Question 1

(Situation P) Below are the results of a survey of America's best graduate and professional schools. The top 25 business
schools, as determined by reputation, student selectivity, placement success, and graduation rate, are listed in the table.
For each school, three variables were measured: (1) GMAT score for the typical incoming student; (2) student acceptance
rate (percentage accepted of all students who applied); and (3) starting salary of the typical graduating student. \[\begin{array} { l l l l l } 
& \text { School } & \text { GMAT } & \text { Acc. Rate } & \text { Salary } \
\hline \text { 1. } & \text { Harvard } & 644 & 15.0 \% & \$ 63,000 \
\text { 2. } & \text { Stanford } & 665 & 10.2 & 60,000 \
\text { 3. } & \text { Penn } & 644 & 19.4 & 55,000 \
\text { 4. } & \text { Northwestern } & 640 & 22.6 & 54,000 \
\text { 5. } & \text { MIT } & 650 & 21.3 & 57,000 \
\text { 6. } & \text { Chicago } & 632 & 30.0 & 55,269 \
\text { 7. } & \text { Duke } & 630 & 18.2 & 53,300 \
\text { 8. } & \text { Dartmouth } & 649 & 13.4 & 52,000 \
\text { 9. } & \text { Virginia } & 630 & 23.0 & 55,269 \
\text { 10. } & \text { Michigan } & 620 & 32.4 & 53.300 \
\text { 11. } & \text { Columbia } & 635 & 37.1 & 52,000 \
\text { 12. } & \text { Cornell } & 648 & 14.9 & 50,700 \
\text { 13. } & \text { CMU } & 630 & 31.2 & 52,050 \
\text { 14. } & \text { UNC } & 625 & 15.4 & 50,800 \
\text { 15. } & \text { Cal-Berkeley } & 634 & 24.7 & 50,000 \
\text { 16. } & \text { UCLA } & 640 & 20.7 & 51,494 \
\text { 17. } & \text { Texas } & 612 & 28.1 & 43,985 \
\text { 18. } & \text { Indiana } & 600 & 29.0 & 44,119 \
\text { 19. } & \text { NYU } & 610 & 35.0 & 53,161 \
\text { 20. } & \text { Purdue } & 595 & 26.8 & 43,500 \
\text { 21. } & \text { USC } & 610 & 31.9 & 49,080 \
\text { 22. } & \text { Pittsburgh } & 605 & 33.0 & 43,500 \
\text { 23. } & \text { Georgetown } & 617 & 31.7 & 45,156 \
\text { 24. } & \text { Maryland } & 593 & 28.1 & 42,925 \
\text { 25. } & \text { Rochester } & 605 & 35.9 & 44,499
\end{array}\] The 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. A simple linear regression of SALARY versus GMAT using the 25 data points
in the table are shown below. $$\beta _ { 0 } = - 92040 \quad \hat { \beta } _ { 1 } = 228 \quad s = 3213 \quad r ^ { 2 } = .66 \quad r = .81 \quad \mathrm { df } = 23 \quad t = 6.67$$
-For the situation above, write the equation of the probabilistic model of interest. A) Salary $= \beta _ { 0 } + \beta _ { 1 }$ (GMAT)
B) Salary $= \beta _ { 0 } + \beta _ { 1 } ($ GMAT $) + \epsilon$
C) GMAT $= \beta _ { 0 } + \beta _ { 1 }$ (SALARY)
D) GMAT $= \beta _ { 0 } + \beta _ { 1 } ($ SALARY $) + \epsilon$

Accepted Answer

The answer of (Situation P) Below are the results of...

