Question

Discuss the strength and the significance of your regression model by using R-square and significance F where α = 0.05.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.919011822
R Square	0.844582728
Adjusted R Square	0.834446819
Standard Error	163.953479
Observations	50
ANOVA
	df	SS	MS	F	Significance F
Regression	3	6719578.309	2239859.44	83.3257999	1.28754E-18
Residual	46	1236514.191	26880.7433
Total	49	7956092.5
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	21.7335244	114.2095971	0.19029508	0.84991523	-208.158471	251.62552	-208.15847	251.62552
sqft	0.546807448	0.076647924	7.13401509	5.738E-09	0.392523179	0.70109172	0.39252318	0.70109172
age	-3.075663237	2.263665569	-1.3587092	0.18086435	-7.632185699	1.48085922	-7.6321857	1.48085922
features	40.54881241	15.65468404	2.59020318	0.0128049	9.0375678	72.060057	9.0375678	72.060057

Answer 1

Multiple Regression

From the given output we can see that R Square is 0.844582728 which means approximately 84% of the total variation in the dependent variable can be explained by the set of independent variables. So the model is good enough strong for prediction.

We see that the significance F is 1.28754E-18 which is smaller than alpha 0.05. It indicates that at 95% level of significance the regression coefficients are significant. Thus we can say that the model is fine and we can continue with this set of independent variables.