40.* Cost of higher education. Are there fundamental differences between liberal arts colleges and universities? In this case, we have information on the top 25 liberal arts colleges and the top 25 universities in the United States. We will consider the type of school as our response variable and will use the percent of students who were in the top 10% of their high school class and the amount of money spent per student by the college or university as our explanatory variables. The output from this logistic regression is given here.

a) Write out the estimated regression equation.

b) Is percent of students in the top 10% of their high school class statistically significant in predicting whether or not the school is a university? Explain.

c) Is the amount of money spent per student statistically significant in predicting whether or not the school is a university?
Explain.

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Logistic Regression Table: Predictor Coeff Intercept Top 10% $/Student SE(Coeff) Z P -13.1461 3.98629 -3.30 0.001 0.0845469 0.0002594 0.0396345 0.0000860 2.13 0.033 3.02 0.003