Question

Read the following statements and choose the correct option.

1. The correlation coefficient and the regression coefficients are of the same sign.
2. The correlation coefficient is the arithmetic mean between the regression coefficients.
3. The product of two regression coefficients is always equal to 1.
4. Both the regression coefficients cannot be numerically greater than unity.

Options

• Only (IV) is correct.

• Only (I) and (II) are correct.

• Only (I) and (IV) are correct.

• Only (III) and (IV) are correct.

Answer 1

Only (I) and (IV) are correct.

Explanation:

Statement (I) is correct because if the correlation is positive, both regression coefficients are positive. If the correlation is negative, both regression coefficients are negative.

Statement (IV) is correct.

Since, `r^2 = b_(xy) xx b_(yx)`

∴ r² ≥ 1