Question

Lowes, a home improvement retailer, has authorized its marketing research department to make a study of customers who have been issued a Lowes charge card. The marketing research department hopes to identify the significant variables that explain the variation in purchases. Once these variables are determined, the department intends to try to attract new customers who would be predicted to make a high volume of purchases. Twenty-five customers were selected at random, and values for the following variables were recorded:

y =        Average monthly purchases (in dollars) at Lowes

x₁ =      Customer age

x₂ =      Customer family income

x₃ =      Family size

Part of the data appear in the Excel worksheet below. A regression model was developed using this sample data. The partial data and Excel regression output are provided below (complete data from all twenty-five customers was used for the analysis). Use this output to answer questions the questions that follow.

Observation	Purchase Volume ($)	Age	Family Income ($)	Family Size
1	75	42	$ 29,000	4
2	129	36	25,000	2
3	105	38	25,000	2
4	42	54	17,000	3
5	17	49	15,000	5
6	?	?	?	?
7	?	?	?	?
8	?	?	?	?
9	?	?	?	?
10	?	?	?	?
11	?	?	?	?
12	?	?	?	?
13	?	?	?	?
14	?	?	?	?
15	?	?	?	?
16	?	?	?	?
17	?	?	?	?
18	?	?	?	?
19	?	?	?	?
20	?	?	?	?
21	105	30	26,000	2
22	121	27	18,250	3
23	14	62	10,250	3
24	37	50	18,100	2
25	43	26	24,500	4

SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error	32.27240363
Observations	25
ANOVA
	df	SS	MS	F
Regression
Residual		21871.66876
Total		38517.76
	Coefficients	Standard Error	t Stat	P-value
Intercept	87.78972947	25.46767899
Age X1	-0.970467501	0.586041665
Family Income X2	0.002334262	0.000745097
Family Size X3	-8.723322293	7.495492501

12.

Required information

           Examine the correlation matrix below.

           

	Purchase Volume ($)	Age	Family Income ($)	Family Size
Purchase Volume ($)	1
Age	-0.41	1
Family Income ($)	0.46	0.05	1
Family Size	-0.24	0.50	0.27

Does there appear to be any problem with multicollinearity in this regression model? Clearly and briefly discuss the criteria you used to arrive at your answer. If multicollinearity is indicated, identify the appropriate variable(s) involved.

Answer 1

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.65739383
R Square	0.432166648
Adjusted R Square	0.351047598
Standard Error	32.27240363
Observations	25
ANOVA
	df	SS	MS	F
Regression	3	16646.09124	5548.69708	5.327560506
Residual	21	21871.66876	1041.508036
Total	24	38517.76
	Coefficients	Standard Error	t Stat	P-value
Intercept	87.78972947	25.46767899	3.44710366	0.002415314
Age X1	-0.9704675	0.586041665	-1.655970145	0.112595788
Family Income X2	0.002334262	0.000745097	3.132829685	0.00502752
Family Size X3	-8.72332229	7.495492501	-1.163809088	0.257554321

Correlation matrix:

The correlation between the variables x1, x2, and x3 has a maximum value of 0.50. Hence, there does not appear to be any problem with multicollinearity in this regression model.