ST 352 Assignment 6: Inference using Multiple Linear Regression One way colleges

Question

ST 352 Assignment 6: Inference using Multiple Linear Regression

One way colleges measure success is by graduation rates. A committee was wondering what factors might have an effect on graduation rates at small colleges or universities (enrollments under 5000). The committee randomly selected 22 colleges or universities in the United States with enrollments under 5000 students. They collected information on the 6-year graduation rate, the median SAT score of students accepted to the college, student-related expenses per full-time student, and whether the college had both males and females or just one sex. The data are in the graduation.csv data set available on Canvas. The variable names and descriptions are given below.

Data Set:

8) (8 points total) Perform a backwards selection process to find a model that includes only significant predictors of the response variable. Use the model obtained after performing the backwards selection process to answer the following questions:

a] Write the regression equation, defining the terms in the equation. (2 points)

b] Predict the graduation rate for a small college that includes both male and female students, has a median SAT of 950, and student related expenses of $12,500. (Note: your final model may not include all of these variables. If it does not, then ignore the values given in this problem for variables not in your final model.) (2 points)

c] What percent of the variation in the response variable is explained by your final regression model? (1 pt)

d] What recommendation would you make to the committee as far as what factor or factors may have a strong impact on graduation rates at small colleges and universities? Briefly discuss. (3 points)

college graduation rate median SAT expense type of student Cornerstone University 0.391 1065 9482 0 Barry University 0.389 950 13149 0 Wilkes University 0.532 1090 9418 0 Colgate University 0.893 1350 26969 0 Lourdes College 0.313 930 8489 0 Cncordia University of Austin 0.315 985 8329 0 Carleton College 0.896 1390 29605 0 Letourneau University 0.545 1170 13154 0 Ohio Valley College 0.288 950 10887 0 Chadron State College 0.469 990 6046 0 Meredith College 0.679 1035 14889 1 Tougaloo College 0.495 845 11694 0 Hawaii Pacific University 0.41 1000 9911 0 University of Michigan-Dearborn 0.497 1065 9371 0 Whittier College 0.553 1065 14051 0 Wheaton College 0.845 1325 18420 0 Southampton College of Long Island 0.465 1035 13302 0 Keene State College 0.541 1005 8098 0 Mount St Mary's College 0.579 918 12999 1 Wellesley College 0.912 1370 35393 1 Fort Lewis College 0.298 970 5518 0 Bowdoin College 0.891 1375 35669 0

Explanation / Answer

8)

a] The regression equation is:

graduation.rate =  -0.3906 + 0.0007602*(median.SAT) + 0.125*(type.of.student)

where -0.3906 is the intercept i.e. the value of the dependent variable if the independent variables are 0;

0.0007602 is the coefficient of the median.SAT score which is positive and thus can be explained by saying that if median.SAT score increases by 1 unit graduation rate increases by 0.0007602.

and 0.125 is the coefficient of the type of student which is binary i.e. if the college contains only males or only females then the graduation rate is likely to increase by 0.125.

Here the expense is not selected by the stepwise regression (backward) process i.e. expense did not turn out to be significant.

b] The prediction of the graduation rate for a small college that includes both male and female students, has a median SAT of 950, and student related expenses of $12,500 is given by the regression model:

graduation.rate =  -0.3906 + 0.0007602*(median.SAT) + 0.125*(type.of.student)

graduation.rate =  -0.3906 + 0.0007602*950 + 0.125*0

graduation.rate = 0.33159

Here median.SAT score is given to be 950 and type of student is zero as the college contains both male and female students. The regression model does not include the expense.

c] The percent of the variation in the response variable that is explained by the final regression model is 0.861 or 86.1% (Multiple R2 value).

Please note: Some people tend to take Adjusted R2 as the final answer. In that case the percent of the variation in the response variable that is explained by the final regression model is 0.8378 or 83.78%

d] Recommendations to the committee as far as what factor or factors may have a strong impact on graduation rates at small colleges and universities is:

It is seen that a only male or only female colleges tend to show an increase in graduation rates than the mixed college ( includes both male and female students ). Also an increase in the SAT score of the students also increases the graduation rates. The graduation rates and type of college is able to explain almost (86%) of the factors explaining the graduation rates.

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