Question

A bank that offers charge cards to customers studies the yearly purchase amount (in thousands of dollars) on the card as related to the age, income (in thousands of dollars), and the and years of education of the cardholder. Using the Excel printout answer the following questions.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.9629
R Square	_ _ _ _
Adjusted R Square	0.9144
Standard Error	0.0871
Observations	21.0000
ANOVA
	df	SS	MS	F
Regression	- - -	- - - - - -	- - - - -	- - - - -
Residual	- - -	0.1290	- - - - -
Total	20	1.7737
	Coefficients	Standard Error	t Stat	P-value
Intercept	-0.8880	0.2604	-3.4108	0.0033
Age	- - -  -	0.0094	3.7191	0.0017
Income	0.0116	0.0156	0.7454	0.4662
Education	0.0075	0.0082	- - - - -	0.3768

1. Fill in the missing values and state the multiple regression equation.
2. Interpret the meaning of the regression coefficient for “Education” in the model.
3. Test to determine if this model is useful in predicting the yearly purchase. Use α = 0.01.

Answer 1

a) R square = 0.9629^2 = 0.927176

df regression= number of independent variable = 3

df residual = 20-3 = 17

SSR = SST-SSE = 1.6447

MSR =SSR/df regression = 0.548233

MSE = SSE/df residual = 0.007588

F = MSR/MSE = 72.2478

Coefficient of age = t*Standard error = 0.03496

T for Education = Coeff/SE = 0.914634

Regression Statistics
Multiple R	0.9629
R Square	0.927176
Adjusted R Square	0.9144
Standard Error	0.0871
Observations	21
ANOVA
	df	SS	MS	F
Regression	3	1.6447	0.548233	72.2478
Residual	17	0.129	0.007588
Total	20	1.7737
	Coefficients	Standard Error	t Stat	P-value
Intercept	-0.888	0.2604	-3.4108	0.0033
Age	0.03496	0.0094	3.7191	0.0017
Income	0.0116	0.0156	0.7454	0.4662
Education	0.0075	0.0082	0.914634	0.3768

Multiple regression equation:

y^ = (-0.8880) + (0.0350)Age + (0.0116)*income + (0.0075)*Education

b)

As the value of education increases by one unit , yearly purchase amount increases by 0.0075 on average keeping age and income constant.

c)

Null and alternative hypothesis:

Ho: β1= β2 = β3 = 0

Ha: at least oneβ ≠ 0

Test statistic:

F = 72.2478

P-value = =F.DIST.RT(72.2478,3,17) = 0.000

As p-value < 0.01, so we reject the null hypothesis.

This model is useful in predicting the yearly purchase at α = 0.01.