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Study on Comparison of LSAT, SAT Verbal and SAT Math


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.


This question belongs to 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.

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