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 R^{2} = 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 R^{2} = 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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