Question

The choir sells tickets to its performances for an assortment of prices and gives some tickets away. The choir

director wants to look at the relationship between the number of seats occupied at each performance and the
ticket revenue for that performance. The data show a linear pattern with the summary statistics shown below:
mean
standard deviation
= number of seats occupied
= 75.8
8 = 14.8
y = ticket revenue (dollars)
Y = 696
Sy = 177.6
r= 0.81
Find the equation of the least-squares regression line for predicting the ticket revenue from the number of
seats occupied
Round your entries to the nearest hundredth.
y
HC

Answer 1

The equation of the least-squares regression line for predicting ticket revenue from the number of seats occupied, rounded to the nearest hundredth, is ŷ = -40.29 + 9.72x.

Step-by-step explanation:

To find the equation of the least-squares regression line for predicting the ticket revenue from the number of seats occupied, we can use the summary statistics provided: the mean of X (number of seats occupied) is 75.8, the standard deviation of X (sx) is 14.8, the mean of Y (ticket revenue) is 696, and the standard deviation of Y (sy) is 177.6. Given the correlation coefficient (r) of 0.81, we can calculate the slope (m) of the regression line using the formula m = r(sy/sx), and the y-intercept (b) of the regression line using the formula b = Y - mX.

First, we calculate the slope:

m = 0.81 (177.6 / 14.8)

m = 0.81 (12.00)

m = 9.72

Next, we calculate the y-intercept:

b = 696 - (9.72 * 75.8)

b = 696 - 736.29

b = -40.29

Thus, the equation of the least-squares regression line is:

Ŷ = -40.29 + 9.72x

Round the values to the nearest hundredth:

Ŷ = -40.29 + 9.72x