As discussed earlier, when variables are linearly related, we have the regression lines of one variable on another variable and correlation coefficient can be computed to tell us about the extent of association between them. However, if the variables are not linearly related but some sort of curvilinear relationship exists between them, the use of r which is a measure of the degree to which the relation approaches a straight line “law” will be misleading. We might come across bivariate distributions where r may be very low or even zero but the regression may be strong, or even zero but the regression may be strong, or even perfect. Correlation ratio ‘η’ is the appropriate measure of curvilinear relationship between the two variables. Just as r measures the concentration of points about the straight line of best fit, η measures the concentration of points about the curve of best fit. If regression is linear η=r otherwise η > r.
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