Statistics Dictionary

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Coefficient of Multiple Determination

The coefficient of multiple determination (R2) measures the proportion of variation in the dependent variable that can be predicted from the set of independent variables in a multiple regression equation. When the regression equation fits the data well, R2 will be large (i.e., close to 1); and vice versa.

The coefficient of multiple correlation can be defined in terms of sums of squares:

SSR = Σ ( ŷ - y )2

SSTO = Σ ( y - y )2

R2 = SSR / SSTO

where SSR is the sum of squares due to regression, SSTO is the total sum of squares, ŷ is the predicted value of the dependent variable, y is the dependent variable mean, and y is the dependent variable raw score.

See also:  Analysis in Multiple Regression