Question
Download Solution PDFIf the regression coefficient bxy > 1 then byx is :
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFThe product of the regression coefficients of Y on X (byx) and X on Y (bxy) is equal to the ratio of variances of X and Y.
⇒ \( b_{yx} \times b_{xy} = \frac{σ_x²}{σ_y²}\)
Assuming that the variances σx² and σy² are positive (since variance can't be negative), then if bxy > 1, it must be the case that byx < 1.
This is because if bxy > 1, then in order for their product to be a positive number less than or equal to 1 (Since, \(\frac{σ_x²}{σ_y²}\) can't be greater than 1 unless the variance of X is greater than that of Y), byx must be less than 1.
Hence, if bxy > 1, then indeed byx < 1. This property is known as the Magnitude property.
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