Use the data in ECONMATH to answer the following questions.

(i) Estimate a model explaining colgpa to hsgpa, actmth, and acteng. Report the results in the usual form. Are all explanatory variables statistically significant?

(ii) Consider an increase in hsgpa of one standard deviation, about .343. By how much does colgpa increase, holding actmth and acteng fixed. About how many standard deviations would the actmth have to increase to change colgpa by the same amount as one standard deviation in hsgpa? Comment.

(iii) Test the null hypothesis that actmth and acteng have the same effect (in the population) against a two-sided alternative. Report the p-value and describe your conclusions.

(iv) Suppose the college admissions officer wants you to use the data on the variables in part (i) to create an equation that explains at least 50 percent of the variation in colgpa. What would you tell the officer?