Question 2

(Situation P) Below are the results of a survey of America's best graduate and professional schools. The top 25 business
schools, as determined by reputation, student selectivity, placement success, and graduation rate, are listed in the table.
For each school, three variables were measured: (1) GMAT score for the typical incoming student; (2) student acceptance
rate (percentage accepted of all students who applied); and (3) starting salary of the typical graduating student. \[\begin{array} { l l l l l } 
& \text { School } & \text { GMAT } & \text { Acc. Rate } & \text { Salary } \
\hline \text { 1. } & \text { Harvard } & 644 & 15.0 \% & \$ 63,000 \
\text { 2. } & \text { Stanford } & 665 & 10.2 & 60,000 \
\text { 3. } & \text { Penn } & 644 & 19.4 & 55,000 \
\text { 4. } & \text { Northwestern } & 640 & 22.6 & 54,000 \
\text { 5. } & \text { MIT } & 650 & 21.3 & 57,000 \
\text { 6. } & \text { Chicago } & 632 & 30.0 & 55,269 \
\text { 7. } & \text { Duke } & 630 & 18.2 & 53,300 \
\text { 8. } & \text { Dartmouth } & 649 & 13.4 & 52,000 \
\text { 9. } & \text { Virginia } & 630 & 23.0 & 55,269 \
\text { 10. } & \text { Michigan } & 620 & 32.4 & 53.300 \
\text { 11. } & \text { Columbia } & 635 & 37.1 & 52,000 \
\text { 12. } & \text { Cornell } & 648 & 14.9 & 50,700 \
\text { 13. } & \text { CMU } & 630 & 31.2 & 52,050 \
\text { 14. } & \text { UNC } & 625 & 15.4 & 50,800 \
\text { 15. } & \text { Cal-Berkeley } & 634 & 24.7 & 50,000 \
\text { 16. } & \text { UCLA } & 640 & 20.7 & 51,494 \
\text { 17. } & \text { Texas } & 612 & 28.1 & 43,985 \
\text { 18. } & \text { Indiana } & 600 & 29.0 & 44,119 \
\text { 19. } & \text { NYU } & 610 & 35.0 & 53,161 \
\text { 20. } & \text { Purdue } & 595 & 26.8 & 43,500 \
\text { 21. } & \text { USC } & 610 & 31.9 & 49,080 \
\text { 22. } & \text { Pittsburgh } & 605 & 33.0 & 43,500 \
\text { 23. } & \text { Georgetown } & 617 & 31.7 & 45,156 \
\text { 24. } & \text { Maryland } & 593 & 28.1 & 42,925 \
\text { 25. } & \text { Rochester } & 605 & 35.9 & 44,499
\end{array}\] The 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. A simple linear regression of SALARY versus GMAT using the 25 data points
in the table are shown below. $$\beta _ { 0 } = - 92040 \quad \hat { \beta } _ { 1 } = 228 \quad s = 3213 \quad r ^ { 2 } = .66 \quad r = .81 \quad \mathrm { df } = 23 \quad t = 6.67$$
-For the situation above, give a practical interpretation of $\hat { \beta } _ { 0 } = - 92040$
A) We expect to predict SALARY to within 2(92040) = $184,080 of its true value using GMAT in a straight-line model.
B) We estimate SALARY to decrease $92,040 for every 1-point increase in GMAT.
C) We estimate the base SALARY of graduates of a top business school to be -$92,040.
D) The value has no practical interpretation since a GMAT of 0 is nonsensical and outside the range of the sample data.

Accepted Answer

The intercept $\hat{\beta}_0 = -92040$ has no practical interpretation because a GMAT score of 0 is not possible and is outside the range of the sample data.

Question 3

(Situation P) Below are the results of a survey of America's best graduate and professional schools. The top 25 business
schools, as determined by reputation, student selectivity, placement success, and graduation rate, are listed in the table.
For each school, three variables were measured: (1) GMAT score for the typical incoming student; (2) student acceptance
rate (percentage accepted of all students who applied); and (3) starting salary of the typical graduating student. \[\begin{array} { l l l l l } 
& \text { School } & \text { GMAT } & \text { Acc. Rate } & \text { Salary } \
\hline \text { 1. } & \text { Harvard } & 644 & 15.0 \% & \$ 63,000 \
\text { 2. } & \text { Stanford } & 665 & 10.2 & 60,000 \
\text { 3. } & \text { Penn } & 644 & 19.4 & 55,000 \
\text { 4. } & \text { Northwestern } & 640 & 22.6 & 54,000 \
\text { 5. } & \text { MIT } & 650 & 21.3 & 57,000 \
\text { 6. } & \text { Chicago } & 632 & 30.0 & 55,269 \
\text { 7. } & \text { Duke } & 630 & 18.2 & 53,300 \
\text { 8. } & \text { Dartmouth } & 649 & 13.4 & 52,000 \
\text { 9. } & \text { Virginia } & 630 & 23.0 & 55,269 \
\text { 10. } & \text { Michigan } & 620 & 32.4 & 53.300 \
\text { 11. } & \text { Columbia } & 635 & 37.1 & 52,000 \
\text { 12. } & \text { Cornell } & 648 & 14.9 & 50,700 \
\text { 13. } & \text { CMU } & 630 & 31.2 & 52,050 \
\text { 14. } & \text { UNC } & 625 & 15.4 & 50,800 \
\text { 15. } & \text { Cal-Berkeley } & 634 & 24.7 & 50,000 \
\text { 16. } & \text { UCLA } & 640 & 20.7 & 51,494 \
\text { 17. } & \text { Texas } & 612 & 28.1 & 43,985 \
\text { 18. } & \text { Indiana } & 600 & 29.0 & 44,119 \
\text { 19. } & \text { NYU } & 610 & 35.0 & 53,161 \
\text { 20. } & \text { Purdue } & 595 & 26.8 & 43,500 \
\text { 21. } & \text { USC } & 610 & 31.9 & 49,080 \
\text { 22. } & \text { Pittsburgh } & 605 & 33.0 & 43,500 \
\text { 23. } & \text { Georgetown } & 617 & 31.7 & 45,156 \
\text { 24. } & \text { Maryland } & 593 & 28.1 & 42,925 \
\text { 25. } & \text { Rochester } & 605 & 35.9 & 44,499
\end{array}\] The 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. A simple linear regression of SALARY versus GMAT using the 25 data points
in the table are shown below. $$\beta _ { 0 } = - 92040 \quad \hat { \beta } _ { 1 } = 228 \quad s = 3213 \quad r ^ { 2 } = .66 \quad r = .81 \quad \mathrm { df } = 23 \quad t = 6.67$$
-For the situation above, give a practical interpretation of r = .81.
A) We estimate SALARY to increase 81% for every 1-point increase in GMAT.
B) There appears to be a positive correlation between SALARY and GMAT.
C) 81% of the sample variation in SALARY can be explained by using GMAT in a straight -line model.
D) We can predict SALARY correctly 81% of the time using GMAT in a straight-line model.

Accepted Answer

The correlation coefficient (r = 0.81) indicates a strong positive linear relationship between SALARY and GMAT.

