analyze the College data frame included in the ISLR package. All analyses must be performed in R using tidyverse, ggplot2, and other packages discussed in class.

3) Last, we will compare relationships between the percentage of students from the top of their high school class and out-of- state tuition at public and private colleges. a. [10 points] Using different colored points for public and private colleges, create a scatterplot with the percentage of students from the top of their high school class on the axis and the out-of-state tuition on the axis. Overlay each set of points with a smoothed line of the same color with confidence bands. Remember to avoid overplotting. b. [10 points] Using faceting, create side-by-side scatterplots for public and private schools, with the number of students from the top of their high school class on each axis and the out-of-state tuition on each axis. Overlay each scatterplot with a smoothed line with confidence bands. Remember to avoid overplotting. c. [5 points) Is the out-of-state tuition generally higher at public or private colleges? d. [5 points] Is the correlation between the percentage of students in the top of their high school class and the out-of- state tuition stronger for public or private colleges? e. [5 points] Why are the confidence bands generally wider for public than for private colleges