13.9 Answers to Select Exercises
1.
- [latex]\begin{eqnarray*}\hat{y} & = & 21.989+0.046x_1-0.196x_2 \\ x_1 & = & \mbox{seating capacity} \\ x_2 & = & \mbox{traffic count (1000s)} \\ \hat{y} & = & \mbox{average weekly profit (\$1000s)} \end{eqnarray*}[/latex]
- For each additional seat in the restaurant, the average weekly profit increases by $46.
- For each additional 1000 cars that pass the restaurant, the average weekly profit decreases by $196.
- $24,519.20
- 0.2250
- 22.50% of the variation in the average weekly profit can be explained by the regression model based on seating capacity and traffic count.
- 4.1675.
- On average, the average weekly profit differs by $4167.50 from the regression model based on seating capacity and traffic count.
- p-value=0.0205; reject the null hypothesis.
- p-value=0.0144; reject the null hypothesis.
- p-value=0.2645; do not reject the null hypothesis.
2.
- [latex]\begin{eqnarray*}\hat{y} & = & 1.692+0.524x_1-0.082x_2 \\ x_1 & = & \mbox{average number of hours spent studying a night} \\ x_2 & = & \mbox{average number of nights go out each week} \\ \hat{y} & = & \mbox{GPA} \end{eqnarray*}[/latex]
- For each additional hour spent studying each night, the student’s GPA increases by 0.524.
- For each additional hour a student goes out each week, the student’s GPA decreases by 0.082.
- 3.54
- 0.5833
- 58.33% of the variation in GPA can be explained by the regression model based on the average number of hours spent studying a night and the average number of nights a student goes out each week.
- 0.6613.
- On average, GPA differs by 0.6613 from the regression model based on the average number of hours spent studying a night and the average number of nights a student goes out each week.
- p-value=0.0002; reject the null hypothesis.
- p-value=0.0009; reject the null hypothesis.
- p-value=0.5083; do not reject the null hypothesis.
3.
- [latex]\begin{eqnarray*}\hat{y} & = & -42.359+1.436x_1+14.758x_2+5.486x_3 \\ x_1 & = & \mbox{age} \\ x_2 & = & \mbox{years of college} \\ x_3 & = & \mbox{years with the company} \\ \hat{y} & = & \mbox{salary (\$1000s)} \end{eqnarray*}[/latex]
- For each additional year of age, the salary increases by $1436.14.
- For each additional year of college, the salary increases by $14,758.04.
- For each additional year with the company, the salary increases by $5486.07.
- $181,221.15
- 0.6959
- 69.59% of the variation in salary can be explained by the regression model based on age, years of college, and years with the company.
- 45.24522.
- On average, salary differs by $45,255.22 from the regression model based on age, years of college, and years with the company.
- p-value=0.0000002; reject the null hypothesis.
- p-value=0.2373; do not reject the null hypothesis.
- p-value=0.0097; reject the null hypothesis.
- p-value=0.0005; reject the null hypothesis.