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Week #22 – Coefficient of Determination

In regression analysis, the coefficient of determination is a measure of goodness-of-fit (i.e. how well or tightly the data fit the estimated model).  The coefficient is

defined as the ratio of two sums of squares:

r2 = SSR

SST

 ,

where SSR is the sum of squares due to regression, SST is the total sum of squares. By “sum of squares” we mean the sum of squared deviations between actual values and the mean (SST), or between predicted values and the mean (SSR). The coefficient of determination takes on values between 0 and 1, with values closer to 1 implying a better fit.