14 other 1 0 77.76 africa 0 1 59.4 other 1 0 75.38 other 1 0 73.82 africa 0 1 77.05 oecd 0 0 76.61 other 1 0 69.4 other 1 0 65.1 africa 0 1 55.44 other 1 0 74.58 other 1 0 78.02 oecd 0 0 82.42 oecd 0 0 81.31 other 1 0 80.66 other 1 0 71.9 other 1 0 73.58 other 1 0 77.73 other 1 0 77.44 other 1 0 67.66 africa 0 1 50.04 africa 0 1 52.72

## lifeExpOnGroup&ln(ppgdp)

 group other africa ln( ppgdp ) lifeExpF other 1 0 6.2126060958 49.49 SUMMARY OUTPUT other 1 0 8.209906872 80.4 africa 0 1 8.4058146034 75 Regression Statistics africa 0 1 8.3714503994 53.17 Multiple R 0.8655396724 other 1 0 9.5288013758 81.1 R Square 0.7491589244 other 1 0 9.122830689 79.89 Adjusted R Square 0.745299831 other 1 0 8.0165488949 77.33 Standard Error 5.1092540244 other 1 0 10.0367720397 77.75 Observations 199 oecd 0 0 10.9528903391 84.27 oecd 0 0 10.7179404457 83.55 ANOVA other 1 0 8.637213722 73.66 df SS MS F Significance F other 1 0 10.0195624635 78.85 Regression 3 15202.846338057 5067.615446019 194.1282143666 2.67925530778766E-58 other 1 0 9.8083028649 76.06 Residual 195 5090.3729537603 26.104476686 other 1 0 6.5078745492 70.23 Total 198 20293.2192918173 other 1 0 9.5817177042 80.26 other 1 0 8.6485722695 76.37 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% oecd 0 0 10.6877269388 82.81 Intercept 49.5292409403 3.3995538651 14.5693355379 5.14239177668032E-33 42.824627035 56.2338548457 42.824627035 56.2338548457 other 1 0 8.4108989066 77.81 other -1.5346826968 1.1736824055 -1.3075791966 0.192555616 -3.8494238919 0.7800584983 -3.8494238919 0.7800584983 africa 0 1 6.608135569 58.66 africa -12.1703652569 1.5574485782 -7.8142966819 0 -15.2419716525 -9.0987588613 -15.2419716525 -9.0987588613 other 1 0 11.4363111237 82.3 ln(ppgdp) 3.1773199909 0.315959718 10.0560919945 1.97277857411405E-19 2.554182955 3.8004570267 2.554182955 3.8004570267 other 1 0 7.6242282848 69.84 other 1 0 7.5897909548 69.4 other 1 0 8.4068648007 78.4 africa 0 1 8.9096270943 51.34 other 1 0 9.2794559026 77.41 other 1 0 10.3935266251 80.64 other 1 0 8.7585852218 77.12 africa 0 1 6.253251722 57.02 africa 0 1 5.1738872882 52.58 other 1 0 6.6811055883 65.1 africa 0 1 7.095561766 53.56 oecd 0 0 10.7442117106 83.49 africa 0 1 8.0845624152 77.7 other 1 0 10.9516465448 83.8 africa 0 1 6.1110237822 51.3 africa 0 1 6.5894765326 51.61 oecd 0 0 9.3832595311 82.35 other 1 0 8.3788502418 75.61 other 1 0 8.7359752452 77.69 africa 0 1 6.602045004 63.18 africa 0 1 7.8879968593 59.33 other 1 0 9.4101825425 76.2454672362 other 1 0 8.9494689926 81.99 africa 0 1 7.0510760984 57.71 other 1 0 9.5338359172 80.37 other 1 0 8.6489930859 81.33 other 1 0 10.2528865912 82.14 oecd 0 0 9.8436738518 81 africa 0 1 5.3013128755 50.56 oecd 0 0 10.9300702206 81.37 africa 0 1 7.1566445467 60.04 other 1 0 8.8566324506 78.2 other 1 0 8.5555288977 76.57 other 1 0 6.5597568705 64.2 other 1 0 8.3120368951 78.91 africa 0 1 7.8837101716 75.52 other 1 0 8.1390319178 77.09 africa 0 1 9.7322483589 52.91 africa 0 1 6.061689992 64.41 oecd 0 0 9.5564375683 79.95 africa 0 1 5.7825936551 61.59 other 1 0 8.1734908807 72.27 oecd 0 0 10.7032826697 83.28 oecd 0 0 10.5852173016 84.9 other 1 0 10.1133026736 78.07 africa 0 1 9.4309848031 64.32 africa 0 1 6.3614751742 60.3 other 1 0 7.8936840075 77.31 oecd 0 0 10.5930558365 82.99 africa 0 1 7.1953373464 65.8 oecd 0 0 10.1850433979 82.58 other 1 0 10.4714314227 71.6 other 1 0 8.9131465392 77.72 other 1 0 7.9663438655 75.1 africa 0 1 6.0579542884 56.39 africa 0 1 6.2904574107 50.4 other 1 0 8.0050333446 73.45 other 1 0 