Question

Compare the two regression models. Does it make sense that spending and household debt could each...

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

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.

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