Question

A statistical program is recommended.

A study investigated the relationship between audit delay (Delay), the length of time from a company's fiscal year-end to the date of the auditor's report, and variables that describe the client and the auditor. Some of the independent variables that were included in this study follow.

Industry	A dummy variable coded 1 if the firm was an industrial company or 0 if the firm was a bank, savings and loan, or insurance company.
Public	A dummy variable coded 1 if the company was traded on an organized exchange or over the counter; otherwise coded 0.
Quality	A measure of overall quality of internal controls, as judged by the auditor, on a five-point scale ranging from "virtually none" (1) to "excellent" (5).
Finished	A measure ranging from 1 to 4, as judged by the auditor, where 1 indicates "all work performed subsequent to year-end" and 4 indicates "most work performed prior to year-end."

A sample of 40 companies provided the following data.

Delay	Industry	Public	Quality	Finished
62	0	0	3	1
45	0	1	3	3
54	0	0	2	2
71	0	1	1	2
91	0	0	1	1
62	0	0	4	4
61	0	0	3	2
69	0	1	5	2
80	0	0	1	1
52	0	0	5	3
47	0	0	3	2
65	0	1	2	3
60	0	0	1	3
81	1	0	1	2
73	1	0	2	2
89	1	0	2	1
71	1	0	5	4
76	1	0	2	2
68	1	0	1	2
68	1	0	5	2
86	1	0	2	2
76	1	1	3	1
67	1	0	2	3
57	1	0	4	2
55	1	1	3	2
54	1	0	5	2
69	1	0	3	3
82	1	0	5	1
94	1	0	1	1
74	1	1	5	2
75	1	1	4	3
69	1	0	2	2
71	1	0	4	4
79	1	0	5	2
80	1	0	1	4
91	1	0	4	1
92	1	0	1	4
46	1	1	4	3
72	1	0	5	2
85	1	0	5	1

a) Develop the estimated regression equation using all of the independent variables. Use x₁ for Industry, x₂ for Public, x₃ for Quality, and x₄ for Finished. (Round your numerical values to two decimal places.)

ŷ =  80.43+11.94x1​−4.82x2​−2.62x3​−4.07x4​

D) On the basis of your observations about the relationship between Delay and Finished, use best-subsets regression to develop an alternative estimated regression equation to the one developed in (a) to explain as much of the variability in Delay as possible. Use x₁ for Industry, x₂ for Public, x₃ for Quality, and x₄ for Finished. (Round your numerical values to two decimal places.)

ŷ =  

Answer 1

Comparision between the original model given in a) and the new regression model.

The Original model has 4 independent avriable with  R-Sq = 38.3% and the new model has 3 independent variable and R-Sq = 36.0%. Now, decreasing an independent variable reduces only 2.3% of the variation on response variable explained by the independent variables. Hence, new model is beter than the original model. Also, the Public independent variable does not have the significant effect on the response variable Delay in original model at 0.05 significance level. From these points, the best-subsets regression to develop an alternative estimated regression equation to the one developed in (a) to explain as much of the variability in Delay as possible is

Delay = 79.7 + 12.6 Industry - 2.82 Quality - 4.19 Finished

or

y^== 79.7 + 12.6 x1 - 2.82 x3 - 4.19 x4