STATS630 University at Buffalo Week 6 MindTap Regression Analysis Instructions
Assignments must be completed on MindTap AND a completed workbook with your full completed solutions must be submitted via Sakai. You must submit both in order to receive any credit.
Hardcopies or copies emailed will not be graded.
There is no option for late submissions in MindTap. Failure to submit your submit your assignment on MindTap before the due date will result in zero credit.
Submit your worked data in one single MS Excel Workbook. Start your solution set by using the assignment shell provided on Sakai. Use appropriately labeled worksheets for each problem/section of a problem.
Pay very close attention to the final presentation of your work and make sure it is print-ready. Prepare all spreadsheets so that they are clear, attractive and easy for the untrained eye to follow and understand. While accurate content and precise execution of the techniques is critical, formatting, typographical and grammatical acuteness is also very important. General sloppiness and inconsistent formatting will lower your grade.
Note: Ignore MindTap warning about text-based answers. All open ended questions will be graded as well. In fact, your grade will depend equally on the accuracy of your analytical techniques and your interpretation of the results.
Assignment files should be named as follows:
Asg#_FirstInitialLastname
e.g. Assignment 1 for Michael Phelps would be named Asg1_MPhelps.xlsx
Question 1. 40 points
The owner of the Original Italian Pizza restaurant chain would like to predict the sales of his specialty, deep-dish pizza. He has gathered data on the monthly sales of deep-dish pizzas at his restaurants and observations on other potentially relevant variables for each of his 15 outlets.
A.Estimate a multiple regression model between the quantity sold (Y) and the explanatory variables in columns C–E.
Let X1 represent the average price.
Let X2 represent the monthly advertising expenditures.
Let X3 represent the disposable income per household.
B.Is there evidence of any violations of the key assumptions of regression analysis?
C.Which of the variables in this equation have regression coefficients that are statistically different from zero at the 5% significance level?
D.Given your findings in part C, which variables, if any, would you choose to remove from the equation estimated in part A?
Why?
Question 2. 60 points
The data are for 204 employees at the (fictional) company Beta Technologies.
A.Run a forward stepwise regression of Annual Salary versus Gender, Age, Prior Experience, Beta Experience, and Education.
Would you say this equation does a good job of explaining the variation in salaries?
What is the R2 for this regression?
What is the standard error of estimate for this regression?
B.Add a new employee to the end of the data set, a top-level executive. The values of Gender through Annual Salary for this person are, respectively, 0, 56, 10, 15, 6, and $500,000.
Run the regression in Part A again, including this executive.
Are the results much different?
What is the R2 for this regression?
What is the standard error of estimate for this regression?
Is it “fair” to exclude this executive when analyzing the salary structure at this company? 1.
Data File
The owner of the Original Italian Pizza restaurant chain would like to predict the sales of his specialty, deep-dish pizza. He has gathered data on the
monthly sales of deep-dish pizzas at his restaurants and observations on other potentially relevant variables for each of his 15 outlets in central
Indiana. These data are provided in the file P11_02.xlsx.
a. Estimate a multiple regression model between the quantity sold (Y) and the explanatory variables in columns C–E.
Let X1 represent the average price.
Let X2 represent the monthly advertising expenditures.
Let X3 represent the disposable income per household.
If required, round your answers to two decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank.
(Example: -300)
Ŷ = _________________ + _________________ X1 + _________________ X2 + _________________ X3
b. Is there evidence of any violations of the key assumptions of regression analysis?
_________________
c. Which of the variables in this equation have regression coefficients that are statistically different from zero at the 5% significance level?
The p-values for _________________ explanatory variables are well less than 0.05, so they’re all _________________ at the 5% level.
d. Given your findings in part c, which variables, if any, would you choose to remove from the equation estimated in part a?
_________________
Why?
The input in the box below will not be graded, but may be reviewed and considered by your instructor.
_________________
2.
Data File
The file P11_30.xlsx includes data on 204 employees at the (fictional) company Beta Technologies.
a. Run a forward stepwise regression of Annual Salary versus Gender, Age, Prior Experience, Beta Experience, and Education. Would you say this
equation does a good job of explaining the variation in salaries?
_________________
2
What is the R for this regression? If required, round your answer to three decimal places.
_________________
What is the standard error of estimate for this regression? If required, round your answer to a one decimal place.
_________________
b. Add a new employee to the end of the data set, a top-level executive. The values of Gender through Annual Salary for this person are, respectively,
0, 56, 10, 15, 6, and $500,000. Run the regression in part a again, including this executive. Are the results much different?
