Is There a Relationship Between the Raises Administrators at County $( x )$

question 91

Multiple Choice

Is there a relationship between the raises administrators at County University receive and their performance on the job?

A faculty group wants to determine whether job rating $( x )$ is a useful linear predictor of raise (y) . Consequently, the group considered the linear regression model
$$E ( y ) = \beta _ { 0 } + \beta _ { 1 } x$$
The faculty group obtained the following prediction equation:
$$\hat { y } = 14,000 - 2,000 x$$
Which of the following statements about the model $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x$ is correct?

• A) The model hypothesizes that, on average, administrators make more money than professors.
• B) The model hypothesizes that knowing an administrator's rating \(( x )\) will determine exactly the administrator's raise \(( y )\).
• C) The model hypothesizes that the raises for the administrators fall in a perfect straight line.
• D) The model hypothesizes a line of means; as rating \(( x )\) increases, the mean raise \(E ( y )\) moves up or down along a straight line.

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Definitions:

Total Revenue

The sum of money a company earns from selling its products or services, prior to deducting any costs.

Elastic

Describes a situation in which the quantity demanded or supplied of a good or service changes significantly as its price changes.

Inelastic

A characteristic of goods whereby a change in price leads to a relatively smaller change in the quantity demanded or supplied.

Total-revenue Test

A method used to determine the price elasticity of demand by observing changes in total revenue as a result of price alterations.