In: Statistics and Probability
Michigan and Michigan State play each other this Saturday in football. Based on data from ESPN, Michigan averages 38.1 points per game with a SD of 8.4 and average 424 yards gained per game with a SD of 72. The correlation between points scored and yards gained is 0.68. Thus:
Average points = 38.1, SD= 8.4
Average yards gained = 424, SD= 72, r = 0.68
Find the slope of the regression equation for predicting number of points scored based on average yards gained per game). Report your answer to 4 decimal places.
If Michigan gains 500 yards in the game against Michigan State, what is Michigan's predicted points scored? Round to the nearest whole number.
Find the answer in the following attachments.
Note: Theory part depicts the elaborate derivations, you can skip the derivation part, if it is not necessary for you.