A statistics class has a midterm and nal exam, both graded out of 100' points. The summary statistics on the exams are: midterm: average = 71}, SD = 12, nal: average = 55, SD = l. The scatter diagram is footballshaped and r =05. (a) (3 points) Find the equation for the regression line predicting nal score from midterm score. (b) [5 points) Of all the people who were at the average on the midterm, about what percent got over the 80th percentile on the nal?I (c) [3 points) Consider the following 3 people: Alice got 53 on the midterm and 59 on the nal. Billy got 64 on the midterm and 71 on the nal. Cathy got 76 on the midterm and 75 on the nal. For each student, explain briey why the student is or is not a good example of the regression effect. No calculation is required. (d) (5 points) Suppose there is a data frame in R called mydctc with two columns named midterm and final. Write code in R to make a scatter plot with midterm on the x axis and nal on the y axis. Include the regression line (without any shaded area around it). Also include a title, \" Midterm and Final Scores\". (e) {2 points) To do part (a) above, is it necessary [or at least better) for the scatter plot to be footballshaped? If so, explain why ONE property of being footballshaped is necessary or useful for the method to be mean ingful. There may be more than one possible correct answer. If it's not necessary or useful to be footballshaped, explain why not. (f) {2 points) Repeat the previous question, but for what is relevant for the answer to part (b). Do not use the same property as you used in the