Suppose students take a midterm worth 100 points. The average number of cups of coffee in the week before the midterm is 6, with an SD of 2. The average midterm score is 66, with an SD of 15. The correlation between cups of coffee and midterm scores is -0.2. The scatter plot is football-shaped.

1. (a)(3 Points) Find the equation for the regression line predicting midterm score from number of cups of coffee drank the week before the midterm. (You can do it in R, but state clearly how you found the line and write the equation.)
2. (b)(2 Points) One student drinks 3 cups of coffee more than another student during the week before the midterm. (That's all you know about the two students.) The student that drinks more coffee should be predicted to have a midterm score about points higher/lower than the other student. If appropriate, fill in the blank and answer either higher or lower. If not appropriate, explain why not.
3. (c)(2 Points) Someone uses this data as evidence that students should drink less coffee before exams. What do you think of this reasoning? Answer briefly (a sentence or two) based only on this data and using terminology from this course.
4. (d)(5 Points) Suppose there is a data frame in R called mydata with two columns named coffee and midterm. Write code in R to make a scatter plot with cups of coffee on the x axis and midterm scores on the y axis, and include the regression line (without any shaded area around it). Also include a title, "Coffee and Midterm Scores".
5. (e)(5 Points) Of all the people who had four cups of coffee during the week before the midterm, about what percent got over the 80th percentile on the midterm?
6. (f)(2 Points) To do part (e) above, is it necessary (or at least better) for the scatter plot to be football-shaped? If so, explain why ONE part of being football-shaped is necessary or useful for the method to be meaningful. There may be more than one possible correct answer. If it's not necessary or useful to be football-shaped, explain why not.