Question

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)- B^o + B^1x. Using th e method of least squares, the faculty group obtained the following prediction equation. Interpret the estimated slope of the line.^y=14,000-2,000x

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

Answer 1

The correct interpretation of the estimated slope -2,000 in the prediction equation is that for a 1-point increase in an administrator's job rating, their raise is estimated to decrease by $2,000, corresponding to option D.

Step-by-step explanation:

The question relates to the interpretation of the slope in a regression equation. The prediction equation in question could be represented as ˈy = 14,000 - 2,000x, where x is the job rating and y is the raise in dollars. The estimated slope of the line is -2,000. This means that for a 1-point increase in an administrator's job rating, we estimate the administrator's raise to decrease by $2,000. Therefore, the correct interpretation of the estimated slope would be option D: For a 1-point increase in an administrator's rating, we estimate the administrator's raise to decrease by $2,000.

Answer 2

The answer is "D".

Step-by-step explanation:

Since the value of b1 is negative, the regression line decreases as b1 increases

For a 1-point increase in an administrators rating, we estimate the administrators raise to decrease $2,000.