Posted by: bibas100 December 11, 2007
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Alright Loote,
I guess geico filled some holes in there but here I go.
You know that F-stat can be represented as R2/(k-1)/((1-R2)/(n-k-1)). As you increase independent variables, R2 will go up (even though Adj-R2 might go down if the variable is insignificant).
R2/(1-R2) will always go up with increase in independent variables. But, since we are taking the degrees of freedom into consideration as well, the net effect of an addition of a variable is an increment of F-stat only if the variable is significant.
Again, I am not the expert in this field.
I guess geico filled some holes in there but here I go.
You know that F-stat can be represented as R2/(k-1)/((1-R2)/(n-k-1)). As you increase independent variables, R2 will go up (even though Adj-R2 might go down if the variable is insignificant).
R2/(1-R2) will always go up with increase in independent variables. But, since we are taking the degrees of freedom into consideration as well, the net effect of an addition of a variable is an increment of F-stat only if the variable is significant.
Again, I am not the expert in this field.