R sq statistic provides a measure of goodness of fit of the estimated regression model to sample data.
It helps to understand the relevance of chosen explanatory variables in the estimated model.The value of R sq necessarily lies between 0 and 1.
When the value of R sq is close to zero,the explanatory variables have not explained any variation of the dependent variable of the model.Hence, we have a bad fit estimated equation.So basically we have failed to identify the explanatory variables that are relevant to explain variation in the dependent variable.
When value of R sq is high and close to 1, we have a ‘good fit’ estimated equation.The explanatory variables considered in the model are quite relevant.
Now we must be very cautious around possible misuses of R sq.Often in empirical research we come across a situation where the value of R sq is high but very few of the estimated coefficients are statistically significant and/or they have expected signs.We should be more concerned about the logical relevance of the explanatory variables to the dependent variable and also their statistical significance.Even if R sq is low it does not mean that the model is necessarily bad when the estimated coefficients have expected signs and statistical significance.
Another point to note that R sq is a non-decreasing function of the number of explanatory variables in the model.Interestingly, R sq values of 2 models having different number of explanatory variables are not comparable.
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