Question

According to the Data, is the regression a better fit than the one with the Dummy...

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

Homework Answers

Answer #1

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 R2 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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