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

question 8

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 p-value for testing whether ?₁ exceeds 0.

• A) There is sufficient evidence (at the ? = 0.05) to conclude that sales revenue (X) is a useful linear predictor of service charge (Y).
• B) Sales revenue (X) is a poor predictor of service charge (Y).
• C) There is insufficient evidence (at the ? = 0.10) to conclude that sales revenue (X) is a useful linear predictor of service charge (Y).
• D) For every $1 million increase in sales revenue, we expect a service charge to increase $0.034.

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Definitions:

Division

A mathematical operation where one quantity is divided by another, resulting in a quotient and sometimes a remainder.

Administration Fee

A fee charged by an entity for the management services it provides.

Membership

A state of belonging to a group, club, or organization which often comes with specific benefits or privileges.

Cancellation

Cancellation refers to the act of terminating or ending a contract, an agreement, or a service before it is completed or takes effect.