You are interested in running a regression of a sample of students’ college GPA

Question

You are interested in running a regression of a sample of students’ college GPA (colgpa) on their percentile rank is high school (hsperc) and their SAT score (sat).

A. Run this regression and interpret the coefficient on the two included independent variables and comment on their sign. Are these signs what we would expect? Explain why or why not.

B. Run this regression again using only the first half of the data (the first 2,070 observations). What is the ratio of the standard errors for the two independent variables, hsperc and sat, in comparing your model from part A to part B? Is this what we would expect? Explain why or why not.   

MS SS Number of obs 4,137 Source df F (2, 4134 777.92 2 245.303353 Prob F Model 490 606706 0.0000 Residual 1303.58897 4,134 315333567 squared 0.2734 Adj R-squared 0.2731 4,136 433799728 Root MSE Total 1794 19567 56155 Coef Std. Err colgpa P>lt I 1953 Conf. Interval] hsperc 0135192 0005495 24.60 0.000 0145965 012442 0014762 0000653 22.60 0.000 0013482 001 6043 Sat 1.251495 1.532018 1.391757 0715424 19.45 0.000 Con

Explanation / Answer

A. Coefficient of hsperc is - 0.0135192

Interpretation : Unit change in hsperc the GPA decreases by 0.0135192

Coefficient of sat is 0.0014762

Interpretation : Unit change in sat the GPA increases by 0.0014762

If sign is positive then GPA increases.

If sign is negative then GPA decreases.

B. The ratio of the standard errors for the two independent variables hsperc and sat for part A is

0.0005495 / 0.0000653 = 8.42

The ratio of the standard errors for the two independent variables hsperc and sat for part B is

0.0007185/0.0000886 = 8.11

The ratio of the standard errors for the part A is greater than part B.

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