Which one of the following statements is false?
A. Both correlation and regression coefficients have same sign
B. Arithmetic mean of the regression coefficients is always more than the correlation coefficient
C. Regression coefficients are independent of both the origin and scale
D. Correlation coefficient is the square root of two regression coefficients
Answer: Option B
Solution(By Examveda Team)
Option A:Both correlation and regression coefficients have the same sign is generally true. Both correlation and regression coefficients can be positive or negative, indicating the direction of the relationship between variables.Option B:
Arithmetic mean of the regression coefficients is always more than the correlation coefficient is false. The arithmetic mean of regression coefficients is not necessarily greater than the correlation coefficient.Option C:
Regression coefficients are independent of both the origin and scale is generally true. Regression coefficients are not affected by changes in the origin or scale of the variables.Option D:
Correlation coefficient is the square root of two regression coefficients is generally true. The correlation coefficient is the square root of the product of the two regression coefficients.Therefore, the correct answer is Option B: Arithmetic mean of the regression coefficients is always more than the correlation coefficient.
This Question Belongs to Commerce >> Business Statistics And Research Methods
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A. The central limit theorem
B. The law of statistical regularly
C. The law of inertia of large numbers
D. None of the above
The difference between sample statistic and its corresponding population parameter is
A. Sampling error
B. Measurement error
C. Coverage error
D. Non-response error
A. Both (A) and (R) are true
B. (A) is true, but (R) is false
C. (A) is false, but (R) is true
D. Both (A) and (R) are false
B and C are false
Regression coefficients are independent of origin but not scale scale
Also, the arithmetic means (am) of both regression coefficients are equal to or greater than the coefficient of correlation. (byx + bxy)/2= equal or greater than r. The regression coefficients are independent of the change of the origin. But, they are not independent of the change of the scale