Question
Download Solution PDFConsider the following statements:
1. Both the regression coefficients have the same sign.
2. If one of the regression coefficients is greater than unity, the other must be less than unity.
Which of the above statements is/are correct?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Properties of Regression Coefficient:
The sign of both the regression coefficients will be the same, i.e. they will be either positive or negative.
It is not possible that one regression coefficient is negative while the other is positive.
The value of the coefficient of correlation cannot exceed unity. Therefore, if one of the regression coefficients is greater than unity, the other must be less than unity.
Hence option 3 is correct.
Note:
The average value of the two regression coefficients will be greater than the value of the correlation.
The regression coefficients are independent of the change of origin, but not of the scale.
The correlation coefficient is the geometric mean of two regression coefficients.
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