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In: Statistics and Probability

A statistical program is recommended. A study investigated the relationship between audit delay (Delay), the length...

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 =

(b)

Did the estimated regression equation developed in part (a) provide a good fit? Explain. (Use α = 0.05. For purposes of this exercise, consider an adjusted coefficient of determination value high if it is at least 50%.)

Yes, testing for significance shows that the overall model is significant and all the individual independent variables are significant.No, the low value of the adjusted coefficient of determination does not indicate a good fit.    Yes, the low p-value and high value of the adjusted coefficient of determination indicate a good fit.No, testing for significance shows that all independent variables except Public are not significant.

(c)

Develop a scatter diagram showing Delay as a function of Finished.

A scatter diagram has 40 points. The horizontal axis ranges from 0 to 5 and is labeled: Finished. The vertical axis ranges from 30 to 100 and is labeled: Delay. All the points fall at either 1, 2, 3, or 4 on the horizontal axis, forming 4 columns of points. Moving from left to right, the top point of the first column of points is located at approximately (1, 94). The top points of all subsequent columns extend downward in a diagonal direction. The bottom points of each column follow this same pattern.

A scatter diagram has 40 points. The horizontal axis ranges from 0 to 5 and is labeled: Finished. The vertical axis ranges from 30 to 100 and is labeled: Delay. All the points fall at either 1, 2, 3, or 4 on the horizontal axis, forming 4 columns of points. Moving from left to right, the top point of the first column of points is located at approximately (1, 92). The top points of the next two columns extend slightly upward in a diagonal direction. The top point of the last column extends downward from the top point of the previous column. Moving from left to right, the bottom point of the first column is located at approximately (1, 54). The bottom point of the next column extends downward. From this point, the bottom two points of the last two columns extend upward in a diagonal direction.

A scatter diagram has 40 points. The horizontal axis ranges from 0 to 5 and is labeled: Finished. The vertical axis ranges from 30 to 100 and is labeled: Delay. All the points fall at either 1, 2, 3, or 4 on the horizontal axis, forming 4 columns of points. Moving from left to right, the top point of the first column of points is located at approximately (1, 94). The top points of the next two columns extend downward in a diagonal direction. The top point of the last column extends upward from the top point of the previous column. The bottom points of each column follow this same pattern.

A scatter diagram has 40 points. The horizontal axis ranges from 0 to 5 and is labeled: Finished. The vertical axis ranges from 30 to 100 and is labeled: Delay. All the points fall at either 1, 2, 3, or 4 on the horizontal axis, forming 4 columns of points. Moving from left to right, the top point of the first column of points is located at approximately (1, 60). The top points of all subsequent columns extend upward in a diagonal direction. The bottom points of each column follow this same pattern.

What does this scatter diagram indicate about the relationship between Delay and Finished?

The scatter diagram suggests no relationship between these two variables.The scatter diagram suggests a linear relationship between these two variables.     The scatter diagram suggests a curvilinear relationship between these two variables.

(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 =

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