A student calculates the regression coefficients from a set of data as $b_{yx} = 2.4$ and $b_{xy} = 0.9$. Comment on the correctness of these values.

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Accepted Answer

**Step 1 — Apply the validity rule.** For any genuine pair of regression coefficients, $b_{yx}\cdot b_{xy} = r^{2}$, and since $-1 \le r \le 1$, it must be true that $b_{yx}\cdot b_{xy} \le 1$.

**Step 2 — Check the given values.**
$$b_{yx}\cdot b_{xy} = 2.4 	imes 0.9 = 2.16$$
This is greater than $1$.

**Step 3 — Conclusion.** Because $r^2$ cannot exceed $1$, no real correlation coefficient corresponds to $r^2 = 2.16$. The given pair of regression coefficients is therefore **not possible** — the student has made a computational error somewhere (commonly, using the wrong denominator while computing one of the two coefficients). …

Q.A student calculates the regression coefficients from a set of data as $b_{yx} = 2.4$ and $b_{xy} = 0.9$ . Comment on the correctness of these values.

Concept understanding — Relationship between Regression Coefficients and Correlation

Q.A student calculates the regression coefficients from a set of data as byx=2.4b_{yx} = 2.4byx​=2.4 and bxy=0.9b_{xy} = 0.9bxy​=0.9. Comment on the correctness of these values.

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Q.A student calculates the regression coefficients from a set of data as $b_{yx} = 2.4$ and $b_{xy} = 0.9$ . Comment on the correctness of these values.

Unlock everything free for 14 days