The Coefficient of Determination

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Pearson’s correlation coefficient is given by

Pearson’s correlation coefficient r tells us how good a fit to a straight line a set of data points is. If the data is a perfect fit to a straight line, and ifthere is absolutely no fit that can be made to a straight line.

Almost as useful is the coefficient of determination,The coefficient of determination is the ratio of the explained variation to the total variation, or the proportion of the variance (fluctuation) of one variable that is predicted from variation in the other variable and allows us to gauge the confidence we should have in a prediction made using the regression line. Ifthen the variation of one variable is perfectly explained by variance in the other.

For example, if r = 0.84, thenso that 70.56 % of the total variation in y can be explained by the linear relationship between x and y using the regression equation. The other 29.44 % cannot is unexplained.

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