Question

Present the regression output below noting the coefficients, assessing the adequacy of the model and the p-value of the model and the coefficients individually.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.2967345
R Square	0.088051364
Adjusted R Square	0.08408637
Standard Error	11.78856107
Observations	694
ANOVA
	df	SS	MS	F	Significance F
Regression	3	9258.409674	3086.136558	22.2071867	9.78014E-14
Residual	690	95889.41876	138.9701721
Total	693	105147.8284
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	34.16092365	1.25201462	27.28476417	9.3282E-112	31.70270814	36.61913917	31.70270814	36.61913917
Gender	-1.678153204	0.901104822	-1.862328514	0.062981635	-3.447389615	0.091083208	-3.447389615	0.091083208
Degree Type	6.287128629	0.986047771	6.376089285	3.32555E-10	4.351114551	8.223142706	4.351114551	8.223142706
Country	-7.938281572	1.289098801	-6.158008651	1.25044E-09	-10.46930846	-5.407254679	-10.46930846	-5.407254679

Answer 1

First of all we test whether the Regression mode is overall significant or not.

Null hypothesis Ho : Overall regression is not significant

Alternative hypothesis H1 : Overall regression is significant

We consider the Significance F value from ANOVA which is the P-value

P-value for the model = 9.78014E-14

Let, level of significance = 0.05

Since, P-value = 9.78014E-14 < 0.05 , we reject Ho and conclude that Overall regression is significant.

Now, we consider the Adjusted R-square for the model.

Adjusted R-square = 0.08408637

A model is said to be adequate if Adjusted R-square > 0.5

Since, Adjusted R-square is close to 0 , we can say that the Model is not Adequate.

Now, we interpret the significance of coefficients of the independent variables.

Null hypothesis : Variable is not significant

Alternative hypothesis : Variable is significant

Decision rule : If P-value < 0.05 (Level of significance) , then reject null hypothesis and conclude that the coefficient of the variables is significantly different from zero or the variables is significant.

We can see from the table that P-value corresponding to Gender =  0.062981635 > 0.05 , hence, we do not reject null hypothesis and conclude that Gender variable is not significant.

We can see from the table that P-value corresponding to Degree Type =  3.32555E-10 < 0.05 , hence, we reject null hypothesis and conclude that Degree Type variable is significant.

We can see from the table that P-value corresponding to Country=  1.25044E-09 < 0.05 , hence, we reject null hypothesis and conclude that Country variable is significant.