Which of the following statements is not true?
2021
Which of the following statements is not true?
Answer: A. Correlation co-efficient is the arithmetic mean between the regression co-efficients — Option A: The correlation coefficient is the arithmetic mean between the regression coefficients. This statement is false. The correlation coefficient is…
- A.
Correlation co-efficient is the arithmetic mean between the regression co-efficients
- B.
Regression co-efficients are independent of change of origin but not of scale
- C.
If r = 0, then the lines of regression are perpendicular to each other
- D.
Both the regression co-efficient and the correlation co-efficient have the same sign
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Correct answer: A
Option A: The correlation coefficient is the arithmetic mean between the regression coefficients.
This statement is false.
The correlation coefficient is related to the two regression coefficients as:
r² = bₓᵧ × bᵧₓ
Therefore,
r = ±√(bₓᵧ × bᵧₓ)
So, the correlation coefficient is obtained from the geometric mean of the two regression coefficients, not their arithmetic mean.
Hence, Option A is the correct answer.
Option B: Regression coefficients are independent of change of origin but not of scale.
This is true. Regression coefficients do not change when the origin is changed, but they can change when the scale or units of measurement are changed.
Option C: If r = 0, the two lines of regression are perpendicular to each other.
This is true. When the correlation coefficient is zero, there is no linear relationship between the variables, and the two regression lines become perpendicular.
Option D: Both the regression coefficient and the correlation coefficient have the same sign.
This is true. Since the correlation coefficient depends on the product of the two regression coefficients, both regression coefficients have the same sign as the correlation coefficient.
Therefore, the final answer is Option A.