# Variable analysis in multiple linear regression

I'm investigating how some weather variables (15) affect electricity demand in a specific area during the last 20 years. I was thinking to perform the following steps: 1. Perform Multiple Linear Regression on each subset of selected variables 2. Save t-statistics (p-values) for each run

Then, I would to show the statistics (median, min, max, quantiles) of the t-statistics for each variable in order to give an idea about which is the most influencing. Finally, I would also show the relationship between each variable and the mean square error obtained with regressions using it.

Do you think this approach makes sense?

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No. There are many variable selection techniques including stepwise, forward and backward selection or if you have only a small number comparing all subsets may be feasible. But the model selection criterion should be something like AIC, BIC or Mallow's $C_p$. These are the most common approaches in the literature.

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I'm not looking for the best model but I just want to analyze the influence of single variables. –  Matteo De Felice Jul 16 '12 at 11:25
Ok, so I won't compare t-statistics and I'll calculate AIC or Mallow's CP for each subset and then I'll evaluate which variable leads to better performances. –  Matteo De Felice Jul 16 '12 at 12:06
Adjusted R-square is another measure you can enter into the mix. For each variable the percentage of variance it explains given the other variables in the model would be an intuitive measure of the variable's importance. This would be a partial R-square. –  Michael Chernick Jul 16 '12 at 13:04