Question 13.135

Use the following data set for Exercises 27–33. Note that $x_{3}$ is a dummy variable.

$y$	$x_{1}$	$x_{2}$	$x_{3}$
−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:

Provide the multiple regression equation for your final model.
Interpret the multiple regression coefficients so that a nonstatistician could understand.
Report and interpret the standard error of the estimate $s$ , and the adjusted coefficient of determination $R_{adj}^{2}$ .

13.3.33

(a) The final multiple regression equation is $\hat{y} = - 3.12 + 1.15 x_{1} + 3.61 x_{3}$ . For $x_{3} = 0$ , the regression equation is $\hat{y} = - 3.12 + 1.15 x_{1}$ . For $x_{3} = 1$ , the regression equation is $\hat{y} = 0.49 + 1.15 x_{1}$ . (b) For each increase in one unit of the variable $x_{1}$ , the estimated value of $y$ increases by 1.15 units. The estimated increase in $y$ for those observations with $x_{3} = 1$ , as compared to those with $x_{3} = 0$ , when $x_{1}$ 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 $y$ is accounted for by this multiple regression equation.