Statement 1: Two regression coefficients cannot have the same sign. Statement 2: Both the…
Statement 1: Two regression coefficients cannot have the same sign.
Statement 2: Both the regression coefficients can be numerically greater than unity.
Which one of the following is correct?
- aStatement 1 is true and Statement 2 is false.
- bStatement 2 is true and Statement 1 is false.
- cBoth the statements are true.
- dBoth the statements are false.
Answer
Answer
AIWritten by AI (gemini-2.5-pro) - it can contain mistakes.
Correct option: d
Answer: (d) Both the statements are false.
Both regression coefficients $b_{yx}$ and $b_{xy}$ must always have the same sign (the sign of correlation coefficient $r$), so Statement 1 is false. In addition, since $r^2 = b_{yx} \cdot b_{xy} \le 1$, both regression coefficients cannot be numerically greater than unity, so Statement 2 is also false.
From ISC 2026 Mathematics Paper 1, question 19(i).