Adjusted R 2
Can help us choose the ‘best’ model
As we add predictors to a model, the R for the model will increase regardless of
whether the added predictor is useful.
Cannot compare useful R ’s if # of predictors is different
R 2adjwas developed to allow such a comparison. It adds a penalty term for each
additional predictor used.
R 2adj 1 – [ n−(k+1) ] [ TSS ]
n = sample size
k is number of predictors
In theory, we choose the model with the highest R 2adj
In practice, we find a group of models with similar R adjand choose the simplest (the one
with the fewest predictors)
Sometimes the change in Y associated with a 1-unit increase in one explanatory variable