Dear R Users,

I am looking for an alternative to AIC or BIC to choose model parameters. 
This is somewhat of a general statistics question, but I ask it in this 
forum as I am looking for a R solution.

Suppose I have one dependent variable, y, and two independent variables, 
x1 an x2. 

I can perform three regressions: 
reg1: y~x1 
reg2: y~x2 
reg3: y~x1+x2 

The AIC of reg1 is 2000, reg2 is 1000 and reg3 is 950. One would, 
presumably, conclude that one should use both x1 and x2.  However, the 
R^2's are quite different: R^2 of reg1 is 0.5%, reg2 is 95% and reg3 is 
95.25%. Knowing that, I would actually conclude that x1 adds litte and 
should probably not be used.

There is the overall question of what potentially explains this outcome, 
i.e. the reduction in AIC in going from reg2 to reg3 even though R^2 does 
not materially improve 
with the addition of x1 to reg 2 (to get to reg3). But that is more of a 
generic statistics issue and not my question here.

The question I do have is, is there a package in R which implements a test 
and provides some diagnostic information I can use to rule out the use of 
x1 in a systematic way as it's addition to the equation adds little in 
terms of explaining the variability of y.

Thanks in advance,
Tolga

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