Question

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
y ^= β0 +β1x.

Using the method of least squares, the faculty group obtained the following prediction equation:

y ^= 14,000 - 2,000x

Interpret the estimated y-intercept of the line.

A) For an administrator who receives a rating of zero, we estimate his or her raise to be $14,000.

B) For a 1-point increase in an administrator's rating, we estimate the administrator's raise to increase $14,000.

C) The base administrator raise at State University is $14,000.

D) There is no practical interpretation, since rating of 0 is nonsensical and outside the range of the sample data.

Answer 1

Answer:

A. For an administrator who receives a rating of zero, we estimate his or her raise to be $14,000.

Step-by-step explanation:

Consider the following linear regression line

y^=βo +β1x.

Here, βo represents intercept of line and β1 represents slope of line.

Intercept βo represents estimated value of dependent variable y when independent variable x is zero i.e. x=0. Sometimes interpretation of intercept is not meaningful in the given context.

We are given the regression equation

y ^= 14,000 - 2,000x.

The intercept βo=14000 represents the raise of administrator having zero ratings. So, intercept can be interpreted as

" For an administrator who receives a rating of zero, we estimate his or her raise to be $14,000".