When comparing multiple linear regressions do you put more emphasis on the adjusted R^2 value or the F value? If one regression has a larger R-squared while the other has the larger F value which one would you choose and why?
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Neither.
First you need to determine if the regressions are "nested", ie., whether one is a statistical special case of the other. If so, (which means you can impose statistical restrictions such as zero parameter values in one model to derive the other model), then you can do a standard F test to see if the restrictions are valid. (This isn't the same thing as comparing regression F values.)
If the regressions are non-nested (ie., one is not a special case of the other), then you can resort to "information criterion" tests; there are several different ones available. The ones I remember from school are Akaike and Hannan-Quinn. They're actually pretty simple to compute.
Start Googling away, and good luck!Comment