Question:
If one regression coefficient is less than unity, then the other will be:
If one regression coefficient is less than unity, then the other will be:
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If one regression coefficient is small (\(<1\)), the other compensates to maintain product \(r^2\).
Updated On: Apr 16, 2026
- less than unity
- equal to unity
- greater than unity
- All of these
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The Correct Option is C
Solution and Explanation
Concept:
\[
b_{xy} \cdot b_{yx} = r^2, \quad 0 \le r^2 \le 1
\]
Also, regression coefficients always have the same sign.
Step 1: Given condition.
Let one regression coefficient be: \[ b_{xy}<1 \]
Step 2: Use relation.
\[ b_{yx} = \frac{r^2}{b_{xy}} \] Since \( r^2 \le 1 \), if \( b_{xy}<1 \), dividing by a number less than 1 increases the value: \[ b_{yx}>r^2 \Rightarrow b_{yx}>1 \; \text{(in general case)} \]
Step 3: Conclusion.
If one regression coefficient is less than unity, the other must be greater than unity.
Step 1: Given condition.
Let one regression coefficient be: \[ b_{xy}<1 \]
Step 2: Use relation.
\[ b_{yx} = \frac{r^2}{b_{xy}} \] Since \( r^2 \le 1 \), if \( b_{xy}<1 \), dividing by a number less than 1 increases the value: \[ b_{yx}>r^2 \Rightarrow b_{yx}>1 \; \text{(in general case)} \]
Step 3: Conclusion.
If one regression coefficient is less than unity, the other must be greater than unity.
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