A professor wants to analyze the relationship between his students' LSAT practice scores and their Verbal SAT and Math SAT scores from high school. The table below represents 15 randomly selected students' raw scores on the various standardized tests.
Student LSAT SAT Verbal SAT Math
1 476 101 68
2 457 92 46
3 540 90 50
4 551 107 59
5 575 98 50
6 698 150 66
7 545 118 54
8 574 110 51
9 645 117 59
10 690 114 80
11 634 130 57
12 637 118 51
13 390 91 44
14 562 118 61
15 560 109 66
a) Construct a regression equation for forecasting LSAT scores, based on the student's respective Math and Verbal SAT scores.
b) Is the regression significant? Why or why not? (Provide evidence.)
c) Apply the regression to predict an LSAT score if a student's Math score was 55 and their Verbal score was 128.
d) Find the 95% confidence interval for the predicted LSAT score from c).
e) Apply the regression to predict an LSAT score if a student's Math score was 40 and their Verbal score was 170.
f) Obtain and interpret the coefficient of determination.
g) Do all independent variables contribute significantly to the regression at the 0.05 level of significance?
h) Are there any issues of collinearity with the model, Yes or No? Provide evidence to substantiate your decision.
Additional Requirement
This kinds of question is a part of Statistics and it is a study about comparing LSAT, SAT Verbal and SAT Math scores for 15 randomly selected students. Various questions such as regression, collinearity, etc have been answered in the solution in detail.
Word limit 510