9. The regression line below gives the relationship between quiz grades and test grades. TG = 40.448 + 5.175QG
where TG = test grade and QG = quiz grade. The linear correlation coefficient r = 0.63830. The test mean was 68 and the quiz grades range between 3 and10. The objective of the regression analysis was to determine if test grades reflect quiz grades.
a). What are the predictor and response variables?
predictor: QG
response: TG
b). Estimate the test grade of a student who scored 6 on the quiz. If the estimate is not possible, explain why not.
71.468
c). Estimate the test grade of a student if the quiz grade was 12. If the estimate is not possible, explain why not.
it is not possible because the highest quiz grade is a 10.
d). Estimate the quiz grade of a student who had 70 on the test. If the estimate is not possible, explain why not.
5.71
To answer these questions, we need to use the given regression line equation: TG = 40.448 + 5.175QG.
a) The predictor variable is QG (quiz grade) because it is used to predict the response variable, TG (test grade).
b) To estimate the test grade of a student who scored 6 on the quiz (QG = 6), we substitute QG = 6 into the regression line equation:
TG = 40.448 + 5.175(6)
TG = 40.448 + 30.225
TG ≈ 71.468
So, the estimated test grade for this student is approximately 71.468.
c) To estimate the test grade of a student if the quiz grade was 12 (QG = 12), we again substitute QG = 12 into the regression line equation:
TG = 40.448 + 5.175(12)
TG = 40.448 + 62.1
TG ≈ 102.548
However, it is not possible to estimate the test grade for a quiz grade of 12 because the highest quiz grade given in the data is 10.
d) To estimate the quiz grade of a student who had 70 on the test (TG = 70), we rearrange the regression line equation to solve for QG:
TG = 40.448 + 5.175QG
70 = 40.448 + 5.175QG
29.552 = 5.175QG
QG ≈ 5.71
Therefore, the estimated quiz grade for a student who had a test grade of 70 is approximately 5.71.