According to the Data, is the regression a better fit than the one with the Dummy variable, explain?
Regression Statistics | |||||
Multiple R | 0.550554268 | ||||
R Square | 0.303110002 | ||||
Adjusted R Square | 0.288887757 | ||||
Standard Error | 2.409611727 | ||||
Observations | 51 | ||||
ANOVA | |||||
df | SS | MS | F | Significance F | |
Regression | 1 | 123.7445988 | 123.7445988 | 21.31238807 | 2.8414E-05 |
Residual | 49 | 284.5052051 | 5.806228676 | ||
Total | 50 | 408.2498039 | |||
Coefficients | Standard Error | t Stat | P-value | Lower 95% | |
Intercept | 5.649982553 | 1.521266701 | 3.713998702 | 0.000522686 | 2.592882662 |
U-rate | 1.826625993 | 0.395670412 | 4.616534206 | 2.84144E-05 |
1.0314965 |
Multiple R | 0.572568188 | ||||
R Square | 0.32783433 | ||||
Adjusted R Square | 0.299827427 | ||||
Standard Error | 2.391005294 | ||||
Observations | 51 | ||||
df | SS | MS | F | Significance F | |
Regression | 2 | 133.8383008 | 66.91915042 | 11.70548313 | 7.23489E-05 |
Residual | 48 | 274.4115031 | 5.716906314 | ||
Total | 50 | 408.2498039 | |||
Coefficients | Standard Error | t Stat | P-value | Lower 95% | |
Intercept | 5.544455947 | 1.511607538 | 3.667920281 | 0.000611846 | 2.50516529 |
U-rate | 1.902604044 | 0.396757094 | 4.79538759 | 1.61238E-05 | 1.104870441 |
Western Dummy | -1.3064495 | 0.983213704 | -1.32875436 | 0.190211431 | -3.283333143 |
From the regression output for the model with dummy variable,
P-value for Western dummy = 0.190211 > 0.05, so at 5% level of significance, we can conclude that the dummy variable has no significant effect on the response variable.
Though there is a slight increase in the coefficient of determination value i..e R^{2} for the second model, but it has been seen that there is no significant effect of the dummy variable on the response, so may exclude the dummy variable from the regression model.
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