Lecture 7
732G21/732G28/732A35
Region
Y (Sales)
X1 (Time)
X2 (MktPoten)
X3 (Adver)
X4 (MktShare)
X5 (Change)
X6 (Accts)
X7 (WkLoad)
X8 (Rating)
1
3669.88
43.10
74065.11
4582.88
2.51
0.34
74.86
15.05
4.9
2
3473.95
108.13
58117.30
5539.78
5.51
0.15
107.32
19.97
5.1
3
2295.10
13.82
21118.49
2950.38
10.91
-0.72
96.75
17.34
2.9
4
4675.56
186.18
68521.27
2243.07
8.27
0.17
195.12
13.40
3.4
5
6125.96
161.79
57805.11
7747.08
9.15
0.50
180.44
17.64
4.6
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25
2799.97
21.14
22809.53
3552.00
9.14
-0.74
88.62
24.96
3.9
Y = (SALES) Sales (100:s of units)
X1 = (TIME) Number of months the representative has worked for the company
X2 = (MKTPOTEN) Total sales of the product in the region (both this companies and competitors products).
X3 = (ADVER) Advertising expenditures ($)
X4 = (MKTSHARE) Average of the company’s market share in the territory for the previous four years
X5 = (CHANGE) Change in the company’s market share in the territory over the previous four years
X6 = (ACCTS) Average number of customers (other companies) per month for the previous four years
X7 = (WKLOAD) Average workload per customer (measured as minutes per month)
X8 = (RATING) a rating of the sales representative’s performance made by a sales manager
2
Matrix Plot of Y (Sales), X1 (Time), X2 (MktPoten, X3 (Adver), ...
0
0
20
0
40
0
00
50
0
10
00
-1
0
1
8
16
24
6000
4000
Y (Sales)
2000
400
200
X1 (Time)
0
60000
X2 (MktPoten)
40000
20000
10000
5000
X3 (Adver)
0
12
8
X4 (MktShare)
4
1
0
X5 (Change)
-1
240
160
X6 (Accts)
80
24
16
X7 (WkLoad)
8
6
4
X8 (Rating)
2
20
00
40
00
60
00
20
00
0
40
00
0
0
60
00
4
8
12
80
16
0
0
24
2
4
6
3
Correlations: Y (Sales), X1 (Time), X2 (MktPoten, X3 (Adver), X4 (MktShare, ...
X1
X2
X3
X4
X5
X6
X7
X8
(Time)
(MktPoten)
(Adver)
(MktShare)
(Change)
(Accts)
(WkLoad)
(Rating)
X5
X6
X7
X8
(Change)
(Accts)
(WkLoad)
(Rating)
Y (Sales)
0.623
0.598
0.596
0.484
0.489
0.754
-0.117
0.402
X4 (MktShare)
0.085
0.403
0.349
-0.024
X1 (Time)
X2 (MktPoten)
X3 (Adver)
0.454
0.249
0.106
0.251
0.758
-0.179
0.101
X5 (Change)
0.174
-0.211
0.268
0.479
-0.259
0.359
X6 (Accts)
0.264
0.377
0.200
-0.272
0.411
X7 (WkLoad)
0.327
-0.288
0.549
-0.199
0.229
-0.277
4
Best subsets regression
Best Subsets Regression: Y (Sales) versus X1 (Time), X2 (MktPoten), ...
