# goodness of fit metric

I am trying to approximate the returns of asset A by means of a linear combination of other assets A'=aB0+bB1+c*B2....

I have this quite figured out but I'm not sure what a good metric for goodness of fit would be, so far I am only considering relative error (e=(rA-rA')/rA), and I'm concerned with distortions when rA is close to 0.

What would a better metric could be? Ideally it would penalize sign errors more than absolue value errors (ie, it is worse that rA' is positive when rA is negative).

Please look up goodness of fit measures such as MSE (mean squared error) , R-squared , and adjusted R squared. There are also a number of others measures that have been developed to penalise complex model to avoid overfitting. These include mallow $$C_P$$, AIC, and BIC. This note would be a good start: