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

question 15

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, $\hat { y } = \beta _ { 0 } + \beta _ { 1 } x$ . Using the method of least squares, the faculty group obtained the following prediction equation, $\mathrm { y } = 14,000 + 2,000 \mathrm { x }$ . Interpret the estimated slope of the line.

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

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