6.4178754197 63.87 other 1 0 7.6139173966 75.92 other 1 0 10.3679665742 86.35 oecd 0 0 9.4637415105 78.47 other 1 0 10.5784198447 83.77 other 1 0 7.2487885269 67.62 other 1 0 7.989323133 71.8 other 1 0 8.56161191 75.28 other 1 0 6.7895346476 72.6 oecd 0 0 10.7411743745 83.17 oecd 0 0 10.2857386211 84.19 oecd 0 0 10.4304945489 84.62 other 1 0 8.4967863816 75.98 oecd 0 0 10.672226782 87.12 other 1 0 8.3996026372 75.17 other 1 0 9.1233326313 72.84 africa 0 1 6.6868592002 59.16 other 1 0 7.2917924397 63.1 other 1 0 10.7239367635 75.89 other 1 0 6.7631918278 72.36 other 1 0 6.9542571126 69.42 other 1 0 9.274535084 78.51 other 1 0 9.1360154532 75.07 africa 0 1 6.8882666024 48.11 africa 0 1 5.3872435757 58.59 africa 0 1 9.3343970206 77.86 other 1 0 9.303420795 78.28 oecd 0 0 11.5626237881 82.67 other 1 0 10.8195822652 83.8 africa 0 1 6.0447683191 68.61 africa 0 1 5.8788556027 55.17 other 1 0 9.0327436356 76.86 other 1 0 8.4520144654 78.7 africa 0 1 6.3949276525 53.14 other 1 0 9.8832440281 82.29 other 1 0 8.0292373817 70.6 africa 0 1 7.0309458895 60.95 africa 0 1 8.9210970815 76.89 oecd 0 0 9.1161066126 79.64 other 1 0 7.8929002061 70.17 other 1 0 7.3937552813 73.48 other 1 0 7.7172177519 72.83 other 1 0 8.7810640128 77.37 africa 0 1 7.9603236291 74.86 africa 0 1 6.0100409327 51.81 other 1 0 6.7755943754 67.87 africa 0 1 8.5418272657 63.04 other 1 0 8.7307065206 57.1 other 1 0 6.281705842 70.05 other 1 0 9.9194150341 79.86 oecd 0 0 10.7559797561 82.79 other 1 0 10.4721904983 80.49 oecd 0 0 10.3850522197 82.77 other 1 0 7.0316529156 77.45 africa 0 1 5.8796946463 55.77 africa 0 1 7.1227053553 53.38 other 1 0 6.2225762681 72.12 oecd 0 0 11.3455559669 83.47 other 1 0 9.9422754797 76.44 other 1 0 6.9109501699 66.88 other 1 0 9.2893178972 72.1 other 1 0 7.5063170171 74.81 other 1 0 8.9377439369 79.07 other 1 0 7.2643102157 65.52 other 1 0 7.9269996323 74.91 other 1 0 8.5961337535 76.9 other 1 0 7.6686078359 72.57 oecd 0 0 9.4143581869 80.56 oecd 0 0 9.9729016686 82.76 other 1 0 10.1834272298 83.2 other 1 0 11.1899325724 78.24 other 1 0 9.9547603467 83.95 other 1 0 8.925640515 77.95 other 1 0 9.2448770552 75.01 africa 0 1 6.2772072402 57.13 other 1 0 8.8064390405 77.54 other 1 0 8.1147136221 76.02 africa 0 1 7.1571901643 66.48 other 1 0 9.6700347935 75.57 africa 0 1 6.9399320107 60.92 other 1 0 8.5415345228 77.05 africa 0 1 9.3457974094 78 africa 0 1 5.8627785395 48.87 other 1 0 10.6870031772 83.71 oecd 0 0 9.6788428751 79.53 oecd 0 0 10.048012049 82.84 other 1 0 7.0846454458 70 africa 0 1 4.7431914839 53.38 africa 0 1 8.8894185977 54.09 other 1 0 10.3268842576 84.76 other 1 0 7.7728790243 78.4 other 1 0 8.7277296057 74.73 africa 0 1 7.50928047 63.82 other 1 0 8.8562335561 74.18 africa 0 1 8.1050659404 48.54 oecd 0 0 10.7976594568 83.65 oecd 0 0 11.1401240427 84.71 other 1 0 7.9832695164 77.72 other 1 0 6.704414355 71.23 africa 0 1 6.2461067655 60.31 other 1 0 8.3971701488 77.14 other 1 0 8.4365903269 77.76 africa 0 1 6.2626360674 59.4 other 1 0 8.1727573291 75.38 other 1 0 9.6293861769 73.82 africa 0 1 8.3480879136 77.05 oecd 0 0 9.2198054366 76.61 other 1 0 8.4310904924 69.4 other 1 0 8.0668980674 65.1 africa 0 1 6.2324480166 55.44 other 1 0 8.0179667035 74.58 other 1 0 10.5872079402 78.02 oecd 0 0 10.5003110399 82.42 oecd 0 0 10.7481942015 81.31 other 1 0 9.388687374 80.66 other 1 0 7.2635398266 71.9 other 1 0 7.9941262812 73.58 other 1 0 9.5106449444 77.73 other 1 0 7.0755552393 77.44 other 1 0 7.2704520552 67.66 africa 0 1 7.1210908893 50.04 africa 0 1 6.3510602216 52.72

