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

question 204

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,a 95% confidence interval for ?₁ is (15,30) .Interpret the interval.

• A) At the ? = 0.05 level, there is no evidence of a linear relationship between service charge (Y) and sales revenue (X).
• B) We are 95% confident that average service charge (Y) will increase between $15 and $30 for every $1 million increase in sales revenue (X).
• C) We are 95% confident that the mean service charge will fall between $15 and $30 per month.
• D) We are 95% confident that the sales revenue (X) will increase between $15 and $30 million for every $1 increase in service charge (Y).

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