_________________
What is the R2 for this regression? If required, round your answer to three decimal places.
_________________
What is the standard error of estimate for this regression? If required, round your answer to a one decimal place.
_________________
Is it “fair” to exclude this executive when analyzing the salary structure at this company?
_________________
Outlet Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Quantity Sold
85,300
40,500
61,800
50,800
60,600
79,400
71,400
70,700
55,600
70,900
77,200
63,200
71,100
55,500
42,100
Average Price
$10.14
$10.88
$12.33
$12.70
$12.29
$9.79
$11.26
$11.23
$11.97
$12.07
$10.68
$12.49
$12.36
$9.96
$11.77
Monthly Advertising Expenditures
$64,800
$42,800
$58,600
$46,500
$50,700
$60,100
$55,600
$57,900
$52,100
$60,700
$64,400
$55,600
$60,900
$47,200
$46,100
Disposable Income per Household
$42,100
$38,300
$41,000
$43,300
$44,000
$41,200
$41,700
$43,600
$39,900
$44,800
$41,800
$44,200
$40,100
$39,100
$38,000
Employee Gender
Age
Prior Experience
Beta Experience
Education Annual Salary
1
1
39
5
12
4
57700
2
0
44
12
8
6
76400
3
0
24
0
2
4
44000
4
1
25
2
1
4
41600
5
0
56
5
25
8
163900
6
1
41
9
10
4
72700
7
1
33
6
2
6
60300
8
0
37
11
6
4
63500
9
1
51
12
16
6
131200
10
0
23
0
1
4
39200
11
0
31
5
4
6
62900
12
1
27
0
8
0
26200
13
0
47
11
9
4
74500
14
1
35
5
5
6
64800
15
1
29
5
4
0
21600
16
0
46
4
15
6
81900
17
1
50
10
17
4
115400
18
0
30
3
6
4
57800
19
1
34
10
1
4
55800
20
1
42
11
8
4
76100
21
1
51
10
15
8
135700
22
0
63
16
20
4
140400
23
0
28
0
5
4
55400
24
1
32
4
1
4
49700
25
0
55
11
16
6
134800
26
1
45
20
2
4
76900
27
0
34
2
12
2
28700
28
0
33
2
7
4
58800
29
1
23
0
1
4
43100
30
0
40
4
13
6
82400
31
1
48
6
15
4
80100
32
1
27
0
6
0
27000
33
1
36
5
5
6
58800
34
0
58
9
22
4
133100
35
0
31
1
1
6
53700
36
1
21
0
1
2
26700
37
0
47
5
16
4
81300
38
1
35
3
7
4
55400
39
1
52
12
14
8
139900
40
0
29
3
3
2
33200
41
1
42
11
7
4
75000
42
0
60
10
21
4
128200
43
1
50
8
13
4
76800
44
1
33
1
2
6
54200
45
0
26
0
5
2
32600
46
0
38
6
6
6
59200
47
1
44
7
12
4
74800
48
0
25
0
3
4
45500
49
1
37
8
5
4
46500
50
0
53
13
13
6
136300
51
0
46
7
18
4
86900
52
1
20
0
1
0
23900
53
1
34
5
1
6
52700
54
1
60
12
13
4
92700
55
1
36
6
7
4
59500
56
0
41
6
3
6
69400
57
1
33
3
1
6
46600
58
0
29
3
8
4
61700
59
0
48
11
9
4
88200
60
1
43
0
4
6
45000
61
1
61
10
5
0
52200
62
0
30
5
1
6
61400
63
1
36
5
19
4
87500
64
1
48
7
23
4
103700
65
1
29
5
6
4
54000
66
0
26
11
23
4
125100
67
1
49
5
11
2
45900
68
0
28
10
2
6
79300
69
1
44
20
5
6
108600
70
1
48
0
13
6
68200
71
0
50
0
21
2
65200
72
1
48
12
14
4
95600
73
1
30
16
12
4
103100
74
1
41
20
23
4
143500
75
0
35
11
5
4
78200
76
1
28
3
3
4
40200
77
1
33
8
5
4
60500
78
1
61
0
7
4
40500
79
1
53
10
8
4
73800
80
1
48
4
4
4
45300
81
0
47
9
1
4
61400
82
