Figure 7.1 shows four specific examples of r and r 2, each produced by taking two very simple sets of X and Y values, namely We will examine the details of calculation for these two measures in a moment, but first a bit more by way of introducing the general concepts. Both of them together give you the whole works. In effect, 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, r 2, gives you the true strength of the correlation but without an indication its direction. The advantage of the coefficient of determination, r 2, is that it provides an equal interval and ratio scale measure of the strength of the correlation. The advantage of the correlation coefficient, r, is that it can have either a positive or a negative sign and thus provide an indication of the positive or negative direction of the correlation. The coefficient of determination can have only positive values ranging from r 2=+1.0 for a perfect correlation (positive or negative) down to r 2=0.0 for a complete absence of correlation. Values falling between r=0.0 and r=+1.0 represent varying degrees of positive correlation, while those falling between r=0.0 and r= ≱.0 represent varying degrees of negative correlation.Ī closely related companion measure of linear correlation is the coefficient of determination, symbolized as r 2, which is simply the square of the correlation coefficient. The midpoint of its range, r=0.0, corresponds to a complete absence of correlation. The primary measure of linear correlation is the Pearson product-moment correlation coefficient, symbolized by the lower-case Roman letter r, which ranges in value from r=+1.0 for a perfect positive correlation to r= ≱.0 for a perfect negative correlation. Some Basic Statistical Concepts and Methods
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