Loose Leaf for Statistical Techniques in Business and Economics (Mcgraw-hill/Irwin Series in Operations and Decision Sciences)
Loose Leaf for Statistical Techniques in Business and Economics (Mcgraw-hill/Irwin Series in Operations and Decision Sciences)
16th Edition
ISBN: 9780077639709
Author: Douglas A. Lind, William G Marchal, Samuel A. Wathen
Publisher: McGraw-Hill Education
bartleby

Concept explainers

bartleby

Videos

Question
Book Icon
Chapter 18, Problem 16E

a.

To determine

The given plot of residuals in the order in which the data are presented.

a.

Expert Solution
Check Mark

Answer to Problem 16E

The plot for the ordered residuals is as follows:

Loose Leaf for Statistical Techniques in Business and Economics (Mcgraw-hill/Irwin Series in Operations and Decision Sciences), Chapter 18, Problem 16E , additional homework tip  1

Explanation of Solution

Step-by-step procedure to obtain the regression using EXCEL:

  • Enter the data for Commissions, Calls, and Driven in EXCEL sheet.
  • Go to Data Menu.
  • Click on Data Analysis.
  • Select Regression and click on OK.
  • Select the column of Commissions under Input Y Range.
  • Select the column of Calls and Driven under Input X Range.
  • Click on OK.

Output for the Regression obtained using Excel is as follows:

Loose Leaf for Statistical Techniques in Business and Economics (Mcgraw-hill/Irwin Series in Operations and Decision Sciences), Chapter 18, Problem 16E , additional homework tip  2

From the Excel output, the regression equation is y^=101.32+0.63Calls+0.02Driven. Note that the answer will be different based on round off the decimal places.

Residual:

Formula for residual is Residual=Actual valuePredicted value.

Commissionsy^Residual=yy^
2233.67−11.67
1326.36−13.36
3344.02−11.02
3855.16−17.16
2333.92−10.92
4757.12−10.12
2947.9−18.9
3853.09−15.09
4146.24−5.24
3235.6−3.6
2026.15−6.15
1329.37−16.37
4759.92−12.92
3856.46−18.46
4451.46−7.46
2933.73−4.73
3845.22−7.22
3756.73−19.73
1426.95−12.95
3446.36−12.36
2535.64−10.64
2740.5−13.5
2532.11−7.11
4355.46−12.46
3447.87−13.87

Step-by-step procedure to obtain the plot for Residuals using EXCEL:

  • Enter the data for Residuals in Excel sheet.
  • Select the column of Residuals.
  • Go to Insert Menu.
  • Select line chart.

Thus, the plot for the ordered residuals is obtained.

b.

To determine

Test the autocorrelation at the 0.01 significance level.

b.

Expert Solution
Check Mark

Answer to Problem 16E

There is a positive autocorrelation among the residuals at the 0.01 significance level.

Explanation of Solution

The null and alternative hypotheses are given below:

H0: There is no autocorrelation among the residuals.

H1: There is a positive residual autocorrelation.

Test Statistic:

The Durbin–Watson statistic for testing the hypothesis is as follows:

d=t=2n(etet1)2t=1n(et)2

yy^et=yy^Lagged Residual, et1(etet1)2et2
2233.67–11.67  136.189
1326.36–13.36–11.672.8561178.49
3344.02–11.02–13.365.4756121.44
3855.16–17.16–11.0237.6996294.466
2333.92–10.92–17.1638.9376119.246
4757.12–10.12–10.920.64102.414
2947.9–18.9–10.1277.0884357.21
3853.09–15.09–18.914.5161227.708
4146.24–5.24–15.0997.022527.4576
3235.6–3.6–5.242.689612.96
2026.15–6.15–3.66.502537.8225
1329.37–16.37–6.15104.448267.977
4759.92–12.92–16.3711.9025166.926
3856.46–18.46–12.9230.6916340.772
4451.46–7.46–18.4612155.6516
2933.73–4.73–7.467.452922.3729
3845.22–7.22–4.736.200152.1284
3756.73–19.73–7.22156.5389.273
1426.95–12.95–19.7345.9684167.703
3446.36–12.36–12.950.3481152.77
2535.64–10.64–12.362.9584113.21
2740.5–13.5–10.648.1796182.25
2532.11–7.11–13.540.832150.5521
4355.46–12.46–7.1128.6225155.252
3447.87–13.87–12.461.9881192.377
    (etet1)2=850.521et2=3,924.62

The test statistic is as follows:

d=t=2n(etet1)2t=1n(et)2=850.5213,924.62=0.22

Thus, the Durbin–Watson statistic is 0.22.

