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 \[x=\] number of seats occupied \[\bar{x}=75.8\] \[s_x=14.8\] \[y=\] ticket revenue (dollars) \[\bar{y}=696\] \[s_y=177.6\] \[r=0.81\] 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.

Certainly! Here's the question in multiple-choice format:
A) y = 31.85x + 398.04
B) y = 398.04x + 31.85
C) y = 10.61x + 398.04
D) y = 398.04x + 10.61

Answer 1

The equation of the least-squares regression line for predicting ticket revenue from the number of seats occupied is y = 9.74x + 31.85.

Step-by-step explanation:

In order to find the equation of the least-squares regression line, we need to use the formula: y = mx + b, where m is the slope of the line and b is the y-intercept. To find the slope, we use the formula: m = r(sy/sx), where r is the correlation coefficient, sy is the standard deviation of the y-values, and sx is the standard deviation of the x-values. Plugging in the values given in the question, we get: m = 0.81(177.6/14.8) = 9.74.

To find the y-intercept, we use the formula: b = &bar;y - m&bar;x, where &bar;y and &bar;x are the means of the y-values and x-values, respectively. Plugging in the values given in the question, we get: b = 696 - 9.74(75.8) = 31.85.

So, the equation of the least-squares regression line is: y = 9.74x + 31.85.