R using tidyverse, ggplot2

For this assignment, you will be analyzing the College data frame included in the ISLR package. The goal of this assignment is to become more familiar with working with data in R. All analyses must be performed in R using tidyverse, ggplot2, and other packages discussed in class. Provide your answers and all code used to obtain them under the respective questions in this Word document, and then save it as a pdf and upload it to Canvas. Note: If you use the same code for multiple questions (e.g., questions 1a and 1b), then you only need to provide your code under the first question (question 1a in this example). There are many ways of getting the same answer for a question, and all that is important here is that your code yields the correct answer. 1) First, we will explore the dataset. a. [5 points] How many colleges are in the dataset?Example: This is where you should provide your answer to question 1a. b. [5 points] How many features are there for each college?c. [5 points] Which feature(s) is(are) categorical?d. [5 points] Which feature(s) is(are) numerical?e. [5 points] How many colleges are private?f. [5 points] What is the mean graduation rate across colleges?g. [5 points] What is the maximum number of undergraduate students at a college? Hint: Make sure that you include both full-time and part-time students in your calculation. 2) Second, we will examine the relationship between the percentage of students from the top 10% of their high school class and the out-of-state tuition at a college. a. [10 points] Create a scatterplot with the percentage of students from the top 10% of their high school class on the 𝑥 axis and the out-of-state tuition on the 𝑦 axis. Overlay the points with a smoothed line and 95% confidence bands. Remember to avoid overplotting.

b. [5 points] Examine your plot from question 2a. Is the correlation between the percentage of students from the top 10% of their high school class and the out-of-state tuition positive or negative?c. [5 points] Explain what this correlation means about the relationship between the percentage of students from the top 10% of their high school class and the out-of-state tuition at a college. d. [5 points] If you were to perform a hypothesis test to evaluate this relationship, what would be the null hypothesis?e. [5 points] Why is the 95% confidence interval widest when the percentage of students from the top 10% of their high school class is largest?3) Last, we will compare relationships between the percentage of students from the top 10% 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 10% of their high school class on the 𝑥 axis and the out-of-state tuition on the 𝑦 axis. Overlay each set of points with a smoothed line of the same color with 95% 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 10% of their high school class on each 𝑥 axis and the out-of-state tuition on each 𝑦 axis. Overlay each scatterplot with a smoothed line with 95% 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 10% 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?

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