Response is Y (Sales)
X
1
Vars
1
1
2
2
3
3
4
4
5
5
6
6
7
7
8
R-Sq
56.8
38.8
77.5
74.6
84.9
82.8
90.0
89.6
91.5
91.2
92.0
91.6
92.2
92.0
92.2
R-Sq(adj)
55.0
36.1
75.5
72.3
82.7
80.3
88.1
87.5
89.3
88.9
89.4
88.9
89.0
88.8
88.3
Mallows
Cp
67.6
104.6
27.2
33.1
14.0
18.4
5.4
6.4
4.4
5.0
5.4
6.1
7.0
7.3
9.0
S
881.09
1049.3
650.39
691.11
545.51
582.64
453.84
463.95
430.23
436.75
428.00
438.20
435.67
440.30
449.03
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X
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X
X
X
X
X
X
X
X
X
X
X
X
X X
X
X X
X X
X X
X X
X X
X X
X X
X X
X X
X
X
X
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X
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X
X
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X X
X X
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X X X
5
Regression Analysis: Y (Sales) versus X1 (Time); X2 (MktPoten); ...
The regression equation is
Y (Sales) = - 1165 + 2.27 X1 (Time) + 0.0383 X2 (MktPoten) + 0.141 X3 (Adver)
+ 222 X4 (MktShare) + 285 X5 (Change) + 4.38 X6 (Accts)
Predictor
Constant
X1 (Time)
X2 (MktPoten)
X3 (Adver)
X4 (MktShare)
X5 (Change)
X6 (Accts)
S = 428.004
Coef
-1165.5
2.269
0.038278
0.14067
221.60
285.1
4.378
SE Coef
420.4
1.699
0.007547
0.03839
50.58
160.6
3.999
R-Sq = 92.0%
T
-2.77
1.34
5.07
3.66
4.38
1.78
1.09
P
0.013
0.198
0.000
0.002
0.000
0.093
0.288
VIF
2.849
1.843
1.396
2.028
1.303
4.352
R-Sq(adj) = 89.4%
Analysis of Variance
Source
Regression
Residual Error
Total
Source
X1 (Time)
X2 (MktPoten)
X3 (Adver)
X4 (MktShare)
X5 (Change)
X6 (Accts)
DF
6
18
24
DF
1
1
1
1
1
1
SS
38082180
3297369
41379549
MS
6347030
183187
F
34.65
P
0.000
Seq SS
16056475
5172530
7701445
8144148
788061
219521
6
Regression Analysis: Y (Sales) versus X1 (Time); X2 (MktPoten); ...
The regression equation is
Y (Sales) = - 1114 + 3.61 X1 (Time) + 0.0421 X2 (MktPoten) + 0.129 X3 (Adver)
+ 257 X4 (MktShare) + 325 X5 (Change)
Predictor
Constant
X1 (Time)
X2 (MktPoten)
X3 (Adver)
X4 (MktShare)
X5 (Change)
S = 430.232
Coef
-1113.8
3.612
0.042088
0.12886
256.96
324.5
SE Coef
419.9
1.182
0.006731
0.03704
39.14
157.3
R-Sq = 91.5%
T
-2.65
3.06
6.25
3.48
6.57
2.06
P
0.016
0.006
0.000
0.003
0.000
0.053
VIF
1.364
1.451
1.286
1.202
1.237
R-Sq(adj) = 89.3%
Analysis of Variance
Source
Regression
Residual Error
Total
Source
X1 (Time)
X2 (MktPoten)
X3 (Adver)
X4 (MktShare)
X5 (Change)
DF
5
19
24
DF
1
1
1
1
1
SS
37862659
3516890
41379549
MS
7572532
185099
F
40.91
P
0.000
Seq SS
16056475
5172530
7701445
8144148
788061
7
8
Stepwise regression
Stepwise Regression: Y (Sales) versus X1 (Time), X2 (MktPoten), ...
