Question

 

Regression Statistics
Multiple R	0.878541582
R Square	0.771835311
Adjusted R Square	0.75472296
Standard Error	552.6878046
Observations	44
ANOVA
	df	SS	MS	F
Regression	3	41332908	13777636	45.10399
Residual	40	12218552	305463.8
Total	43	53551461
	Coefficients	Standard Error	t Stat	P-value
Intercept	2095.365223	841.1044	2.491207	0.016979
Income	51.95408819	5.100341	10.1864	0.00
Years of Education	288.9485028	56.13512	5.147375	0.00
Size of Household	207.4655622	121.5576	1.706727	0.095626

1. What is the estimated regression equation using Account Balance as the dependent variable, and Income, Years of Education, as well as Size of Household as the independent variable?

b. Comment on the goodness of fit of the model using the coefficient of determination.

c. Conduct an F test with the critical value approach to see whether the overall model is significant. Use α = 0.01.

d. Perform a t test with p-value approach for the significance of the Income variable. Use α = 0.05.

e. Perform a t test with the p-value approach for the significance of the Size of Household variable. Use α = 0.05.

f. Estimate the Account Balance of a customer who has an income of $62 thousand, 14 years of education, and a household size of 3.

 

Answer 1

a). Regression equation:

b) Coefficient of determination, R² = 0.7718

adjusted R² = 0.7547

Around 75.47% of the variability of Account balance can be explained by the linear relationship.

It is a good fit.

c) Test statistic, F = 45.10399

p-value = F.DIST.RT(45.10399, 3, 40) = 0.00

As p-value = 0 <0.01, we reject the null hypothesis.

The model is significant.

d) T-test for income variable, t = 10.1864

and p-value = 0.00

As p-value = 0 < 0.05, we reject the null hypothesis.

The independent variable income is significant.

e) T-test for Size of Household variable, t =1.706727

and p-value = 0.0956

As p-value = 0.0956 > 0.05, we fail to reject the null hypothesis.

The independent variable income is not significant.

f) Estimated Account Balance of a customer who has an income of $62 thousand, 14 years of education, and a household size of 3.