5) The mean and standard deviation for the six-year graduation rate (%) for a ra

Question

5) The mean and standard deviation for the six-year graduation rate (%) for a random sample of the undergraduate public universities and colleges in the U.S. with enrollments between 10,000 and 20,000 is 42.5 and 9.1 respectively. The mean and standard deviation for the median SATs of students at these same schools is 1013 and 52.2 respectively. Also the correlation coefficient for the linear relationship predicting graduation rate from median SAT score is 0.76. a) Find the slope and y-intercept of the LSRL and then write its equation. b) Find the residual for the university that had a median SAT score of 930 and a graduation rate of 37.

Explanation / Answer

a) here as slope b1 =r*Sy/Sx =0.76*9.1/52.2=0.1325

interept bo=Ybar -b1*Xbar =42.5-0.1325*1013=-91.7128

therefore linear regression equation: Graduatiion rate Y =-91.7128+0.1325*X (median SAT score)

b)

for SAT score of 930 predicted graduation rate =-91.7128+0.1325*9630 =31.5033

hence residual =actual-predicted value =37-31.5033=5.4967

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