Financial Tutorial

Financial Statistics: Coefficient of determination

COEFFICIENT OF DETERMINATION

Symbolized as r², the coefficient of determination is the square of the correlation coefficient.

The coefficient of determination can have only positive values ranging from r² = +1.0 for a perfect correlation (positive or negative) down to r² = 0.0 for a complete absence of correlation. The advantage of the correlation coefficient, r, is that it  provides you with  the positive or negative direction of the correlation. The advantage of the coefficient of determination, r², is that it provides a measure of the strength of the correlation. The correlation coefficient, r, gives you the true direction of the correlation (+ or  -) but only the square root of the strength of the correlation; while the coefficient of determination, r², gives you the true strength of the correlation but without an indication of its direction. Both of them together give you the whole picture.

We can also say that the coefficient of determination gives you the percentage of the explained variation (by the linear regression) compared to the total variation of the model.

If the coefficient of determination between X and Y is 0.55 (55%), the correlation coefficient is either +0.74 or -0.74, we can say that 55% of the variability in X is explained by a variability in Y.

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