1
48
4
7
6
64800
83
1
55
11
3
6
75600
84
0
32
1
19
6
95800
85
0
60
11
4
8
126700
86
0
50
10
2
4
67000
87
1
49
16
12
4
102600
88
0
22
4
3
4
52000
89
1
51
9
10
4
76000
90
1
22
0
3
8
83000
91
1
47
8
13
4
80800
92
1
41
10
10
6
91100
93
0
24
3
1
0
30100
94
1
64
5
7
4
55700
95
1
43
0
11
4
51400
96
0
22
3
1
4
43800
97
1
59
0
1
4
25000
98
0
32
10
15
2
80600
99
1
45
8
5
2
39600
100
0
47
0
1
2
13400
101
1
29
6
18
4
88200
102
0
61
9
15
6
109100
103
1
57
3
1
4
34200
104
1
65
4
9
4
57800
105
0
34
6
7
4
68100
106
0
54
6
13
6
94900
107
1
30
5
5
6
63200
108
1
39
6
16
4
82700
109
0
32
7
8
6
85600
110
1
24
2
7
2
27100
111
0
40
10
3
4
69800
112
0
52
13
4
4
81300
113
0
28
11
5
4
78400
114
0
53
20
9
6
127300
115
0
43
0
24
4
93700
116
0
30
5
6
6
74400
117
0
46
3
3
4
48300
118
1
38
10
13
6
98900
119
0
28
0
16
4
73300
120
1
46
11
19
6
117300
121
1
30
5
5
0
37800
122
1
43
6
14
4
77400
123
1
29
11
1
8
111200
124
0
48
11
4
4
75300
125
0
42
7
17
4
96900
126
0
18
10
19
6
123600
127
0
35
6
2
4
55200
128
1
22
0
1
0
12400
129
1
44
4
15
4
73900
130
1
47
20
4
4
94100
131
1
34
10
8
4
74300
132
1
37
11
4
4
66900
133
1
49
0
4
2
12500
134
0
32
0
18
6
90200
135
1
37
5
8
4
59000
136
1
29
10
19
6
114700
137
0
24
7
15
2
71700
138
0
43
20
18
0
125500
139
1
54
11
17
4
100200
140
1
26
0
4
6
45400
141
0
47
10
4
4
72200
142
1
31
5
12
4
69500
143
0
33
11
1
4
67900
144
0
42
2
7
6
67500
145
1
34
2
1
4
31800
146
1
59
0
10
2
27800
147
1
43
5
4
6
60200
148
1
30
2
2
4
34500
149
1
45
7
12
6
87000
150
1
50
0
4
2
12500
151
0
23
0
15
8
122700
152
1
44
5
7
4
56200
153
0
48
10
6
2
56900
154
1
47
4
12
4
66000
155
0
20
11
4
4
76000
156
1
31
0
16
2
44100
157
0
30
0
18
4
78500
158
1
42
5
13
4
71800
159
1
25
9
7
6
80700
160
1
24
2
15
2
47800
161
0
36
13
13
4
105000
162
0
32
6
15
6
100700
163
1
27
2
1
0
18300
164
0
55
12
12
6
110600
165
0
36
0
2
4
36800
166
1
22
0
4
6
45500
167
1
25
0
14
6
71400
168
1
47
5
14
4
74300
169
0
43
16
11
8
160600
170
1
53
0
7
6
52500
171
0
38
5
7
4
65000
172
0
39
12
14
4
104500
173
1
35
5
18
4
85000
174
1
23
3
10
8
110200
175
0
43
10
7
4
80100
176
1
33
3
3
4
40000
177
1
44
10
1
4
55900
178
1
33
0
16
4
64600
179
1
31
0
13
6
68600
180
1
36
7
8
4
65100
181
1
45
13
19
4
111700
182
1
45
12
1
4
62000
183
0
39
2
7
4
55800
184
0
45
5
11
2
54600
185
0
25
1
1
4
37600
186
1
34
0
7
4
41200
187
1
53
0
6
6
49900
188
0
35
4
6
4
59400
189
1
52
3
13
4
65500
190
1
33
10
3
6
73200
191
1
49
0
3
4
30500
192
1
59
6
17
4
84800
193
1
35
16
9
4
95200
194
1
44
11
11
4
84900
195
1
61
11
18
4
102600
196
1
43
11
1
4
59000
197
0
30
0
5
4
44800
198
0
32
11
2
4
70500
199
0
57
10
4
6
83700
200
1
44
10
18
4
100000
201
1
44
2
4
4
39300
202
1
45
0
7
2
20400
203
0
43
0
12
6
74300
204
0
33
11
19
4
114500
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