Statistical Techniques in Business and Economics
Statistical Techniques in Business and Economics
16th Edition
ISBN: 9780077639723
Author: Lind
Publisher: Mcgraw-Hill Course Content Delivery
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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:

Statistical Techniques in Business and Economics, 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:

Statistical Techniques in Business and Economics, 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.

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Chapter 18 Solutions

Statistical Techniques in Business and Economics

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