Question

Using the data on 4137 college students, the following equation was estimated

Using the data on 4137 college students, the following equation was estimated

by OLS

colgpai =β0 +β1hsperci +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 ***

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Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

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

1. (i) Why does it make sense for the coefficient on hsperc to be negative?

2. (ii) Interpret the coefficient of hsperc.

3. (iii) Is it statistically different than zero at the 5% level?

4. (iv) What other factors do you think might be relevant for explaining colgpa?

5. (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

ANSWER:

i) It makes sense for the coefficient on hsperc to be negative because the lower a student's percentile will be in the high school graduating class, the higher will be his/her intelligence level and higher will be his/her college GPA, i.e. a lower high school percentile causes a higher college GPA.

ii) The coefficent on hsperc is -0.0170349. Its interpretation:-
When high school graduating percentile increases by 1 per cent, the college GPA, on an average, decreases by 0.017 points.

iii) The t-statistic is given to be -30.5. The critical t-value at 5 percent level is 1.96. Hence, we reject the null hypothesis that the coefficent of hsperc is equal to zero. Hence, it is statistically different from zero at 5 percent level.

iv) Other factors relevant that might affect/explain a student's college GPA is his family's income level, health condition etc.
A rich student can afford tuitions, books, and other resources more easily than a poor stuent, and hence perform better in academics.
A physically/mentally healthy student is expected to perform better than a unhealthy student.