Statistics for Business Decisions Assignment
Assignment 1 -
QUESTION 1 - Time Series Regression
The table below presents the number of students attending Statistics lectures in weeks 1 to 10.
|
Week
|
Number of students
|
|
1
|
90
|
|
2
|
82
|
|
3
|
75
|
|
4
|
70
|
|
5
|
59
|
|
6
|
51
|
|
7
|
48
|
|
8
|
40
|
|
9
|
41
|
|
10
|
35
|
Required:
(a) Write down the estimated Linear Trend Regression equation.
(b) Use the estimated equation to forecast the number of students present in week 11.
QUESTION 2 - ANOVA
In early 2015, the economy was experiencing a Global Financial Crisis. But how was the crisis affecting the stock market? Shown are data from a sample of 15 companies. Shown for each company is the price per share of stock on January 1 and April 30.
|
Company
|
January 1 ($)
|
April 30 ($)
|
|
Applied Materials
|
10.13
|
12.21
|
|
Bank of New York
|
28.33
|
25.48
|
|
ChevronTexaco
|
73.97
|
66.10
|
|
Cisco Systems
|
16.30
|
19.32
|
|
Coco Cola
|
45.27
|
43.05
|
|
Comcast
|
16.88
|
15.46
|
|
Ford Motors
|
2.29
|
5.98
|
|
General Electric
|
16.20
|
12.65
|
|
Johnson & Johnson
|
59.83
|
52.36
|
|
JP Morgan Chase
|
31.53
|
33.00
|
|
Microsoft
|
19.44
|
20.26
|
|
Oracle
|
17.73
|
19.34
|
|
Pfiser
|
17.71
|
13.36
|
|
Philip Morris
|
43.51
|
36.18
|
|
Procter & Gamble
|
61.82
|
49.44
|
Required:
a. What is the change in the mean price per share of stock over the four-month period?
b. Provide a 90% confident interval estimate of the change in the mean price per share of stock. Interpret the results.
c. What was the percentage change in the mean price per share of stock over the four- month period?
d. If this same percentage change were to occur for the next four months and again for the four months after that, what would be the mean price per share of stock at the end of the year 2015.
QUESTION 3 - Multiple regression
|
Company
|
Profitability
|
Total Asset
|
D/E
|
Sales
|
ROE
|
M/B
|
|
Atlanta
|
60.60
|
45.40
|
37.00
|
74.00
|
9.90
|
31.30
|
|
Boston
|
59.10
|
46.00
|
36.70
|
77.80
|
7.70
|
31.10
|
|
Brooklyn
|
33.30
|
42.50
|
34.20
|
77.70
|
11.90
|
28.50
|
|
Charlotte
|
10.60
|
41.40
|
29.50
|
74.60
|
10.30
|
28.70
|
|
Chicago
|
75.80
|
45.20
|
37.50
|
72.20
|
13.90
|
32.80
|
|
Cleveland
|
31.80
|
42.20
|
34.60
|
71.60
|
12.70
|
29.50
|
|
Dallas
|
54.50
|
44.30
|
33.90
|
77.10
|
10.10
|
32.70
|
|
Denver
|
57.60
|
47.60
|
33.20
|
73.50
|
11.20
|
31.90
|
|
Detroit
|
37.90
|
43.80
|
34.60
|
75.20
|
11.70
|
28.50
|
|
Golden State
|
34.80
|
45.70
|
38.80
|
77.00
|
9.70
|
29.50
|
|
Houston
|
51.50
|
44.90
|
35.90
|
78.20
|
11.70
|
30.50
|
|
Indiana
|
63.60
|
43.80
|
36.80
|
78.20
|
12.50
|
31.40
|
|
LA Clippers
|
60.60
|
45.50
|
35.70
|
68.00
|
12.10
|
29.40
|
|
LA Lakers
|
62.10
|
45.70
|
32.60
|
75.60
|
12.10
|
34.10
|
|
Memphis
|
62.10
|
44.70
|
32.60
|
75.90
|
12.60
|
29.50
|
|
Miami
|
