Professor X at College Y has compiled data on grade point averages of the colleg

Question

Professor X at College Y has compiled data on grade point averages of the college seniors in his class and the grade point averages of those same students from their senior year in high school. The professor wants to test the hypothesis that college students’ grade point averages have no relationship with their grade point averages in high school. His model is as follows: Ci = a + bHSi , where Ci is student i's college grade point average and HSi is that student’s high school grade point average. He gets the following least-squares regression results (these results are fictional): (a) Interpret the estimated coefficient 0.324 of the variable HS. Answer: (b) Is the estimated coefficient for the variable HS statistically significant at the 5% significance level? Explain. Answer:

Explanation / Answer

Answer to part a)

The estimated coefficient 0.324, indicates a small positive correlation.

r = 0.324

this provides us the coefficient of determination = (0.324)^2 = 0.1049

This implies that only 10.49% of the variation in the college grade points can be explained by the high school grade points. This indicates a very weak correlation or kind of no correlation.

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