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 $ million. Data for 21 companies who use the bank's services were used to fit the model E(y) = ?? + ??x. The results of the simple linear regression are provided below. ? = 2,700 + 20x, s = 65, 2-tailed p-value = .064 (for testing ??) Interpret the p-value for testing whether ?? exceeds 0. There is sufficient evidence (at ? = .05) to conclude that service charge (y) is positively linearly related to sales revenue (x) . For every $1 million increase in sales revenue (x), we expect a service charge (y) to increase $.064. Sales revenue (x) is a poor predictor of service charge (y). There is insufficient evidence (at ? = .05) to conclude that service charge (y) is positively linearly related to sales revenue (x).
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In this case, the null hypothesis is that B1 (the coefficient for sales revenue) equals 0, which would mean that there is no relationship between sales revenue and the service charge. The p-value is 0.064, which is greater than the significance level of 0.05. Show more…
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Sri K.
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 the service charge to a company is the company's sales revenue (x), measured in $ million. Data for 21 companies who use the bank's services were used to fit the model Ey = Bo + B1x. The results of the simple linear regression are provided below: Y = 2,700 + 20x, s = 65, 2-tailed p-value = 0.064 (for testing B1) Interpretation of the p-value for testing whether B1 exceeds 0: There is sufficient evidence (at a = 0.05) to conclude that the service charge (Y) is positively linearly related to sales revenue (x). For every $1 million increase in sales revenue (x), we expect a service charge (Y) to increase by $0.064. However, sales revenue (x) is a poor predictor of service charge (Y). There is insufficient evidence (at a = 0.05) to conclude that the service charge (Y) is positively linearly related to sales revenue (x).
Madhur L.
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