For Exercises 13, 15, and 21 in Section 10€“1, find the mean of the x and y variables. Then substitute the mean of the x variable into the corresponding regression line equations found in Exercises 13, 15, and 21 in this section and find y€™. Compare the value of y€™ with for each exercise. Generalize the results.
Exercise 13:
The yearly data have been published showing the number of releases for each of the commercial movie studios and the gross receipts for those studios thus far. Based on these data, can it be concluded that there is a relationship between the number of releases and the gross receipts?

Exercise 15:
The director of an alumni association for a small college wants to determine whether there is any type of relationship between the amount of an alumnus€™s contribution (in dollars) and the years the alumnus has been out of school. The data follow.

Exercise 21:
The number of faculty and the number of students are shown for a random selection of small colleges. Is there a significant relationship between the two variables? Switch x and y and repeat the process. Which do you think is really the independent variable?

No. of releasesr | 361 270 306 22 35 10 8 12 21 Gross receipts y (million $) 3844 1962 1371 1064 334 241 188 154 125 1 5 3 10 7 6 500 100 300 50 75 80 Years x Contributiony 5 Faculty 99 10 3 16 138 174 220 Students 1353 1290 1091 1213 1384 1283 2075