A researcher reports the regression coefficients of a bivariate data set as byx=1.6 and bxy=0.9. Is this resul

Exercises · Q11

b_{yx}=1.6

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Step 1 — Apply the product rule. For genuine regression coefficients, $b_{yx}\cdot b_{xy}=r^{2}$ , and since $r$ can range only from $-1$ to $+1$ , $r^{2}$ can be at most $1$ . So a valid pair of coefficients must satisfy $b_{yx}\cdot b_{xy}\le 1$ .

Step 2 — Check the reported values.

b_{yx}\cdot b_{xy}=1.6\times0.9=1.44

Step 3 — Compare. $1.44 > 1$ , so this would require $r^{2}=1.44$ , i.e. $r=\pm1.2$ — a correlation coefficient outside the possible $[-1,1]$ range, which cannot exist. …

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The coefficient of determination equals $r^2$ , the square of the correlation coefficient — option (b).

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Q.A researcher reports the regression coefficients of a bivariate data set as $b_{yx}=1.6$ and $b_{xy}=0.9$ . Is this result possible? Justify your answer with a calculation.

Concept understanding — Relationship between Regression Coefficients and Correlation

Q.A researcher reports the regression coefficients of a bivariate data set as byx=1.6b_{yx}=1.6byx​=1.6 and bxy=0.9b_{xy}=0.9bxy​=0.9. Is this result possible? Justify your answer with a calculation.

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Q.A researcher reports the regression coefficients of a bivariate data set as $b_{yx}=1.6$ and $b_{xy}=0.9$ . Is this result possible? Justify your answer with a calculation.

Unlock everything free for 14 days