For Exercises 23–37, follow these steps. You have already calculated the regression equation in Exercises 37–51 in Section 4.2. Do the following.

  1. Calculate the sum of squares error, SSE.
  2. Compute and interpret the standard error of the estimate, .
  3. Calculate the total sum of squares, SST.
  4. Find the sum of squares regression, SSR.
  5. Calculate and interpret the coefficient of determination, .
  6. Use to calculate and interpret the correlation coefficient, .

Question 4.232

31. Completing College. See Exercise 45 in Section 4.2.

4.3.31

(a) 23.800 (b) 1.72483%. The typical difference between the predicted percent of a state's population that completes college and the actual observed percent of the state's population that completes college is 1.74283%. (c) 154.156 (d) 130.356 (e) 0.8456. Therefore, 84.56% of the variability in the percent of a state's population that completes college is accounted for by the linear relationship between the percent of a state's population that completes college and the percent of a state's population that attends college. (f) 0.9196.

This value of is very close to the maximum value . We would therefore say that the percent of a state's population that completes college and the percent of a state's population that attends college are positively correlated. As the percent of a state's population that attends college increases, the percent of a state's population that completes college tends to increase.