Question

Graduation Rates. Graduation rate-the percentage of entering freshmen attending full time and graduating within 5 yearsand what influences it is a concern in U.S. colleges and universities. U.S. News and World Report's "College Guide" provides data on graduation rates for colleges and universities as a function of the percentage of freshmen in the top $10\%$of their high school class, total spending per student, and student-to-faculty ratio. A random sample of 10 universities gave the following data on student-to-faculty ratio (S/F ratio) and graduation rate (Grad rate).

Discuss what satisfying the assumptions for regression inferences would mean with student-to-faculty ratio as the predictor variable and graduation rate as the response variable.

Short answer

There are constants ${\beta }_0,{\beta }_1$and $\sigma$ such that, for each stucent-to-faculty$x$

Step-by-step solution

Step 1:Given information

Step 2:Explaination

There are constants, ${\beta }_0,{\beta }_1$, and $\sigma$, such that, for each student-to-faculty ratio, $x$, the graduation rates for all universities with that students-to-faculty ratio are normally distributed with mean ${\beta }_0+{\beta }_{1}x$and standard deviation $\sigma$.