A Large National Bank Charges Local Companies for Using Their $$Y _ { 1 } = b _ { 0 } + b _ { 1 } x _ { 1 } + \varepsilon _ { j }$$

question 42

Multiple Choice

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:
$$Y _ { 1 } = b _ { 0 } + b _ { 1 } x _ { 1 } + \varepsilon _ { j }$$
The results of the simple linear regression are provided below:
$$\hat { Y } = - 2,700 + 20 X , S _ { Y X } = 65 \text {, two-tailed } p \text {-value } = 0.034 \text { (for testing } \theta _ { 1 } \text { ) }$$
-Referring to Instruction 12.1,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 $130 of the least squares line.
• B) About 95% of the observed service charges fall within $65 of the least squares line.
• C) About 95% of the observed service charges equal their corresponding predicted values.
• D) For every $1 million increase in sales revenue, we expect a service charge to increase $65.

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Definitions:

Market Rate

The prevailing interest rate available in the financial markets for a similar instrument or the going rate for goods or services in a certain market.

Issuance Price

Refers to the price at which a company's securities, such as stocks or bonds, are sold to investors when they are first made available.

Straight-line Method

A method of calculating depreciation of an asset by evenly spreading its cost over the expected useful life.

Semiannual Interest

Interest payments made twice a year on loans, bonds, or deposits.