SAT College

A movie studio wishes to determine the relationship between the revenue from rental of comedies on streaming services and the revenue generated from the theatrical release of such movies. The studio has the following bivariate data from a sample of fifteen comedies released over the past five years. These data give the revenue I from theatrical release (in millions of dollars) and the revenue y from streaming service rentals (in millions of dollars) for each of the fifteen movies. Also shown are the scatter plot and the least-squares regression line for the data. The equation for this line is = 3.45+0.15x, Theater revenue, x (in millions of dollars) 61.9 60.0 20.2 30.9 44.8 50.0 28.0 27.6 24.9 7.3 66.8 25.0 36.5 15.0 13.8 Send data to calculator Rental revenue, y (in millions of dollars) 10.0 16.5 5.7 6.1 6.6 16.5 3.1 12.1 7.2 2.4 9.3 8.3 11.7 1.8 10.3 Based on the studio's data and the regression line, complete the following. Rental revenue (In millions of dollars) 18- 16- 14- 12- 10+ 0 X X X Theater revenue (in millions of dollars) (a) For these data, values for theater revenue that are greater than the mean of the values for theater revenue tend to be paired with values for rental revenue that are less than the mean of the values for rental revenue. (b) According to the regression equation, for an increase of one million dollars in theater revenue, there is a corresponding Increase of how many million dollars in rental revenue? ​

Answers

Answer 1

a. The statement is false because the values for rental revenue (y) are not less than the mean of the values for rental revenue when the values for theater revenue (x) are greater than the mean of the values for theater revenue.

b. For an increase of one million dollars in theater revenue, there is a corresponding increase of 0.15 million dollars in rental revenue.

How to calculate the value

(a) Mean of theater revenue (x):

(61.9 + 60.0 + 20.2 + 30.9 + 44.8 + 50.0 + 28.0 + 27.6 + 24.9 + 7.3 + 66.8 + 25.0 + 36.5 + 15.0 + 13.8) / 15 ≈ 34.01

Mean of rental revenue (y):

(10.0 + 16.5 + 5.7 + 6.1 + 6.6 + 16.5 + 3.1 + 12.1 + 7.2 + 2.4 + 9.3 + 8.3 + 11.7 + 1.8 + 10.3) / 15 ≈ 8.20

The statement is false because the values for rental revenue (y) are not less than the mean of the values for rental revenue when the values for theater revenue (x) are greater than the mean of the values for theater revenue.

(b) According to the regression equation, for an increase of one million dollars in theater revenue, there is a corresponding increase of 0.15 million dollars in rental revenue.

Therefore, for an increase of one million dollars in theater revenue, there is a corresponding increase of 0.15 million dollars in rental revenue.

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