Question

Compare the two regression models. Does it make sense that spending and household debt could each be predicted by annual household income? Why or why not?

1. Predicting spending by household income

Regression Statistics
Multiple R	0.859343186
R Square	0.738470711
Adjusted R Square	0.737149856
Standard Error	1602.157625
Observations	200

ANOVA
	df	SS	MS	F	Significance F
Regression	1	1435121315	1435121315	559.085376	1.42115E-59
Residual	198	508247993.2	2566909.056
Total	199	1943369308

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-1209.21246	444.997983	-2.717343687	0.007164032	-2086.75626	-331.6686596	-2086.75626	-331.6686596
X Variable 1	0.18316543	0.007746481	23.64498628	1.42115E-59	0.167889235	0.198441625	0.167889235	0.198441625

2. Predicting household debt by household income

Regression Statistics
Multiple R	0.001989374
R Square	3.95761E-06
Adjusted R Square	-0.005046527
Standard Error	8605.170404
Observations	200

ANOVA
	df	SS	MS	F	Significance F
Regression	1	58025.4985	58025.4985	0.00078361	0.977695901
Residual	198	14661693620	74048957.68
Total	199	14661751645

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	15668.85874	2390.079111	6.555790838	4.69845E-10	10955.58096	20382.13652	10955.58096	20382.13652
X Variable 1	-0.001164685	0.04160626	-0.027993034	0.977695901	-0.083212957	0.080883586	-0.083212957	0.080883586

Answer 1

1. Predicting spending by household income, using first model,

coefficient of determination R² = 0.7385 = 73.85%

That means 73.85% of variation in spending can be explained by the household income.

But when predicting household debt by household income, using the second model

coefficient of determination R² = 0

That means 0% of variation in household debt can be explained by the household income.

So, household income should not be used to predict household debt.