Question

Question #1 - Using the data on 4137 college students, the following equation was estimated
by OLS
colgpai = β0 + β1 hsperci + ui
, i = 1, 2, . . . , 4137
where colgpa is measured on a four-point scale and hsperc is the percentile in the
high school graduating class (defined so that, for example, hsperc = 5 means the top
5 percent of the class).
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 2.9803872 0.0141800 210.2 <2e-16 ***
hsperc -0.0170349 0.0005585 -30.5 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
2
Residual standard error: 0.5952 on 4135 degrees of freedom
Multiple R-squared: 0.1836, Adjusted R-squared: 0.1834
F-statistic: 930.2 on 1 and 4135 DF, p-value: < 2.2e-16
(i) Why does it make sense for the coefficient on hsperc to be negative?
(ii) Interpret the coefficient of hsperc.
(iii) Is it statistically different than zero at the 5% level?
(iv) What other factors do you think might be relevant for explaining colgpa?
(v) Are these other factors likely to be correlated with hsperc? If so, what can you
say about the interpretation of the coefficients on hsperc?

Answer 1