## The F Statistic

F statistic

Offers evidence if explained variation in Y is significant

Both the coefficient of determination, R2, and corrected coefficient of determination, R2, provide evidence on whether or not the proportion of explained variation is relatively "high" or "low." However, neither tells if the independent variables as a group explain a statistically significant share of variation in the dependent Y variable. The F statistic provides evidence on whether or not a statistically significant proportion of total variation in the dependent variable has been explained. Like R2 , the F statistic is adjusted for degrees of freedom and is defined as

F = Explained Variation/^ - 1) k-1,n-k Unexplained Variation/(n - k)

Once again, n is the number of observations (data points) and k is the number of estimated coefficients (intercept plus the number of slope coefficients). Also like R2, the F statistic can be calculated in terms of the coefficient of determination, where

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