A business school committee was charged with studying admissions criteria to the school. Until that time, only juniors were admitted. Part of the committee’s task was to see whether freshman courses would be equally good predictors of success as freshman and sophomore courses combined. Here, we take “success” to mean doing well in I-core. The file P11_61.xlsx contains data on 250 students who had just completed I-core. For each student, the file lists their grades in the following courses:
• M118 (freshman)—finite math
• M119 (freshman)—calculus
• K201 (freshman)—computers
• W131 (freshman)—writing
• E201, E202 (sophomore)—micro- and macroeconomics
• L201 (sophomore)—business law
• A201, A202 (sophomore)—accounting
• E270 (sophomore)—statistics
• I-core (junior)—finance, marketing, and operations
Except for I-core, each value is a grade point for a specific course (such as 3.7 for an A–). For I-core, each value is the average grade point for the three courses comprising I-core.
a. The I-core grade point is the eventual dependent variable in a regression analysis. Look at the correlations between all variables. Is multicollinearity likely to be a problem? Why or why not?
b. Run a multiple regression using all of the potential explanatory variables. Now, eliminate the variables as follows. Any variable whose confidence interval contains the value zero is a candidate for exclusion. For all such candidates, eliminate the variable with the t-value lowest in magnitude. Then rerun the regression, and use the same procedure to possibly exclude another variable.
Keep doing this until 95% confidence intervals of the coefficients of all remaining variables do not include zero. Report this final equation, its R2 value, and its standard error of estimate se.
c. Give a quick summary of the properties of the final equation in part b. Specifically,
(1) Do the variables have the “correct” signs,
(2) Which courses tend to be the best predictors,
(3) Are the predictions from this equation likely to be much good, and
(4) Are there any obvious violations of the regression assumptions?
d. Redo part b, but now use as your potential explanatory variables only courses taken in the freshman year. As in part b, report the final equation, its R2, and its standard error of estimate se.
e. Briefly, do you think there is enough predictive power in the freshman courses, relative to the freshman and sophomore courses combined, to change to a sophomore admit policy?