Use the following data set for Exercises 27–33. Note that is a dummy variable.

−0.7 2 0.1 0
6.4 4 −2.5 1
2.8 6 2.7 0
9.4 8 2.8 1
8.6 10 −1.6 0
13.1 12 1.0 1
12.2 14 −1.4 0
19.1 16 −0.5 1
18.8 18 1.0 0
23.2 20 −2.3 1

Question 13.135

33. Report and interpret your final model from Exercise 31, by doing the following:

  1. Provide the multiple regression equation for your final model.
  2. Interpret the multiple regression coefficients so that a nonstatistician could understand.
  3. Report and interpret the standard error of the estimate , and the adjusted coefficient of determination .

13.3.33

(a) The final multiple regression equation is . For , the regression equation is . For , the regression equation is . (b) For each increase in one unit of the variable , the estimated value of increases by 1.15 units. The estimated increase in for those observations with , as compared to those with , when is held constant, is 3.61. (c) Using the multiple regression equation in (a), the size of the typical prediction error will be about 0.959129. 98.4% of the variability in is accounted for by this multiple regression equation.