I have had this kind of result before. That is R-squared negative and F significant. The results are contradictory. The R-squared implies that the model does not explain any variation in the data. This is an inadequate model. On the other hand, significant F shows that the model is adequate.

It shows that all is not well with the model. Clearly another model should be sought to better explain the variation that is in the data.

Hello Srikanth,

In ordinary least squares (OLS) regression, the total variation of the dependent variable (DV) Y is expressed as a sum of squares: SS(y) or SS(total). Further, it can be separated into two independent quantities, SS(regression) and SS(residual), where SS(regression) is the variation of predicted/estimated scores about the mean of Y and SS(residual) is the variation of observed scores about the predicted/estimated values of Y (e.g., the errors of estimate).

When you use two-stage least squares regression, you can no longer partition the sum of squares (SS) of the dependent variable (DV) Y, into two independent components as in OLS regression. In other words, SS(total) isn't necessarily equal to SS(regression) + SS(residual) because the residuals are not independent of the "instrumental" variable(s). So, any software that estimates R-squared via 1 - [SS(residual) / SS(total)] may yield a negative value in this situation. Further, R-squared really isn't any longer a simple estimate of proportion of variance explained in Y (as is the case for OLS regression).

Negative R-squared values do not occur in OLS regression (unless you specify that the equation goes through the origin, in which case the fit may be worse than simply specifying a horizontal line at y = mean(y)). This last instance is what Safa's links are referring to.

Good luck with your work!

thank you very much Prof. David Morse for your valuable answer.

Dear Srikanth, think this problem is due to the collinearity problem in your model.