As per the heading, is it possible to add AIC to some previously computed models based on the stats I have (which include $r^2$, its p-value, $\sigma$ for each variable individually)?
They are all bivariate models, though with some calibration parameters (I know the number of parameters in each model to feed into AIC).
(Footnote)
(If that's not enough I also have bivariate linear regression results (parameters for best fit line, including $F$ statistic, and $\sigma$ and $t$ for the gradient and intercept); though I don't think, for a bivariate model in which I don't care about the means, that fundamentally tells me anything different does it?)
Best Answer
I'm not sure how to exactly get AIC (i.e., which term to add) but you can use the likelihood ratio $\chi^2$ statistic minus twice the degrees of freedom as a substitute in many cases, and $\chi^{2} = - n \times \log(1 - R^{2})$ for a Gaussian model.