Question 4

(Situation P) Below are the results of a survey of America's best graduate and professional schools. The top 25 business
schools, as determined by reputation, student selectivity, placement success, and graduation rate, are listed in the table.
For each school, three variables were measured: (1) GMAT score for the typical incoming student; (2) student acceptance
rate (percentage accepted of all students who applied); and (3) starting salary of the typical graduating student. \[\begin{array} { l l l l l } 
& \text { School } & \text { GMAT } & \text { Acc. Rate } & \text { Salary } \
\hline \text { 1. } & \text { Harvard } & 644 & 15.0 \% & \$ 63,000 \
\text { 2. } & \text { Stanford } & 665 & 10.2 & 60,000 \
\text { 3. } & \text { Penn } & 644 & 19.4 & 55,000 \
\text { 4. } & \text { Northwestern } & 640 & 22.6 & 54,000 \
\text { 5. } & \text { MIT } & 650 & 21.3 & 57,000 \
\text { 6. } & \text { Chicago } & 632 & 30.0 & 55,269 \
\text { 7. } & \text { Duke } & 630 & 18.2 & 53,300 \
\text { 8. } & \text { Dartmouth } & 649 & 13.4 & 52,000 \
\text { 9. } & \text { Virginia } & 630 & 23.0 & 55,269 \
\text { 10. } & \text { Michigan } & 620 & 32.4 & 53.300 \
\text { 11. } & \text { Columbia } & 635 & 37.1 & 52,000 \
\text { 12. } & \text { Cornell } & 648 & 14.9 & 50,700 \
\text { 13. } & \text { CMU } & 630 & 31.2 & 52,050 \
\text { 14. } & \text { UNC } & 625 & 15.4 & 50,800 \
\text { 15. } & \text { Cal-Berkeley } & 634 & 24.7 & 50,000 \
\text { 16. } & \text { UCLA } & 640 & 20.7 & 51,494 \
\text { 17. } & \text { Texas } & 612 & 28.1 & 43,985 \
\text { 18. } & \text { Indiana } & 600 & 29.0 & 44,119 \
\text { 19. } & \text { NYU } & 610 & 35.0 & 53,161 \
\text { 20. } & \text { Purdue } & 595 & 26.8 & 43,500 \
\text { 21. } & \text { USC } & 610 & 31.9 & 49,080 \
\text { 22. } & \text { Pittsburgh } & 605 & 33.0 & 43,500 \
\text { 23. } & \text { Georgetown } & 617 & 31.7 & 45,156 \
\text { 24. } & \text { Maryland } & 593 & 28.1 & 42,925 \
\text { 25. } & \text { Rochester } & 605 & 35.9 & 44,499
\end{array}\] The 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. A simple linear regression of SALARY versus GMAT using the 25 data points
in the table are shown below. $$\beta _ { 0 } = - 92040 \quad \hat { \beta } _ { 1 } = 228 \quad s = 3213 \quad r ^ { 2 } = .66 \quad r = .81 \quad \mathrm { df } = 23 \quad t = 6.67$$
-For the situation above, write the equation of the least squares line.
A) SALARY = -92040 + 228 (GMAT)
B) SALARY = 228 + 92040 (GMAT)
C) GMAT = -92040 + 228 (SALARY)
D) GMAT = 228 - 92040 (SALARY)

Accepted Answer

The equation of the least squares line is SALARY = -92040 + 228 (GMAT). This is because the slope of the line is 228 and the y-intercept is -92040.

