Hi,

from what you write, I understand you have two variables: CEA and IP.

Therefore, you must first understand what kind of relationship exists between the two variables, using Gini index and Pearson.

Regards

You generally want to include all of the variables you can, particularly if they could jointly affect CEA and IP. Adding a variable controls to the regression helps to control for it, and you want to control for as many things as possible.

If you use too few independent variables, you could have "omitted variable bias."  If you use too many, with overlapping information, you could have problems with collinearity, and increase variance.  The estimated variance of the prediction error is only designed to detect degree of variance, but bias does impact it, and thus it can be a good measure of accuracy.  

I suggest that you withhold some data when you estimate model parameters, and then compare the performances of your simple versus multiple regressions in predicting the response values that you had, but withheld.  You might also research "cross-validation."  You could just generally research model validation. 

Cheers. 

A relation between two variables is said to SPURIOUS.  There are no two variables in isolation. Each variable is affected by and it affects so many variables. The number of variables brought explicitly into your regression model is determined by:

-  Theory

-  Previous research

-  Logical basis 

Hi colleagues.

There is a difference between univariate vs multivariate and single vs multiple/simultaneous equation models.

Multivariate models (instead of univariate ones) are used to avoid omitted variable bias in estimated coefficients. So, it is strongly recommended to include additional (control) variables / constructs in your equation.

But there is another choice to take into account. Related to endogeneity. If you think that a feedback between CEA and IP is possible, a multiple equation approach (instrumental variables, simultaneous equations) will be necessary. Otherwise, there will be an endogeneity bias in estimated coeficients.

For the first problem (to chose the final specification among many equation alternatives with different control variables), you can try our software GSREG, available for free online.

Hope it helps

In general you should consider including all potentially relevant variables in the model. This will increase the sensitivity of your analysis enabling you to find significant effects.  Omitting an important variable from the model increases the residual variance and reduces the chances of finding a significant correlation for the variables in the model. As noted by J. R. above there are downsides to this approach which must be taken into consideration. In any event the multiple regression approach is the way to go.  We live in a multivariate world.