The Coefficient of Determination

Pearson's correlation coefficient is given by

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

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

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

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