Question

Brews 4 U is a local chain of coffee shops. Managers are interested in the costs of the stores and believe that the costs can be explained in large part by the number of customers patronizing the stores. Monthly data regarding customer visits and costs for the preceding year for one of the stores have been entered into the regression analysis.
Average monthly customer-visits 1,462
Average monthly total costs $4,629
Regression results: Intercept $1,496
b coefficient $2.08
R2 0.86814

Required:
a. In a regression equation expressed as y= a + bx, how is the letter b best described?
b. How is the letter y in the regression equation best described?
c. How is the letter x in the regression equation best described?
d. Based on the data derived from the regression analysis, what are the estimated costs for 370 customer-visits in a month?
e. What is the percent of the total variance that can be explained by the regression equation?

Answer 1

Answer:

Explanation:

a. In a regression equation expressed as y= a + bx, how is the letter b best described?

Here, b is the slope and best described as the estimate of the cost when there's a visit of an additional customer.

b. How is the letter y in the regression equation best described?

The letter y is the observed store cost for that particular month.

c. How is the letter x in the regression equation best described?

The letter x is the observed customer visit for that particular month.

d. Based on the data derived from the regression analysis, what are the estimated costs for 370 customer-visits in a month?

The estimated cost for 370 customer visit will be:

Y = a + bx

where,

a =$1496

b = $2.08

x = 370 customer visit

Y = $1496 + ($2.08 × 370 customer visit)

= $1496 + $769.6

= $2265.6

e. What is the percent of the total variance that can be explained by the regression equation?

The percent of total variance which the regression equation explain will be:

R2 = 0.86814 or 86.814%