SCENARIO 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 charges 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:
Y i =$\beta$ 0 +$\beta$ 1 X i +$\varepsilon$ i
The results of the simple linear regression are provided below.
? = -2,700 +20 X ,S Y X = 65,two-tail p value = 0.034 (for testing $\beta$ 1 )

-Referring to Scenario 13-1,interpret the estimate of ?,the standard deviation of the random error term (standard error of the estimate)in the model.
A)About 95% of the observed service charges fall within $65 of the least squares line.
B)About 95% of the observed service charges equal their corresponding predicted values.
C)About 95% of the observed service charges fall within $130 of the least squares line.
D)For every $1 million increase in sales revenue,we expect a service charge to increase $65.

Question

SCENARIO 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 charges 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:
Y i =$\beta$ 0 +$\beta$ 1 X i +$\varepsilon$ i 
The results of the simple linear regression are provided below. 
? = -2,700 +20 X ,S Y X   = 65,two-tail p value = 0.034 (for testing $\beta$ 1 )
 
-Referring to Scenario 13-1,interpret the estimate of ?,the standard deviation of the random error term (standard error of the estimate)in the model.
A)About 95% of the observed service charges fall within $65 of the least squares line. 
B)About 95% of the observed service charges equal their corresponding predicted values. 
C)About 95% of the observed service charges fall within $130 of the least squares line. 
D)For every $1 million increase in sales revenue,we expect a service charge to increase $65.

Quizplus · Accepted Answer

The standard error of the estimate (also known as the estimated standard deviation of the error term) is the square root of the mean squared error, which in this case is $130. This means that about 95% of the observed service charges fall within $130 of the least squares line. Therefore, option C is the correct choice. Option A is incorrect because it only considers the magnitude of the error term, not its standard deviation. Option B is incorrect because it assumes that all observed service charges are equal to their predicted values, which is not necessarily true. Option D is incorrect because it refers to the regression coefficient, not the standard error of the estimate.

SCENARIO 13-1 a Large National Bank Charges Local Companies for Using

SCENARIO 13-1
a Large National Bank Charges Local Companies for Using