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

question 105

Multiple Choice

Is there a relationship between the raises administrators at State 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 straight-line regression model
$$E ( y ) = \beta _ { 0 } + \beta _ { 1 } x .$$
Using the method of least squares, the faculty group obtained the following prediction equation:
$$\hat { y } = 14,000 - 2,000 x$$
Interpret the estimated $y$ -intercept of the line.

• A) There is no practical interpretation, since rating of 0 is nonsensical and outside the range of the sample data.
• B) For a 1-point increase in an administrator's rating, we estimate the administrator's raise to increase \(\$ 14,000\).
• C) For an administrator who receives a rating of zero, we estimate his or her raise to be \(\$ 14,000\).
• D) The base administrator raise at State University is \(\$ 14,000\).

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