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 4.236

35. Consumer Sentiment. See Exercise 49 in Section 4.2.

4.3.35

(a) 358.82 (b) 5.99013. The typical difference between the predicted consumer sentiment for incomes $75,000 or higher and the actual observed consumer sentiment for incomes $75,000 or higher is 5.99013. (c) 440.01 (d) 81.19 (e) 0.1845. Therefore, 18.45% of the variability in the consumer sentiment for incomes $75,000 or higher is accounted for by the linear relationship between the consumer sentiment for incomes $75,000 or higher and the consumer sentiment for incomes under $75,000. (f) 0.4295. This value of is positive. We would therefore say that the consumer sentiment for incomes $75,000 or higher and the consumer sentiment for incomes under $75,000 are positively correlated. As the consumer sentiment for incomes under $75,000 increases, the consumer sentiment for incomes $75,000 or higher also tends to increase.