Faculty Salary, Completion Rate, and Control We look at the relationship between monthly faculty salary $($Fac$-$Salary$)$ and student six$-$year graduation rate $($CompRate$)$ for the data on four$-$year colleges in CollegeScores$4$yr$.$ We want to account for possible differences between Public and Private schools $($while omitting the for profit schools$).$

$($a$)$ Using the data in CollegeScores$4$yr$,$ which type of four$-$year school $($Private or Public$)$ has a higher mean faculty salary?

$($b$)$ Which has a higher mean completion rate?

$($c$)$ Based only on your answers to parts $($a$)$ and $($b$),$ would you expect completion rates to increase or decrease a faculty salaries increase.

$($d$)$ Figure below shows a scatterplot of FacSalary vs CompRate with separate regression lines for Private and Public colleges. Which type of control $($private or public$)$ is represented by the blue circles and solid blue regression line?

Completion rate vs faculty salary for public and private four$-$year colleges

$($e$)$ Is the association displayed in the scatterplot for both types of schools consistent with your answer to part $($c$)$ which was based only on the sample means?