A Large National Bank Charges Local Companies for Using Their $$E ( y ) = \beta _ { 0 } + \beta _ { 1 } x .$$

Short Answer

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 $$E ( y ) = \beta _ { 0 } + \beta _ { 1 } x .$$
The results of the simple linear regression are provided below.
$$\hat { y } = 2,700 + 20 x , s = 65,2 \text {-tailed } p \text {-value } = .064 \text { (for testing } \beta _ { 1 } \text { ) }$$
Interpret the $p$ -value for testing whether $\beta _ { 1 }$ exceeds 0 .
A) There is sufficient evidence (at $\alpha = .05$ ) to conclude that service charge $( y )$ is positively linearly related to sales revenue $( x )$ .
B) For every $\$ 1$ million increase in sales revenue $( x )$ , we expect a service charge $( y )$ to increase $\$ .064$ .
C) There is insufficient evidence (at $\alpha = .05$ ) to conclude that service charge ( $y$ ) is positively linearly related to sales revenue $( x )$ .
D) Sales revenue $( x )$ is a poor predictor of service charge $( y )$ .