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

question 83

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 $\hat { \beta _ { 0 } } = - 92040$ .

• A) The value has no practical interpretation since a GMAT of 0 is nonsensical and outside the range of the sample data.
• B) We expect to predict SALARY to within \(2 ( 92040 ) = \$ 184,080\) of its true value using GMAT in a straight-line model.
• C) We estimate SALARY to decrease \(\$ 92,040\) for every 1 -point increase in GMAT.
• D) We estimate the base SALARY of graduates of a top business school to be \(\$ - 92,040\).

---

Definitions:

Surprising Example

An unexpected case or illustration that deviates from what is considered common or typical.

Gender And Suicide

The study of how gender influences suicidal behavior and suicide rates, often identifying differences between males and females.

Lethal Means

Methods or objects capable of causing death, often discussed in the context of suicide prevention.

Subintentional Death

A death in which the victim plays an indirect, hidden, partial, or unconscious role.