Question

1) Consider the following data for two variables, x and y.

x	9	32	18	15	26
y	10	20	21	17	21

(a) Develop an estimated regression equation for the data of the form

ŷ = b₀ + b₁x.

(Round b₀ to two decimal places and b₁ to three decimal places.)  ŷ =  

2)

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 =

−5.21x4​−1.80x3​+1.65x2​+12.11x1​+78.83

  

(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.

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 =

−38.56x4​−2.28x3​+7.45x2​+14.27x1​+113.01

  

  

Answer 1

1)

x	y	(x-x̅)²	(y-ȳ)²	(x-x̅)(y-ȳ)
9	10	121.0000	60.8400	85.800
32	20	144.0000	4.8400	26.400
18	21	4.0000	10.2400	-6.400
15	17	25.0000	0.6400	4.000
26	21	36.0000	10.2400	19.200

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	100.00	89.00	330.00	86.80	129.00
mean	20.00	17.80	SSxx	SSyy	SSxy

Sample size,   n =   5      
here, x̅ = Σx / n=   20.000          
ȳ = Σy/n =   17.800          
SSxx =    Σ(x-x̅)² =    330.0000      
SSxy=   Σ(x-x̅)(y-ȳ) =   129.0      
              
estimated slope , ß1 = SSxy/SSxx =   129/330=   0.3909      
intercept,ß0 = y̅-ß1* x̄ =   17.8- (0.3909 )*20=   9.9818      
              
Regression line is, Ŷ=   9.98 + (   0.391   )*x