Regression Statistics

Multiple R0.72108

R Square0.519956

Standard Error0.93049

Observations199

ANOVA

dfSSMSFSignificance F

Regression1184.7462184.7462213.37933.16E-33

Residual197170.56480.865811

Total198355.3109

CoefficientsStandard Errort StatP-valueLower 95%Upper 95%

Intercept8.0096690.36529121.926799.34E-557.2892858.730053

ln(ppgdp)-0.620090.04245-14.60753.16E-33-0.7038-0.53637

Regression Statistics

Multiple R0.464675

R Square0.215923

Standard Error0.394984

Observations199

ANOVA

dfSSMSFSignificance F

Regression18.4637948.46379454.250824.72E-12

Residual19730.734420.156012

Total19839.19821

CoefficientsStandard Errort StatP-valueLower 95%Upper 95%

Intercept1.0583450.03431530.842412.43E-770.9906731.126016

ppgdp-1.1E-051.52E-06-7.365524.72E-12-1.4E-05-8.2E-06

Regression Statistics

Multiple R0.725248

R Square0.525985

Standard Error0.307111

Observations199

ANOVA

dfSSMSFSignificance F

Regression120.6176720.61767218.59879.06E-34

Residual19718.580540.094317

Total19839.19821

CoefficientsStandard Errort StatP-valueLower 95%

Intercept2.6655070.12056622.108332.94E-552.427742

ln(ppgdp)-0.207150.014011-14.78519.06E-34-0.23478