Interpret the Slope and the Y-Intercept of the Least-Squares Regression $\hat { y } = \beta _ { 0 } + \beta 1 \mathrm { x }$

question 36

Multiple Choice

Interpret the Slope and the y-intercept of the Least-Squares Regression Line
-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, $\hat { y } = \beta _ { 0 } + \beta 1 \mathrm { x }$ . Using the method of least squares, the faculty group obtained the following prediction equation, $\hat { \mathrm { y } } = 14,000 + 2,000 \mathrm { x }$ . 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) The base administrator raise at State University is \(\$ 14,000\).
• C) For a 1-point increase in an administrator's rating, we estimate the administrator's raise to increase \(\$ 14,000\).
• D) There is no practical interpretation, since rating of 0 is nonsensical and outside the range of the sample data.