A teacher believes that the third homework assignment is a key predictor in how well students will do on the midterm. Let x represent the third homework score and y the midterm exam score. A random sample of last terms students were selected and their grades are shown below. Assume scores are normally distributed. a) Calculate the correlation coefficient using technology (you can copy and paste the data into Excel). Round answer to 4 decimal places. HW3 Midterm13.1 59.81121.9 87.5398.8 53.72824.3 95.2835.4 39.17413.2 66.09220.9 89.72918.5 78.98520 86.215.4 73.27425 93.259.7 52.2576.4 43.98420.2 79.76221.8 84.25823.1 92.91122 87.8211.4 54.03414.9 71.86918.4 76.70415.1 70.43115 65.1516.8 77.208b) Find the y-intercept and slope for the regression equation using technology (you can copy and paste the data into Excel). Round answer to 4 decimal places. hat(y=)? + ?xc) Find the predicted midterm score when the homework 3 score is 15. Do not round until the end, then round answer to 4 decimal places.