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. 5,400 43, 800 Average monthly customer visits Average monthly total costs Regression results: Intercept b coefficient 687.65 7.59 0.79754 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 a)  The letter b is best described as the estimate of the cost for an additional customer visit.

Answer b)  The letter y is best described as the observed store cost for a given month.

Answer c)  The letter x is best described as observed customer visit for a given month.

Answer d)  The estimated cost for 370 customer visits is

Y = a + bx

a =$ 687.65 b = $ 7.59 x = 370 customer visits

Y = $ 687.65 + ($ 7.59 * 370 customer visit) = $ 687.65 + $ 2,808.3  = $ 3,495.95

Answer e)  The percent of total variance that can be explained by regression equation is R2 = 0.79754 or 79.754%