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 =

(c)  Develop a scatter diagram showing Delay as a function of Finished.

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

(A)

We have the 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

EXCEL-->DATA-->DATA ANALYSIS-->REGRESSION;

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.618518551
R Square	0.382565198
Adjusted R Square	0.312001221
Standard Error	10.92351796
Observations	40
ANOVA
	df	SS	MS	F	Significance F
Regression	4	2587.661436	646.915359	5.421536774	0.001665508
Residual	35	4176.313564	119.3232447
Total	39	6763.975
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	80.42857175	5.91586135	13.59541189	1.57309E-15	68.41873472	92.43840878	68.41873472	92.43840878
X Variable 1	11.94418923	3.797800763	3.145027865	0.003379559	4.234243788	19.65413466	4.234243788	19.65413466
X Variable 2	-4.816257126	4.229181312	-1.138815475	0.262515036	-13.40195164	3.769437385	-13.40195164	3.769437385
X Variable 3	-2.623635035	1.183593557	-2.216668907	0.033238643	-5.026457698	-0.220812372	-5.026457698	-0.220812372
X Variable 4	-4.072510795	1.851430781	-2.199655982	0.034527054	-7.831115103	-0.313906486	-7.831115103	-0.313906486

Y=80.42857175+11.94418923 X1 -4816257126 X2- 2.62365035 X3-4.072510795 X4

R²=0.618518551 hence there is 0.618518551 or 61.85% variability in Y due to x₁ for Industry, x₂ for Public, x₃ for Quality, and x₄ for Finished

(C)

We have:

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

HENCE, Y=-4.3824X+80.226

this means that for 1 unit increase in FINISHED there is 4.3824 units decrease in delay.

R²=0.0993 hence there is 0.0993 or 9.93% variability in DELAY due to FINISHED.

please rate my answer and comment for doubts.