Interpret the Slope and the Y-Intercept of the Least-Squares Regression

question 108

Multiple Choice

Interpret the Slope and the y-intercept of the Least-Squares Regression Line
-Each year a nationally recognized publication conducts its "Survey of America's Best Graduate and Professional Schools." An academic advisor wants to predict the typical starting salary of a graduate at a top business school using GMAT score of the school as a predictor variable. Total GMAT scores range from 200 to 800. A simple linear regression of SALARY versus GMAT using 25 data points shown below.
$$\hat { \beta _ { 0 } } = - 92040 \hat { \beta } 1 = 228 \mathrm {~s} = 3213 \mathrm { R } ^ { 2 } = 0.66 \mathrm { r } = 0.81 \mathrm { df } = 23 \mathrm { t } = 6.67$$
Give a practical interpretation of $\hat { \beta } 1 = 228$ .

• A) We estimate SALARY to increase \(\$ 228\) for every 1 -point increase in GMAT.
• B) We expect to predict SALARY to within \(2 ( 228 ) = \$ 456\) of its true value using GMAT in a straight-line model.
• C) We estimate GMAT to increase 228 points for every \(\$ 1\) increase in SALARY.
• D) The value has no practical interpretation since a GMAT of 0 is nonsensical and outside the range of the sample data.

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