1. A dean of a business school has fit a regression model to predict college GPA
ID: 3259600 • Letter: 1
Question
1. A dean of a business school has fit a regression model to predict college GPA based on a student's SAT score (SAT_Score), the percentile at which the student graduated high school (HS_Percentile) (for instance, graduating 4th in a class of 500 implies that 496 other students are at or below that student, so the percentile is 496/500 x 100 = 99), and the total college hours the student has accumulated (Total_Hours). The regression results are shown below.
For testing the hypothesis that Total_Hours has a significant relationship with GPA (refer to an earlier problem), what would be the conclusion at the 0.05 level of significance, in the context of the problem? Read carefully.
2.
A dean of a business school has fit a regression model to predict college GPA based on a student's SAT score (SAT_Score), the percentile at which the student graduated high school (HS_Percentile) (for instance, graduating 4th in a class of 500 implies that 496 other students are at or below that student, so the percentile is 496/500 x 100 = 99), and the total college hours the student has accumulated (Total_Hours). The regression results are shown below.
Which of the following correctly specifies the hypothesis test for testing whether Total_Hours has a significant relationship with GPA? Read carefully.
3. A dean of a business school has fit a regression model to predict college GPA based on a student's SAT score (SAT_Score), the percentile at which the student graduated high school (HS_Percentile) (for instance, graduating 4th in a class of 500 implies that 496 other students are at or below that student, so the percentile is 496/500 x 100 = 99), and the total college hours the student has accumulated (Total_Hours). The regression results are shown below.
What would be the estimated mean GPA for a student with an SAT score of 1120, a high school percentile rank of 55, and total accumulated hours of 19? Because the estimated coefficients have such small values, in the calculation and answer, use four decimal places.
Regression Statistics Multiple R 0.5329 R Square 0.284 Adjusted R Square 0.2835 Standard Error 0.5575 Observations 4137 ANOVA df SS MS F Significance F Regression 3 509.5632 169.8544 546.4662 4.0431E-299 Residual 4133 1284.6325 0.3108 Total 4136 1794.1957 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept -0.0427 0.0702 -0.60816 0.5431 -0.1803 0.0949 SAT_Score 0.0015 0.00006 22.99086 3.6E-110 0.0014 0.0016 HS_Percentile 0.0131 0.0005 23.86919 4.5E-118 0.012 0.0142 Total_Hours 0.0019 0.0002 7.809486 7.23E-15 0.0014 0.0024Explanation / Answer
Answer:
1. A dean of a business school has fit a regression model to predict college GPA based on a student's SAT score (SAT_Score), the percentile at which the student graduated high school (HS_Percentile) (for instance, graduating 4th in a class of 500 implies that 496 other students are at or below that student, so the percentile is 496/500 x 100 = 99), and the total college hours the student has accumulated (Total_Hours). The regression results are shown below.
For testing the hypothesis that Total_Hours has a significant relationship with GPA (refer to an earlier problem), what would be the conclusion at the 0.05 level of significance, in the context of the problem? Read carefully.
H0: 3=0 H1: 30
Calculated t=7.809486, P=0.0000 which is < 0.05 level. Ho is Rejected. Total_Hours has a significant relationship with GPA.
2.
A dean of a business school has fit a regression model to predict college GPA based on a student's SAT score (SAT_Score), the percentile at which the student graduated high school (HS_Percentile) (for instance, graduating 4th in a class of 500 implies that 496 other students are at or below that student, so the percentile is 496/500 x 100 = 99), and the total college hours the student has accumulated (Total_Hours). The regression results are shown below.
Which of the following correctly specifies the hypothesis test for testing whether Total_Hours has a significant relationship with GPA? Read carefully.
H0: 3=0 H1: 30
3. A dean of a business school has fit a regression model to predict college GPA based on a student's SAT score (SAT_Score), the percentile at which the student graduated high school (HS_Percentile) (for instance, graduating 4th in a class of 500 implies that 496 other students are at or below that student, so the percentile is 496/500 x 100 = 99), and the total college hours the student has accumulated (Total_Hours). The regression results are shown below.
What would be the estimated mean GPA for a student with an SAT score of 1120, a high school percentile rank of 55, and total accumulated hours of 19?
The regression line
GPA = -0.0427+0.0015*SAT+0.0131*Rank+0.0019*hours
estimated mean GPA =-0.0427+0.0015*1120+0.0131*55+0.0019*19
=2.3939
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