Question 5

(Situation P) Below are the results of a survey of America's best graduate and professional schools. The top 25 business
schools, as determined by reputation, student selectivity, placement success, and graduation rate, are listed in the table.
For each school, three variables were measured: (1) GMAT score for the typical incoming student; (2) student acceptance
rate (percentage accepted of all students who applied); and (3) starting salary of the typical graduating student. \[\begin{array} { l l l l l } 
& \text { School } & \text { GMAT } & \text { Acc. Rate } & \text { Salary } \
\hline \text { 1. } & \text { Harvard } & 644 & 15.0 \% & \$ 63,000 \
\text { 2. } & \text { Stanford } & 665 & 10.2 & 60,000 \
\text { 3. } & \text { Penn } & 644 & 19.4 & 55,000 \
\text { 4. } & \text { Northwestern } & 640 & 22.6 & 54,000 \
\text { 5. } & \text { MIT } & 650 & 21.3 & 57,000 \
\text { 6. } & \text { Chicago } & 632 & 30.0 & 55,269 \
\text { 7. } & \text { Duke } & 630 & 18.2 & 53,300 \
\text { 8. } & \text { Dartmouth } & 649 & 13.4 & 52,000 \
\text { 9. } & \text { Virginia } & 630 & 23.0 & 55,269 \
\text { 10. } & \text { Michigan } & 620 & 32.4 & 53.300 \
\text { 11. } & \text { Columbia } & 635 & 37.1 & 52,000 \
\text { 12. } & \text { Cornell } & 648 & 14.9 & 50,700 \
\text { 13. } & \text { CMU } & 630 & 31.2 & 52,050 \
\text { 14. } & \text { UNC } & 625 & 15.4 & 50,800 \
\text { 15. } & \text { Cal-Berkeley } & 634 & 24.7 & 50,000 \
\text { 16. } & \text { UCLA } & 640 & 20.7 & 51,494 \
\text { 17. } & \text { Texas } & 612 & 28.1 & 43,985 \
\text { 18. } & \text { Indiana } & 600 & 29.0 & 44,119 \
\text { 19. } & \text { NYU } & 610 & 35.0 & 53,161 \
\text { 20. } & \text { Purdue } & 595 & 26.8 & 43,500 \
\text { 21. } & \text { USC } & 610 & 31.9 & 49,080 \
\text { 22. } & \text { Pittsburgh } & 605 & 33.0 & 43,500 \
\text { 23. } & \text { Georgetown } & 617 & 31.7 & 45,156 \
\text { 24. } & \text { Maryland } & 593 & 28.1 & 42,925 \
\text { 25. } & \text { Rochester } & 605 & 35.9 & 44,499
\end{array}\] The 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. A simple linear regression of SALARY versus GMAT using the 25 data points
in the table are shown below. $$\beta _ { 0 } = - 92040 \quad \hat { \beta } _ { 1 } = 228 \quad s = 3213 \quad r ^ { 2 } = .66 \quad r = .81 \quad \mathrm { df } = 23 \quad t = 6.67$$
-For the situation above, give a practical interpretation of s = 3213.
A) We expect to predict SALARY to within 2(3213) = $6,426 of its true value using GMAT in a straight-line model.
B) We estimate SALARY to increase $3,213 for every 1-point increase in GMAT.
C) Our predicted value of SALARY will equal 2(3213) = $6,426 for any value of GMAT.
D) We expect the predicted SALARY to deviate from actual SALARY by at least 2(3213) = $6,426 using GMAT in a straight-line model.

Accepted Answer

The standard deviation of the residuals (s = 3213) indicates that the predicted salary will typically be within $3,213 of the actual salary, assuming the linear model is appropriate.

Question 6

(Situation P) Below are the results of a survey of America's best graduate and professional schools. The top 25 business
schools, as determined by reputation, student selectivity, placement success, and graduation rate, are listed in the table.
For each school, three variables were measured: (1) GMAT score for the typical incoming student; (2) student acceptance
rate (percentage accepted of all students who applied); and (3) starting salary of the typical graduating student. \[\begin{array} { l l l l l } 
& \text { School } & \text { GMAT } & \text { Acc. Rate } & \text { Salary } \
\hline \text { 1. } & \text { Harvard } & 644 & 15.0 \% & \$ 63,000 \
\text { 2. } & \text { Stanford } & 665 & 10.2 & 60,000 \
\text { 3. } & \text { Penn } & 644 & 19.4 & 55,000 \
\text { 4. } & \text { Northwestern } & 640 & 22.6 & 54,000 \
\text { 5. } & \text { MIT } & 650 & 21.3 & 57,000 \
\text { 6. } & \text { Chicago } & 632 & 30.0 & 55,269 \
\text { 7. } & \text { Duke } & 630 & 18.2 & 53,300 \
\text { 8. } & \text { Dartmouth } & 649 & 13.4 & 52,000 \
\text { 9. } & \text { Virginia } & 630 & 23.0 & 55,269 \
\text { 10. } & \text { Michigan } & 620 & 32.4 & 53.300 \
\text { 11. } & \text { Columbia } & 635 & 37.1 & 52,000 \
\text { 12. } & \text { Cornell } & 648 & 14.9 & 50,700 \
\text { 13. } & \text { CMU } & 630 & 31.2 & 52,050 \
\text { 14. } & \text { UNC } & 625 & 15.4 & 50,800 \
\text { 15. } & \text { Cal-Berkeley } & 634 & 24.7 & 50,000 \
\text { 16. } & \text { UCLA } & 640 & 20.7 & 51,494 \
\text { 17. } & \text { Texas } & 612 & 28.1 & 43,985 \
\text { 18. } & \text { Indiana } & 600 & 29.0 & 44,119 \
\text { 19. } & \text { NYU } & 610 & 35.0 & 53,161 \
\text { 20. } & \text { Purdue } & 595 & 26.8 & 43,500 \
\text { 21. } & \text { USC } & 610 & 31.9 & 49,080 \
\text { 22. } & \text { Pittsburgh } & 605 & 33.0 & 43,500 \
\text { 23. } & \text { Georgetown } & 617 & 31.7 & 45,156 \
\text { 24. } & \text { Maryland } & 593 & 28.1 & 42,925 \
\text { 25. } & \text { Rochester } & 605 & 35.9 & 44,499
\end{array}\] The 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. A simple linear regression of SALARY versus GMAT using the 25 data points
in the table are shown below. $$\beta _ { 0 } = - 92040 \quad \hat { \beta } _ { 1 } = 228 \quad s = 3213 \quad r ^ { 2 } = .66 \quad r = .81 \quad \mathrm { df } = 23 \quad t = 6.67$$
-For the situation above, give a practical interpretation of $r ^ { 2 } = .66$.
A) We expect to predict SALARY to within $2 ( \sqrt { .66 } )$ of its true value using GMAT in a straight-line model.
B) We estimate SALARY to increase $\$ .66$ for every 1 -point increase in GMAT.
C) $66 \%$ of the sample variation in SALARY can be explained by using GMAT in a straight -line model.
D) We can predict SALARY correctly $66 \%$ of the time using GMAT in a straight-line model.

