In previous posts I’ve looked at R squared in linear regression, and argued that I think it is more appropriate to think of it is a measure of explained variation, rather than goodness of fit.
Jonathan Bartlett
Adjusting for baseline covariates in randomized controlled trials
Randomized controlled trials constitute what are generally considered to be the gold standard design for evaluating the effects of some intervention or treatment of interest. The fact that participants are randomized to the two (sometimes more) groups ensures that, at least in expectation, the two treatment groups are balanced in respect of both measured, and importantly, unmeasured factors which may influence the outcome. As a consequence, differences in outcomes between the two groups can be attributed to the effect of being randomized to the treatment rather than the control (which often would be another treatment).
R squared and goodness of fit in linear regression
I’ve been teaching a modelling course recently, and have been reading and thinking about the notion of goodness of fit. R squared, the proportion of variation in the outcome Y, explained by the covariates X, is commonly described as a measure of goodness of fit. This of course seems very reasonable, since R squared measures how close the observed Y values are to the predicted (fitted) values from the model.