Alpha-to-Enter: 0.15
Alpha-to-Remove: 0.15
Response is Y (Sales) on 8 predictors, with N = 25
Step
1
2
3
4
Constant
X6 (Accts)
T-Value
P-Value
709.32
50.30
-327.23
-1441.93
-1285.94
21.7
5.50
0.000
19.0
6.41
0.000
15.6
5.19
0.000
9.2
3.22
0.004
8.2
2.92
0.009
0.227
4.50
0.000
0.216
4.77
0.000
0.175
4.74
0.000
0.154
4.09
0.001
0.0219
2.53
0.019
0.0382
4.79
0.000
0.0376
4.90
0.000
190
3.82
0.001
197
4.10
0.001
X3 (Adver)
T-Value
P-Value
X2 (MktPoten)
T-Value
P-Value
X4 (MktShare)
T-Value
P-Value
X5 (Change)
T-Value
P-Value
S
R-Sq
R-Sq(adj)
Mallows Cp
5
263
1.61
0.124
881
56.85
54.97
67.6
650
77.51
75.47
27.2
583
82.77
80.31
18.4
454
90.04
88.05
5.4
437
91.24
88.94
5.0
9
Forward selection
Stepwise Regression: Y (Sales) versus X1 (Time), X2 (MktPoten), ...
Forward selection.
Alpha-to-Enter: 0.25
Response is Y (Sales) on 8 predictors, with N = 25
Step
Constant
X6 (Accts)
T-Value
P-Value
1
2
3
4
5
6
709.32
50.30
-327.23
-1441.93
-1285.94
-1165.48
21.7
5.50
0.000
19.0
6.41
0.000
15.6
5.19
0.000
9.2
3.22
0.004
8.2
2.92
0.009
4.4
1.09
0.288
0.227
4.50
0.000
0.216
4.77
0.000
0.175
4.74
0.000
0.154
4.09
0.001
0.141
3.66
0.002
0.0219
2.53
0.019
0.0382
4.79
0.000
0.0376
4.90
0.000
0.0383
5.07
0.000
190
3.82
0.001
197
4.10
0.001
222
4.38
0.000
263
1.61
0.124
285
1.78
0.093
X3 (Adver)
T-Value
P-Value
X2 (MktPoten)
T-Value
P-Value
X4 (MktShare)
T-Value
P-Value
X5 (Change)
T-Value
P-Value
X1 (Time)
T-Value
P-Value
S
R-Sq
R-Sq(adj)
Mallows Cp
2.3
1.34
0.198
881
56.85
54.97
67.6
650
77.51
75.47
27.2
583
82.77
80.31
18.4
454
90.04
88.05
5.4
437
91.24
88.94
5.0
428
92.03
89.38
5.4
10
Stepwise Regression: Y (Sales) versus X1 (Time), X2 (MktPoten), ...
Backward elimination. Alpha-to-Remove: 0.1
Response is Y (Sales) on 8 predictors, with N = 25
Step
1
2
3
4
Constant
-1508
-1486
-1165
-1114
X1 (Time)
T-Value
P-Value
2.0
1.04
0.313
2.0
1.10
0.287
2.3
1.34
0.198
3.6
3.06
0.006
0.0372
4.54
0.000
0.0373
4.75
0.000
0.0383
5.07
0.000
0.0421
6.25
0.000
X3 (Adver)
T-Value
P-Value
0.151
3.21
0.006
0.152
3.51
0.003
0.141
3.66
0.002
0.129
3.48
0.003
X4 (MktShare)
T-Value
P-Value
199
2.97
0.009
198
3.09
0.007
222
4.38
0.000
257
6.57
0.000
X5 (Change)
T-Value
P-Value
291
1.56
0.139
296
1.80
0.090
285
1.78
0.093
325
2.06
0.053
X6 (Accts)
T-Value
P-Value
5.6
1.16
0.262
5.6
1.23
0.234
4.4
1.09
0.288
X7 (WkLoad)
T-Value
P-Value
20
0.59
0.565
20
0.61
0.550
X8 (Rating)
T-Value
P-Value
8
0.06
0.950
S
R-Sq
R-Sq(adj)
Mallows Cp
449
92.20
88.31
9.0
X2 (MktPoten)
T-Value
P-Value
436
92.20
88.99
7.0
428
92.03
89.38
5.4
Backward elimination
430
91.50
89.26
4.4
11