# 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/