SUMMARY OUTPUT Multiple R R Square Adjusted R Square Standard Error Observations
ID: 3324867 • Letter: S
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SUMMARY OUTPUT Multiple R R Square Adjusted R Square Standard Error Observations 0.989894408 0.97989094 0.946375839 0.093997207 ANOVA MS FSignificance F Regression Residual Total S 1.291627011 0.258325402 29.23729686 0.009507436 3 0.026506425 0.008835475 P-value Lower 95% Upper 95% Coefficients Standard Error t Stat 2.000000 1.000000 0.116964675 7.144529794 0.005645963 0.46342381 1.207891408 1.000000 0.250000 0.199040522 12.23566447 0.001175553 1.801957267 3.068828814 Intercept GPA Fin Major Gender NYC MajorXGender 0.221410557 -4.794091072 0.017265888 -1.766089586 -0.356835166 0.115122597 -2.041317871 0.133876794 -0.601373298 0.131369669 -0.500000 0.130770483 -4.049701664 0.027116334 -0.945751481 0.113411402 0.5000000 10. For the regression results above, use the variable names in the output and write the regression equation being represented. The Y variable is the log of earnings in the first year out of school. Considering the Y variable and the continuous variable GPA, would this equation come under the "Diminishing Returns" "Explosive Growth" or "Elasticity" characterization discussed in class.Explanation / Answer
Q10. For the summary output given above the equation is Y = 2 + 1.0*GPA - 1.0 Fin Major -0.25*Gender -0.5* NYC + 0.5*MajorXGender
This multiple regression equation helps predict Y for a given set of values on which it is dependent. The R^2 is 0.97 which means the model is almost a perfect fit and accounts for 97% of the variablity
As Y here is the log of earnings and its slope is 1 with respect to GPA. For every unit increase in GPA will give a unit increase in log(earnings) which means means earnings itself will grow exponentially. Hence this is case of "Explosive Growth"
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