Estimate the Model and Add the Income Variable Statistical Questions

Lecture 6 FieldworkConsider the following sample data from our customers. Let X represent Sales (in thousands) and let Y
represent profits (in thousands)
x
y
12
28
23
43
11
21
23
40
14
33
21
41
18
37
16
32
a. Construct a scatterplot and verify that estimating a simple linear regression model is
appropriate in this problem.
b. Calculate b1 and b0. What is the sample regression equation?
c. Find the predicted value for y if x =10, 15 and 20?
30 observations were used to estimate y = βo + β1 x + ε
These are the Excel results:
Coefficients
Standard Error
t-Stat
p-value
Intercept
41.82
8.58
4.87
3.93 e-05
x
0.49
0.10
4.81
4.65e-05
a. What is the estimate for β1? Interpret this value.
b. What is the sample regression equation?
c. If x=30, then what is yhat?
Trust3.sav
Open the Trust data-set in SPSS.
a. Run a multiple regression where expenditure on chicken (q5) is the dependent variable
and the explanatory variables are:
i. Price ( price )
ii. General attitude toward chicken ( q 9)
iii. Perceived risk from chicken consumption (q27d)
b. What is the goodness-of-fit?
c. Estimate the model again and add the income variable ( income ) and the number of
household components (q56). What is the goodness-of-fit now? Which goodness-of-fit
indicator allows comparison between the two models?
d. Estimate the regression equation again with the stepwise method. Which variables are
kept in the model?
e. Interpret the coefficients, relating unitary changes in the explanatory variables to changes
in the dependent variables.
That’s Entertainment is a club marketer of videos. They are testing a new music club
concept. A 25,000 sample of names from the That’s Entertainment database was test
mailed for this brand new music club concept. For those names that joined the new club,
they received 10 free CDs and agreed to purchase 2 more CD’s over the next 12 months.
The test had a response rate of 40% for the initial offer of 10 free CD’s. All customer data
was saved point-in-time of the promotion for future analysis purposes.
That’s Entertainment has decided to roll-out with the new music club concept. They do not
wish to promote all names on their customer database. As such, they have requested the
build of a response model to help them select the names most likely to join the club.
Using the frozen file, you will build a multiple regression response model predicting who is
most likely to join the new music club. You will use Excel for this exercise and base the
analysis on a sub sample of 150 names randomly drawn from the 25,000 sample.
1. Run a multiple regression model using all three variables simultaneously (TSLO,
DOLL_CR, and NM_ORD) as your predictors and using the order indicator (ORDER) as the
dependent variable.
2. Examine the output. Do you see any problems with the coefficients that may be due to
multicollinearity? If so, run a correlation analysis to confirm. What do you notice?
3. If there is a problem with one of the variables being correlated with another, determine
which variable to delete and rerun your model. Explain how you determined which variable
to delete.
4. Once all issues of multicollinearity are taken care of, examine the p-values associated with
your predictor coefficients and comment?
5. What is your final model?
6. How would you run a stepwise regression analysis?
Cust_ID
TSLO
NM_ORD
DOLL_CR
1001
2
3
66
1002
4
1
26
1003
3
2
50
1004
12
3
56
1005
15
4
83
1006
5
9
220
1007
3
6
150
1008
2
7
155
1009
1
2
52
1010
2
2
42
1011
5
1
26
1012
4
2
42
1013
2
1
29
1014
4
3
77
1015
16
1
18
1016
18
2
36
1017
7
3
60
1018
4
7
160
1019
3
10
240
1020
9
2
38
1021
7
2
42
1022
4
1
27
1023
5
2
35
1024
9
4
84
1025
10
2
39
1026
3
4
86
1027
7
2
42
1028
1
1
31
1029
9
2
40
1030
7
2
42
1031
5
5
122
1032
12
3
55
1033
4
2
55
1034
3
3
76
1035
6
3
77
1036
6
6
133
1037
12
3
60
1038
8
3
60
1039
7
4
84
1040
5
1
21
1041
10
2
38
1042
4
5
114
ORDER
1
0
0
1
1
1
1
1
1
1
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1043
10
2
40
1044
7
1
20
1045
6
1
21
1046
5
8
191
1047
7
7
158
1048
4
5
121
1049
2
2
46
1050
5
4
85
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
3
10
240
2
7
155
3
6
150
2
3
66
1
2
52
3
2
50
2
2
46
2
2
42
1
1
31
2
1
29
4
7
160
4
5
121
4
5
114
3
4
86
4
3
77
3
3
76
4
2
42
4
2
55
4
1
27
4
1
26
5
9
220
5
8
191
6
6
133
5
5
122
5
4
85
6
3
77
5
2
35
5
1
26
5
1
21
6
1
21
7
7
158
7
4
84
9
4
84
7
3
60
8
3
60
0
0
0
1
0
1
1
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
9
2
38
7
2
42
7
2
42
7
2
42
7
1
20
15
4
83
12
3
56
12
3
55
12
3
60
10
2
39
10
2
38
18
2
36
9
2
40
10
2
40
16
1
18
3
10
240
2
7
155
3
6
150
2
3
66
1
2
52
3
2
50
2
2
46
2
2
42
1
1
31
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
1
1
2
1
29
0
4
7
160
1
4
5
121
0
4
5
114
3
4
86
4
3
77
3
3
76
4
2
42
4
2
55
4
1
27
4
1
26
5
9
220
5
8
191
6
6
133
5
5
122
5
4
85
6
3
77
5
2
35
5
1
26
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
1146
1147
1148
1149
1150
5
1
21
6
1
21
7
7
158
7
4
84
9
4
84
7
3
60
8
3
60
9
2
38
7
2
42
7
2
42
7
2
42
7
1
20
15
4
83
12
3
56
12
3
55
12
3
60
10
2
39
10
2
38
18
2
36
9
2
40
10
2
40
16
1
18
0
1
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
TSLO: Time spent in between orders. NM_ORD: Number of orders DOLL_CR: Dollars cre
Make the dependent variable Highway MPG for Step 6
Resources for extra credit: https://support.sas.com/resources/papers/proceedings12/333-2
rs/proceedings12/333-2012.pdf, https://stats.idre.ucla.edu/sas/dae/logit-regression/