Stepwise Regression
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3. A researcher used stepwise regression to create regression models to predict BirthRate (births per 1,000) using five predictors: LifeExp (life expectancy in years), InfMort (infant mortality rate), Density (population density per square kilometer), GDPCap (Gross Domestic Product per capita), and Literate (literacy percent). Interpret these results. BirthRates2
Regression Analysis?Stepwise Selection (best model of each size)
153 observations
BirthRate is the dependent variable
p-values for the coefficients
Nvar LifeExp InfMort Density GDPCap Literate s Adj R2 R2
1 .0000 6.318 .722 .724
2 .0000 .0000 5.334 .802 .805
3 .0000 .0242 .0000 5.261 .807 .811
4 .5764 .0000 .0311 .0000 5.273 .806 .812
5 .5937 .0000 .6289 .0440 .0000 5.287 .805 .812
4.An expert witness in a case of alleged racial discrimination in a state university school of nursing introduced a regression of the determinants of Salary of each professor for each year during an 8-year period (n = 423) with the following results, with dependent variable Year (year in which the salary was observed) and predictors YearHire (year when the individual was hired), Race (1 if individual is black, 0 otherwise), and Rank (1 if individual is an assistant professor, 0 otherwise). Interpret these results.
Variable Coefficient t p
Intercept − 3,816,521 − 29.4 .000
Year 1,948 29.8 .000
YearHire − 826 − 5.5 .000
Race − 2,093 − 4.3 .000
Rank − 6,438 − 22.3 .000
R2= 0.811 R2 adj =0.809 s = 3,318
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Solution Summary
The interpretation of a stepwise regression output and multiple regression output are discussed in the solution.
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Solution 1
Here the output represents the results of Stepwise regression model with forward selection method to predict BirthRate using five predictors: LifeExp, InfMort, Density, GDPCap, and Literate.
The predictor InfMort entered the regression equation first. The R2 value corresponding to this regression model involving the only predictor InfMort is 0.724. This indicates that 72.4% of the variation in the Birthrate is explained by the predictor InfMort and 27.6% left unexplained.
The predictor Literate entered the regression equation next. The R2 value corresponding to this regression model involving the predictors InfMort and Literate is 0.805. This indicates that 80.5% of the variation in the ...
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