# Question

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?

• 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?

## Answer to relevant Questions

The file P11_62.xlsx has (somewhat old) data on several countries. The variables are listed here.• Country: name of country• GNPCapita: GNP per capita• PopGrowth: average annual percentage change in population, ...The Pierce Company manufactures drill bits. The production of the drill bits occurs in lots of 1000 units. Due to the intense competition in the industry and the correspondingly low prices, Pierce has undertaken a study of ...Do the previous problem, but use the football data on all NFL teams in the file P03_57.xlsx.a. Rearrange the data so that there are six columns: Team, Year, Salary Last Year, Salary This Year, Wins Last Year, and Wins This ...The number of employees on the payroll at a food processing plant is recorded at the start of each month. These data are provided in the file P12_03.xlsx. Perform a runs test and find a few auto-correlations to determine ...The file P12_12.xlsx contains five years of monthly data on sales (number of units sold) for a particular company. The company suspects that except for random noise, its sales are growing by a constant percentage each month ...Post your question

1