Question

1. Evaluate the following regression.

A model of Gross State Product in 1999 for the 50 states.

gsp                               Real Gross State Product (millions of 1996 dollars) in 1999

income                         Personal Income (thousands of dollars) in 1999

employment                Total Nonfarm Employment (thousands of workers)

gsp	Coefficient	Std. Error
_cons	-3077.709	3324.345
income	0.001206	0.0000863
employment	-2.413470	5.881976
R-squared	0.995249
Adjusted R-squared	0.995047
F-statistic	4922.769
Durbin-Watson stat	2.256130
Log likelihood	-550.2366

Correlation Matrix

	GSP	INCOME	EMPLOYMENT
GSP	1.000000
INCOME	0.997613	1.000000
EMPLOYMENT	0.987681	0.990610	1.000000

VIF(b_INCOME) = 53.5 = VIF(b_EMPLOYMENT)

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Answer 1

The following are a few statistics that we can use to evaluate a regression model-

1. R Squared

2. Adjusted R Squared

3. F Statistics

4. RMSE / MSE / MAE

Lets see them one by one.

Our R squared is 0.995249, which is very high (a R squared can take values between 0 and 1). This will usually point towards overfitting of the model. But, we can see that our adjusted R squared (which is supposed to adjust for overfitting) is also very high at 0.995047. This means that overfitting isn't a problem. This leaves us with 2 options- either the model really is that good or there is something else that is causing very high adjusted r squared.

The other reason for extremely high R squared is that there is very high correlation between the variables. So we see the correlation matrix and we see that there is indeed very high correlation between all the variables. This will lead to very high r squared. We can see that the VIF between income and employment is 53.5! This is extremely high and is pointing that these factors are inflated very heavily because of the presence of the other factor.

We can conclude that the model is not a good model due to extremely high correlation between the variables.