Critical value:

From the given information table, there are two independent variables. That is, k=2.

The level of significance is 0.01 and the sample size is 25.

From Table Appendix B.9C: Critical values for the Durbin–Watson d Statistic (α=.01), for k=2 and n=25, The value of dL is 0.98 and the value of dU is 1.30.

Rejection Rule:

  • If d<dL, then reject the null hypothesis.
  • If d>dU, then do not reject the null hypothesis.
  • If dL<d<dU, provide inconclusive results.

Conclusion:

The value of d is 0.22 that is less than 0.98.

That is, d(=0.22)<dL(=0.98).

From the rejection rule, reject the null hypothesis.

It can be concluded that there is a positive autocorrelation among the residuals.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
Calculate the 90% confidence interval for the population mean difference using the data in the attached image. I need to see where I went wrong.
Microsoft Excel snapshot for random sampling: Also note the formula used for the last column 02 x✓ fx =INDEX(5852:58551, RANK(C2, $C$2:$C$51)) A B 1 No. States 2 1 ALABAMA Rand No. 0.925957526 3 2 ALASKA 0.372999976 4 3 ARIZONA 0.941323044 5 4 ARKANSAS 0.071266381 Random Sample CALIFORNIA NORTH CAROLINA ARKANSAS WASHINGTON G7 Microsoft Excel snapshot for systematic sampling: xfx INDEX(SD52:50551, F7) A B E F G 1 No. States Rand No. Random Sample population 50 2 1 ALABAMA 0.5296685 NEW HAMPSHIRE sample 10 3 2 ALASKA 0.4493186 OKLAHOMA k 5 4 3 ARIZONA 0.707914 KANSAS 5 4 ARKANSAS 0.4831379 NORTH DAKOTA 6 5 CALIFORNIA 0.7277162 INDIANA Random Sample Sample Name 7 6 COLORADO 0.5865002 MISSISSIPPI 8 7:ONNECTICU 0.7640596 ILLINOIS 9 8 DELAWARE 0.5783029 MISSOURI 525 10 15 INDIANA MARYLAND COLORADO
Suppose the Internal Revenue Service reported that the mean tax refund for the year 2022 was $3401. Assume the standard deviation is $82.5 and that the amounts refunded follow a normal probability distribution. Solve the following three parts? (For the answer to question 14, 15, and 16, start with making a bell curve. Identify on the bell curve where is mean, X, and area(s) to be determined. 1.What percent of the refunds are more than $3,500? 2. What percent of the refunds are more than $3500 but less than $3579? 3. What percent of the refunds are more than $3325 but less than $3579?

Chapter 18 Solutions

Loose Leaf for Statistical Techniques in Business and Economics (Mcgraw-hill/Irwin Series in Operations and Decision Sciences)

Knowledge Booster
Background pattern image
Statistics
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Text book image
Big Ideas Math A Bridge To Success Algebra 1: Stu...
Algebra
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:Houghton Mifflin Harcourt
Text book image
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Text book image
Functions and Change: A Modeling Approach to Coll...
Algebra
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Cengage Learning
Correlation Vs Regression: Difference Between them with definition & Comparison Chart; Author: Key Differences;https://www.youtube.com/watch?v=Ou2QGSJVd0U;License: Standard YouTube License, CC-BY
Correlation and Regression: Concepts with Illustrative examples; Author: LEARN & APPLY : Lean and Six Sigma;https://www.youtube.com/watch?v=xTpHD5WLuoA;License: Standard YouTube License, CC-BY