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.

---

Definitions:

Glycolipids

Lipid molecules that contain carbohydrate groups, involved in cell recognition and signaling.

ATP Synthesis

The process by which cells produce ATP (adenosine triphosphate), involving the transfer of electrons through the electron transport chain and ATP synthase.

Kidney Tubule

A tiny tube in the kidney where urine is formed after filtration, consisting of the proximal tubule, loop of Henle, and distal tubule.

Proteases

Enzymes that catalyze the breakdown of proteins into smaller peptides or amino acids by cleaving peptide bonds.