Question

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

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.