TABLE 13-1 A large national bank charges local companies for using their services. A bank official reported the results of a regression analysis designed to predict the bank's charges (Y) -- measured in dollars per month -- for services rendered to local companies. One independent variable used to predict service charge to a company is the company's sales revenue (X) -- measured in millions of dollars. Data for 21 companies who use the bank's services were used to fit the model: E(Y) = β 0 + β 1 X The results of the simple linear regression are provided below. Y = -2,700 + 20X, S YX = 65, two-tail p value of 0.034 (for testing β 1 ) -Referring to Table 13-1, a 95% confidence interval for β₁is (15, 30). Interpret the interval. A) We are 95% confident that the mean service charge will fall between $15 and $30 per month. B) We are 95% confident that the sales revenue (X) will increase between $15 and $30 million for every $1 increase in service charge (Y). C) We are 95% confident that average service charge (Y) will increase between $15 and $30 for every $1 million increase in sales revenue (X). D) At the α = 0.05 level, there is no evidence of a linear relationship between service charge (Y) and sales revenue (X).

Question

Quizplus · Accepted Answer

A 95% confidence interval for β11 means that we are 95% confident that the true population slope falls between the given interval. In this case, the interval is (15, 30), which means that we are 95% confident that the average service charge (Y) will increase between $15 and $30 for every $1 million increase in sales revenue (X). Choice A can be eliminated because the interval is not for the mean service charge itself, but for the slope parameter. Choice B can be eliminated because it has the roles of X and Y reversed. Choice D is incorrect because the regression coefficient is significant at the α = 0.05 level (given by the two-tail p-value of 0.034).

TABLE 13-1 A Large National Bank Charges Local Companies for Using Their