An Academic Advisor Wants to Predict the Typical Starting Salary $$\hat { \beta } _ { 0 } = - 92040 \hat { \beta } 1 = 228 \quad s = 3213 \quad \mathrm { df } = 23 \quad t = 6.67$$

question 75

Multiple Choice

An academic advisor wants to predict the typical starting salary of a graduate at a top business school using the GMAT score of the school as a predictor variable. A simple linear regression of
SALARY versus GMAT using 25 data points is shown below. $$\hat { \beta } _ { 0 } = - 92040 \hat { \beta } 1 = 228 \quad s = 3213 \quad \mathrm { df } = 23 \quad t = 6.67$$
Set up the null and alternative hypotheses for testing whether a linear relationship exists between SALARY and GMAT.

• A) \(H _ { 0 } : \beta _ { 1 } > 0\) vs. \(\mathrm { H } _ { \mathrm { a } } : \beta _ { 1 } < 0\)
• B) \(H _ { 0 } : \beta _ { 1 } = 0\) vs. \(H _ { \mathrm { a } } : \beta _ { 1 } \neq 0\)
• C) \(H _ { 0 } : \beta _ { 1 } = 0\) vs. \(H _ { \mathrm { a } } : \beta _ { 1 } > 0\)
• D) \(H _ { 0 } : \hat { \beta } 1 = 228\) vs. \(H _ { \mathrm { a } } : \hat { \beta } _ { 1 } > 228\)

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Definitions:

Sum of Squares

The total of the squared differences between data points and their mean, reflecting the total variation within a data set.

Error Sum of Squares

A measure of the discrepancy between the data and an estimation model, quantifying the amount of variation in the data that is not explained by the model.

F-Test Statistic

A statistical measure used primarily in ANOVA and regression analysis to evaluate the significance of groups of variables, determining whether variances between sample means are greater than the variance within the samples.

SSE

SSE stands for Sum of Squared Errors, a measure used in statistics to quantify the deviation of predicted values from the actual values in a regression analysis.