13.9 Answers to Select Exercises

1.

1. [latex]\begin{eqnarray*}\hat{y}&=&21.989+0.046x_1-0.196x_2\\x_1&=&\text{seating capacity}\\x_2&=&\text{traffic count (1000s)}\\\hat{y}&=&\text{average weekly profit (\$1000s)}\end{eqnarray*}[/latex]
2. For each additional seat in the restaurant, the average weekly profit increases by $46.
3. For each additional 1000 cars that pass the restaurant, the average weekly profit decreases by $196.
4. $24,519.20
5. 0.2250
6. 22.50% of the variation in the average weekly profit can be explained by the regression model based on seating capacity and traffic count.
7. 4.1675.
8. On average, the average weekly profit differs by $4167.50 from the regression model based on seating capacity and traffic count.
9. p-value=0.0205; reject the null hypothesis.
10. p-value=0.0144; reject the null hypothesis.
11. p-value=0.2645; do not reject the null hypothesis.

2.

1. [latex]\begin{eqnarray*}\hat{y}&=&1.692+0.524x_1-0.082x_2\\x_1&=&\text{average number of hours spent studying a night}\\x_2&=&\text{average number of nights go out each week}\\\hat{y}&=&\text{GPA}\end{eqnarray*}[/latex]
2. For each additional hour spent studying each night, the student’s GPA increases by 0.524.
3. For each additional hour a student goes out each week, the student’s GPA decreases by 0.082.
4. 3.54
5. 0.5833
6. 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.
7. 0.6613.
8. 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.
9. p-value=0.0002; reject the null hypothesis.
10. p-value=0.0009; reject the null hypothesis.
11. p-value=0.5083; do not reject the null hypothesis.

3.

1. [latex]\begin{eqnarray*}\hat{y}&=&-42.359+1.436x_1+14.758x_2+5.486x_3\\x_1&=&\text{age}\\x_2&=&\text{years of college}\\x_3&=&\text{years with the company}\\\hat{y}&=&\text{salary (\$1000s)}\end{eqnarray*}[/latex]
2. For each additional year of age, the salary increases by $1436.14.
3. For each additional year of college, the salary increases by $14,758.04.
4. For each additional year with the company, the salary increases by $5486.07.
5. $181,221.15
6. 0.6959
7. 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.
8. 45.24522.
9. On average, salary differs by $45,255.22 from the regression model based on age, years of college, and years with the company.
10. p-value=0.0000002; reject the null hypothesis.
11. p-value=0.2373; do not reject the null hypothesis.
12. p-value=0.0097; reject the null hypothesis.
13. p-value=0.0005; reject the null hypothesis.