Accepted Answer

The answer of (Situation P) Below are the results of...

Question 7

A 95% prediction interval for SALARY when GMAT = 600 is ($37,915, $51,948). Interpret this interval for the situation above.
A) We are 95% confident that the SALARY of a top business school graduate with a GMAT of 600 will fall between $37,915 and $51,984.
B) We are 95% confident that the mean SALARY of all top business school graduates with GMATs of 600 will fall between $37,915 and $51,984.
C) We are 95% confident that the increase in SALARY for a 600-point increase in GMAT will fall between $37,915 and $51,984.
D) We are 95% confident that the SALARY of a top business school graduate will fall between $37,915 and $51,984.

Accepted Answer

A 95% prediction interval provides a range in which we expect the salary of an individual graduate with a GMAT score of 600 to fall, with 95% confidence.

Question 8

For the situation above, which of the following is not an assumption required for the simple linear regression analysis to be valid?
A) The errors of predicting SALARY are normally distributed.
B) The errors of predicting SALARY have a mean of 0.
C) The errors of predicting SALARY have a variance that is constant for any given value of GMAT.
D) SALARY is independent of GMAT.

Accepted Answer

Simple linear regression assumes that there is a linear relationship between the independent variable (GMAT) and the dependent variable (SALARY), not that they are independent.

Question 9

Set up the null and alternative hypotheses for testing whether a positive linear relationship exists between SALARY and GMAT in the situation above. A) $H _ { 0 } : \beta _ { 1 } = 0$ vs. $H _ { a } : \beta _ { 1 } > 0$
B) $H _ { 0 } : \beta _ { 1 } = 0$ vs. $H _ { \mathrm { a } } : \beta _ { 1 } \neq 0$
C) $H _ { 0 } : \beta _ { 1 } = 228$ vs. $H _ { \mathrm { a } } : \beta _ { 1 } > 228$
D) $H _ { 0 } : \beta _ { 1 } > 0$ vs. $H _ { \mathrm { a } } : \beta _ { 1 } < 0$

Accepted Answer

The answer of Set up the null and alternative hypotheses...

