13.8 Exercises

1. A local restaurant advocacy group wants to study the relationship between a restaurant’s average weekly profit, the restaurant’s seating capacity and average daily traffic that passes the restaurant’s location.  The group took a sample of restaurants and recording their average weekly profit (in $1000s), the seating restaurant’s seating capacity, and the average number of cars (in 1000s) that passes the restaurant’s location.  The data is recorded in the following table:

Seating Capacity Traffic Count (1000s) Weekly Net Profit ($1000s)
120 19 23.8
180 8 29.2
150 12 22
180 15 26.2
220 16 33.5
235 10 32
115 18 22.4
110 12 20.4
165 21 23.7
220 20 34.7
140 24 27.1
145 24 23.3
140 13 20.9
200 14 29.6
210 14 31.4
175 12 23.2
175 15 31.1
190 17 28.2
100 23 25.2
145 20 20.7
135 13 37.2
25 13 26.3
140 25 20
130 14 28.2
135 10 24.6
160 23 23.7
  1. Find the regression model to predict the average weekly profit from the other variables.
  2. Interpret the coefficient for seating capacity.
  3. Interpret the coefficient for traffic count.
  4. Predict the average weekly profit for a restaurant with a seating capacity of 150 and a traffic count of 25,000 cars.
  5. Find the adjusted coefficient of determination.
  6. Interpret the adjusted coefficient of determination.
  7. Find the standard error of the estimate.
  8. Interpret the standard error of the estimate.
  9. At the 5% significance level, test the validity of the model.
  10. At the 5% significance level, test the coefficient of seating capacity.
  11. At the 5% significance level, test the coefficient of traffic count.

2. A local university wants to study the relationship between a student’s GPA, the average number of hours they spend studying each night and the average number of nights they go out each week.  The university took a sample of students and recorded the following data:

GPA Average Number of Hours Spent Studying Each Night Average Number of Nights Go Out Each Week
3.72 5 1
3.88 3 1
3.67 2 1
3.87 3 4
2.49 1 4
1.29 1 2
1.01 2 4
2.12 1 1
1.9 1 5
3.42 3 2
1.33 1 4
1.07 0 2
2.75 3 1
3.82 4 1
3.91 5 0
2.25 2 3
2.06 1 5
2.92 3 2
3.06 3 1
3.65 2 2
3.69 4 1
  1. Find the regression model to predict GPA from the other variables.
  2. Interpret the coefficient for the average number of hours spent studying each night.
  3. Interpret the coefficient for the average number of nights a student goes out each week.
  4. Predict the GPA for a student who spends an average of 4 hours a night studying and goes out an average of 3 nights a week.
  5. Find the adjusted coefficient of determination.
  6. Interpret the adjusted coefficient of determination.
  7. Find the standard error of the estimate.
  8. Interpret the standard error of the estimate.
  9. At the 1% significance level, test the validity of the model.
  10. At the 1% significance level, test the coefficient of the average number of hours spent studying each night.
  11. At the 1% significance level, test the coefficient of the average number of nights a student goes out each week.

3. A very large company wants to study the relationship between the salaries of employees in management positions, their age, the number of years the employee spent in college, and the number of years the employee has been with the company.  A sample management employees is taken and the data recorded below:

Age Years of College Years with Company Salary ($1000s)
60 8 29 317.3
33 3 5 97.3
57 6 27 263.1
32 4 5 101.3
31 6 3 114.2
61 8 19 350.4
41 7 8 146.9
35 4 2 91.7
51 6 21 198.2
50 8 10 196.5
57 5 15 105.7
49 6 18 118.3
62 7 27 305.2
52 8 26 239.9
39 4 8 145.9
42 7 5 175.4
62 4 24 219.4
60 4 22 202.1
65 3 21 196.3
40 4 10 143.9
62 6 29 408.7
53 7 5 145.2
48 8 5 175.1
61 5 6 152.7
38 7 3 99.7
40 7 12 174.9
45 7 7 149.2
58 7 14 282.8
38 4 3 95.7
41 5 18 232.8
  1. Find the regression model to predict salary from the other variables.
  2. Interpret the coefficient for age.
  3. Interpret the coefficient for years of college
  4. Interpret the coefficient for years with the company.
  5. Predict the salary for a 47 year old management employee who spent 5 years in college and has been with the company for 15 years.
  6. Find the adjusted coefficient of determination.
  7. Interpret the adjusted coefficient of determination.
  8. Find the standard error of the estimate.
  9. Interpret the standard error of the estimate.
  10. At the 1% significance level, test the validity of the model.
  11. At the 1% significance level, test the coefficient of age.
  12. At the 1% significance level, test the coefficient of the years of college.
  13. At the 1% significance level, test the coefficient for the years with the company.

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Introduction to Statistics Copyright © 2022 by Valerie Watts is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.