RELATIONSHIP BETWEEN CORRELATION AND REGRESSION COEFFICIENTS

The following points about the regression should be noted:

1) The geometric mean of the two regression coefficients (byx and bxy) gives coefficient of correlation. That is, r = ±√ (bxy) (byx)




Consider the values of regression coefficients from the previous illustration to know the degree of correlation between advertising expenditure and sales.

r = ±√0.093 × 5.801 = 0.734 

2) Both the regression coefficients will always have the same sign (+ or –).

3) Coefficient of correlation will have the same sign as that of regression coefficients. If both are positive, then r is positive. In case both are negative, r is also negative. For example, bxy = –1.3 and byx = –0.65, then r is:

 ±√−1.3x − 0.65 = − 0.919 but not + 0.919

4) Regression coefficients are independent of change of origin, but not of scale.

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