Question 10

(Situation P) Below are the results of a survey of America's best graduate and professional schools. The top 25 business
schools, as determined by reputation, student selectivity, placement success, and graduation rate, are listed in the table.
For each school, three variables were measured: (1) GMAT score for the typical incoming student; (2) student acceptance
rate (percentage accepted of all students who applied); and (3) starting salary of the typical graduating student. \[\begin{array} { l l l l l } 
& \text { School } & \text { GMAT } & \text { Acc. Rate } & \text { Salary } \
\hline \text { 1. } & \text { Harvard } & 644 & 15.0 \% & \$ 63,000 \
\text { 2. } & \text { Stanford } & 665 & 10.2 & 60,000 \
\text { 3. } & \text { Penn } & 644 & 19.4 & 55,000 \
\text { 4. } & \text { Northwestern } & 640 & 22.6 & 54,000 \
\text { 5. } & \text { MIT } & 650 & 21.3 & 57,000 \
\text { 6. } & \text { Chicago } & 632 & 30.0 & 55,269 \
\text { 7. } & \text { Duke } & 630 & 18.2 & 53,300 \
\text { 8. } & \text { Dartmouth } & 649 & 13.4 & 52,000 \
\text { 9. } & \text { Virginia } & 630 & 23.0 & 55,269 \
\text { 10. } & \text { Michigan } & 620 & 32.4 & 53.300 \
\text { 11. } & \text { Columbia } & 635 & 37.1 & 52,000 \
\text { 12. } & \text { Cornell } & 648 & 14.9 & 50,700 \
\text { 13. } & \text { CMU } & 630 & 31.2 & 52,050 \
\text { 14. } & \text { UNC } & 625 & 15.4 & 50,800 \
\text { 15. } & \text { Cal-Berkeley } & 634 & 24.7 & 50,000 \
\text { 16. } & \text { UCLA } & 640 & 20.7 & 51,494 \
\text { 17. } & \text { Texas } & 612 & 28.1 & 43,985 \
\text { 18. } & \text { Indiana } & 600 & 29.0 & 44,119 \
\text { 19. } & \text { NYU } & 610 & 35.0 & 53,161 \
\text { 20. } & \text { Purdue } & 595 & 26.8 & 43,500 \
\text { 21. } & \text { USC } & 610 & 31.9 & 49,080 \
\text { 22. } & \text { Pittsburgh } & 605 & 33.0 & 43,500 \
\text { 23. } & \text { Georgetown } & 617 & 31.7 & 45,156 \
\text { 24. } & \text { Maryland } & 593 & 28.1 & 42,925 \
\text { 25. } & \text { Rochester } & 605 & 35.9 & 44,499
\end{array}\] The 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. A simple linear regression of SALARY versus GMAT using the 25 data points
in the table are shown below. $$\beta _ { 0 } = - 92040 \quad \hat { \beta } _ { 1 } = 228 \quad s = 3213 \quad r ^ { 2 } = .66 \quad r = .81 \quad \mathrm { df } = 23 \quad t = 6.67$$
-For the situation above, give a practical interpretation of $\hat { \beta } _ { 1 } = 228$
A) We expect to predict SALARY to within 2(228) = $456 of its true value using GMAT in a straight-line model.
B) We estimate SALARY to increase $228 for every 1-point increase in GMAT.
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 228 is nonsensical and outside the range of the sample data.

Accepted Answer

We estimate SALARY to increase $228 for every 1-point increase in GMAT.

Question 11

For the situation above, give a practical interpretation of t = 6.67.
A) There is evidence (at ? = .05) to indicate that $\beta _ { 1 } = 0$
B) Only 6.67% of the sample variation in SALARY can be explained by using GMAT in a straight -line model.
C) We estimate SALARY to increase $6.67 for every 1-point increase in GMAT.
D) There is evidence (at ? = .05) of at least a positive linear relationship between SALARY and GMAT.

Accepted Answer

The answer of For the situation above, give a practical...

Quiz 11: Simple Linear Regression

A 95% prediction interval for SALARY when GMAT = 600 is ($37,915, $51,948) . Interpret this interval for the situation above.

For the situation above, which of the following is not an assumption required for the simple linear regression analysis to be valid?

For the situation above, give a practical interpretation of t = 6.67.