Test Index

Correlation and Regression

Question : 86 of 156

Marks: +1, -0

r, bxy, byx all have _________ sign

Solution:

Concept:

The correlation coefficient

r

and the regression coefficients

b_{xy}

and

b_{yx}

always share the same algebraic sign.

Explanation:

b_{yx} = r \cdot \frac{\sigma_y}{\sigma_x}

and

b_{xy} = r \cdot \frac{\sigma_x}{\sigma_y}

Since standard deviations

\sigma_x

and

\sigma_y

are positive, the sign of each regression coefficient equals the sign of

r

Thus all three have identical signs.

Answer:

Same

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