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What determines the amount of college tuition students at different schools must pay? A random sample of n American colleges and universities is selected. The

What determines the amount of college tuition students at different schools must pay? A random sample of n American colleges and universities is selected. The values of several variables are recorded: average annual tuition (y), percentage of students in the top 25% of their high school graduating class (x1), student-to-faculty ratio (x2), average faculty compensation (x3), acceptance rate (x4), and percentage of faculty with a Ph.D. (x5). Some example observations are listed below.

ID X1 X2 X3 X4 X5
1 23 19.1 55000 0.75 89
2 50 15.3 68000 0.60 77
3 28 22.7 72000 0.35 92

For students with a% in the top 25% of their high school graduating class and b% of faculty with a Ph.D., the 'a' and 'b' values were applied for building this linear regression model. As a result, the regression equation is as follows:

  1. If the % of students who graduated in the top 25% in high school is 35, the studentfaculty ratio at this university is 19.1, and faculty compensation is $56,000. There is a 0.821 acceptance rate, and 88% of faculty have a Ph.D. What is the predicted average annual tuition?
  2. If we sampled 18 American universities, how many degrees of freedom associated with error will be in the ANOVA table?

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