[R] Strange R squared, possible error

[derek]

Exuse me, I don't claim R^2 can't be negative. What I say if I get R^2
negative then the data are useless.
I know, that what Thomas said is true in general case. But in my special
case of data, using nonzero intercept is nonsense, and to get R^2 less than
0.985 is considered poor job (standard R^2>0.995). (R^2 given by R^2 = 1 -
Sum(R[i]^2) / Sum((y[i])^2) )

Because lm() uses two differrent formulas for computing R^2,
it is confusing to get R^2 closer to 1 when linear model with zero intercept
y=a*x (a = slope) is used, rather than in case with model y=a*x+b (a=slope,
b= nonzero intercept).

I think R^2 is only measure of good fit for least squares optimization and
it doesn't matter which formula is used: (R^2 = 1 - Sum(R[i]^2) /
Sum((y[i])^2) or R^2 = 1 - Sum(R[i]^2) / Sum((y[i])^2-y*)), but using both
is confusing.

So I would like to know why two different formulas for R^2 are used? 



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