69.70
|
46.90
|
35.90
|
77.50
|
10.40
|
31.20
|
|
Milwaukee
|
47.00
|
44.30
|
34.50
|
77.40
|
12.40
|
30.00
|
|
Minnesota
|
39.40
|
43.30
|
33.20
|
77.10
|
12.10
|
31.70
|
|
New Orleans
|
31.80
|
45.10
|
33.30
|
75.70
|
11.00
|
30.20
|
|
New York
|
54.50
|
44.30
|
33.60
|
74.10
|
11.30
|
30.50
|
|
Oklahoma City
|
71.20
|
47.10
|
35.80
|
80.60
|
11.00
|
32.70
|
|
Orlando
|
56.10
|
44.10
|
37.50
|
66.00
|
11.20
|
31.20
|
|
Philadelphia
|
53.00
|
44.80
|
36.20
|
74.20
|
10.70
|
32.50
|
|
Phoenix
|
50.00
|
45.80
|
34.30
|
75.70
|
10.90
|
30.80
|
|
Portland
|
42.40
|
44.30
|
34.60
|
79.60
|
11.10
|
29.50
|
|
Sacramento
|
33.30
|
43.60
|
31.60
|
73.60
|
13.40
|
29.50
|
|
San Antonio
|
75.80
|
47.80
|
39.30
|
74.80
|
10.30
|
32.60
|
|
Toronto
|
34.80
|
44.00
|
34.00
|
77.00
|
10.60
|
31.40
|
|
Utah
|
54.50
|
45.60
|
32.30
|
75.40
|
13.00
|
31.10
|
|
Washington
|
30.30
|
44.10
|
32.00
|
72.70
|
11.70
|
29.90
|
|
Regression Statistics
|
|
Multiple R
|
0.8764
|
|
R Square
|
0.7680
|
|
Adjusted R Square
|
0.7197
|
|
Standard Error
|
8.2663
|
|
Observations
|
30
|
ANOVA
|
df
|
SS
|
MS
|
F
|
Significance F
|
|
Regression
|
5
|
5429.4550
|
1085.8910
|
15.8916
|
6.1314E-07
|
|
Residual
|
24
|
1639.9520
|
68.3313
|
|
|
|
Total
|
29
|
7069.407
|
|
|
|
|
Coefficients
|
Standard Error
|
t Stat
|
P-value
|
|
Intercept
|
-407.9703
|
68.9533
|
-5.9166
|
.00041
|
|
TA
|
4.9612
|
1.3676
|
3.6276
|
0.0013
|
|
D/E
|
2.3749
|
0.8074
|
2.9413
|
0.0071
|
|
Sales
|
0.0049
|
0.5182
|
0.0095
|
0.9925
|
|
ROE
|
3.4612
|
1.3462
|
2.5711
|
0.0168
|
|
M/B
|
3.6853
|
1.2965
|
2.8425
|
0.0090
|
|
Profitability
|
Total Asset
|
D/E
|
Sales
|
ROE
|
M/B
|
|
Profitability
|
1.00
|
|
|
|
|
|
|
Total Asset
|
0.73
|
1.00
|
|
|
|
|
|
D/E
|
0.57
|
0.46
|
1.00
|
|
|
|
|
Sales
|
0.00
|
0.11
|
-0.04
|
1.00
|
|
|
|
ROE
|
0.01
|
-0.29
|
-0.29
|
-0.24
|
1.00
|
|
|
M/B
|
0.67
|
0.55
|
0.29
|
0.08
|
-0.10
|
1.00
|
(a) Test the hypothesis that there is no significant relationship between the dependent and all independent variables.
(b) Write down the estimated regression equation.
(c) Interpret individual slope coefficients and at the .05 level of significance, test for a significant relationship.
(d) For the estimated regression equation developed in part (c), remove any independent variables that are not significant at the .05 level of significance and develop a new estimated regression equation using the remaining independent variables.
(e) Interpret the correlation coefficient for each variables. Is there any multicollinearity problem in the data?
(f) Interpret the coefficient of determination? How does this model fit?
(g) Assuming the estimated regression equation developed in part (d) can be used, predict the profitability for a firm with the following values for the four independent variables: TA 45, D/E 35, ROE 12, and M/B 30.
