Question

A statistical analysis of first year GPA's and SAT scores is taken by a university admissions office. The scatter diagram of the data is football shaped, i.e., assume that fitting a regression line to the data is appropriate in this case. A summary of the data is:

Average GPA=2.3 with an SD=0.5
Average SAT=1025 with an SD=150.r=0.8.
(a) Predict the first year GPA of an applicant.
(b) Predict the first year GPA of an applicant that scored 1100 on the SAT.
Expert Answer

Answer 1

To predict the first year GPA of an applicant, use a linear regression line with the given data. Substitute the SAT score to find the predicted GPA.

Step-by-step explanation:

The given problem involves a statistical analysis of first year GPA's and SAT scores. Since the scatter diagram of the data is football-shaped, it is appropriate to fit a regression line to the data. To predict the first year GPA of an applicant, we can use the formula for a linear regression line:

GPA = a + b(SAT)

where 'a' is the intercept and 'b' is the slope of the regression line. In this case, the slope can be calculated using the correlation coefficient (r), which is 0.8. The predicted GPA can then be calculated using the student's SAT score. Given an SAT score of 1100, we can substitute it into the equation to find the corresponding predicted GPA.