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

Short Answer

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