Assignment 2 -
QUESTION 1 - Time series regression
The table below presents the number of student attending the class during the semester.
|
Week
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11
|
12
|
|
Number of students
|
20
|
19
|
19
|
18
|
16
|
17
|
15
|
16
|
14
|
12
|
12
|
10
|
|
Regression Statistics
|
|
Multiple R
|
?
|
|
R Square
|
0.941
|
|
Adjusted R Square
|
0.935
|
|
Standard Error
|
0.811
|
|
Observations
|
12
|
ANOVA
|
df
|
SS
|
MS
|
F
|
Significance F
|
|
Regression
|
1
|
104.08
|
104.08
|
158.12
|
1.87977E-07
|
|
Residual
|
10
|
6.58
|
0.66
|
|
|
|
Total
|
11
|
110.67
|
|
|
|
|
Coefficients
|
Standard Error
|
t Stat
|
P-value
|
Lower 95%
|
Upper 95%
|
|
Intercept
|
21.21
|
0.50
|
?
|
0.00
|
20.10
|
22.32
|
|
Week
|
-0.85
|
0.07
|
?
|
0.00
|
-1.00
|
-0.70
|
a) Write down the estimated regression equation.
b) Interpret the intercept.
c) Interpret the slope coefficient.
d) Interpret the correlation coefficient.
e) How well the model fits the data?
QUESTION 2 - ANOVA
The data in the table below presents attendance rates for 3 subjects over the first 10 weeks of the trimester. Conduct ANOVA for these data.
|
Economics
|
Statistics
|
Accounting
|
|
90
|
98
|
68
|
|
85
|
80
|
98
|
|
75
|
75
|
67
|
|
85
|
65
|
68
|
|
65
|
40
|
58
|
|
98
|
68
|
68
|
|
41
|
98
|
74
|
|
75
|
69
|
81
|
|
80
|
75
|
55
|
|
91
|
80
|
69
|
Anova: Single Factor
|
SUMMARY
|
|
Groups
|
Count
|
Sum
|
Average
|
Variance
|
|
Economics
|
10
|
785
|
78.5
|
263.167
|
|
Statistics
|
10
|
748
|
74.8
|
279.733
|
|
Accounting
|
10
|
706
|
70.6
|
145.378
|
|
ANOVA
|
|
Source of Variation
|
SS
|
df
|
MS
|
F
|
P-value
|
F crit
|
|
Between Groups
|
312.47
|
2
|
?
|
?
|
?
|
3.35
|
|
Within Groups
|
6194.50
|
27
|
?
|
|
|
|
|
Total
|
6506.97
|
29
|
|
|
|
|
a) State the null and alternative hypotheses for single factor ANOVA.
b) State the decision rule.
c) Calculate the test statistics.
d) Make conclusion.
QUESTION 3 - Factor analysis
What is the purpose of factor analysis? Give examples when factor analysis is the best approach to analysis of data.
QUESTION 4 - Multiple regression
The data in the table below presents the
|
Sales revenue $'000
|
Advertising Expenditure, $'000
|
Price of the product, $
|
|
158
|
5
|
24
|
|
258
|
10
|
26
|
|
198
|
6
|
24
|
|
140
|
2
|
25
|
|
269
|
8
|
26
|
|
258
|
6
|
24
|
|
199
|
5
|
25
|
|
202
|
5
|
28
|
|
207
|
5
|
25
|
|
264
|
6
|
24
|
|
Regression Statistics
|
|
Multiple R
|
0.787
|
|
R Square
|
?
|
|
Adjusted R Square
|
0.511
|
|
Standard Error
|
31.857
|
|
Observations
|
10
|
ANOVA
|
df
|
SS
|
MS
|
F
|
Significance F
|
|
Regression
|
2
|
11562.2
|
5781.1
|
?
|
0.03400529
|
|
Residual
|
7
|
7103.9
|
1014.8
|
|
|
|
Total
|
9
|
18666.1
|
|
|
|
|
|
Coefficients
|
Standard Error
|
t Stat
|
P-value
|
Lowe 95%
|
Upper 95
|
|
Intercept
|
170.44
|
207.50
|
?
|
?
|
-320.21
|
661.09
|
|
Advertising Expenditure, $'000
|
17.27
|
5.14
|
?
|
?
|
5.12
|
29.42
|
|
Price of the product, $
|
-2.20
|
8.38
|
?
|
?
|
-22.02
|
17.61
|
a) Test the hypothesis that there is no significant relationship between the dependent and all independent variables.
b) Interpret individual slope coefficients.
c) Test the estimated slope coefficients for individual variables for significance.
d) Construct a 95% confidence interval for the slope coefficients for individual variables.
e) Interpret the correlation coefficient.
f) Calculate and interpret the coefficient of determination.
Note - Attempt all questions. Answer ALL questions in the booklet. Formulas and tables are at the end of the exam and within the paper.
Attachment:- Assignment Files.rar