Question

A university made an analysis of the relationship between the Math SAT scores (range 200-800) and first-year GPAs(range 0 to 4.0) for students who complete the first year. The average SAT score is 531 and the SD is 76 and the average GPA is 2.75 and the SD is 0.65. Suppose the correlation coefficient is found to be 0.7.

a) A student is chosen at random and has a SAT score of 678. Use regression to predict this student's GPA. ………...

b) Suppose the percentile rank of another student on the SAT is 70.88 percent. Predict his percentile rank on his GPA. Assume that both the SAT scores and GPAs follow the normal curve.(Hint: See examples 1 and 2 from pg 165-166 of the textbook.) ………..

Answer 1

Ans:

slope=0.7*(0.65/76)=0.005987

intercept=(2.75-0.005987*531)=-0.4291

regression eqn:

GPA=0.005987*SAT score-0.4291

a)

when SAT score=678

GPA=0.005987*678-0.4291

GPA=3.63

b)

z=normsinv(0.7088)=0.55

SAT score=531+0.55*76=572.8

predicted GPA=0.005987*572.8-0.4291=3.00

z=(3.00-2.75)/0.65=0.385

Percentile for GPA=normsdist(0.385)=0.6497 or 64.97%