Is There a Relationship Between the Raises Administrators at State $$E ( y ) = \beta _ { 0 } + \beta _ { 1 } x$$

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