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

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 slope of the line.

A) For a $\$ 1$ increase in an administrator's raise, we estimate the administrator's rating to decrease 2,000 points.
B) For a 1-point increase in an administrator's rating, we estimate the administrator's raise to decrease $\$ 2,000$ .
C) For an administrator with a rating of 1.0, we estimate his/her raise to be $\$ 2,000$ .
D) For a 1-point increase in an administrator's rating, we estimate the administrator's raise to increase $\$ 2,000$ .