What is the difference between Rsquare and Adjusted Rsquare?
R-squared is the squared correlation between our predicted Y values and the actual Y values for each case. It gives us a percentage of variation in Y that can be explained by our prediction equation. R-squared can be over-estimated if we throw in too many IV’s, especially if sample size is small. To check to see if our R-squared is inflated, statistical software can compute an adjusted R-square using the formula: Adj.R-square=1-((1-R-sq)(N-1/N-k-1)) You don’t need to remember this formula, only that it takes into account both sample size and the number of IV’s. With a sufficiently large sample size and a sufficiently small number of IV’s, our adjusted R-square and R-square will be nearly equal. But when sample size is small and/or there are a large number of IV’s, the adjusted R-square will be smaller. The difference between adjusted R-square and R-square is called shrinkage: Rsquare – adjusted Rsquare = shrinkage If there is only a small amount of shrinkage (say .00 to.05), then we wo
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