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Assertion (A): If regression coefficient of X on Y is greater than one, regression coefficient of Y on X must be less than one.
Reason (R): The geometric mean between two regression coefficients is the coefficient of correlation.

Assertion (A): If regression coefficient of X on Y is greater than one, regression coefficient of Y on X must be less than one.
Reason (R): The geometric mean between two regression coefficients is the coefficient of correlation. Correct Answer Both (A) and (R) are true

Related Questions

Which of the following statements relating to correlation and reegression are true?
1. The coefficient of correlation is independent of change of origin and scale
2. The coefficient of correlation between the two variables is the arithmetic average of the two regression coefficients
3. The probable error of the coefficient correlation is 0.6745 times of its standard error
4. Coefficient of correlation multiplied by the ratio between the standard deviations of the two variables denotes the slope of the regression line
Select the correct answer:
Assertion (A): If regression coefficient of X on Y is greater than one, regression coefficient of Y on X must be less than one.
Reason (R): The geometric mean between two regression coefficients is the co-efficient of correlation.
On the basis of the above, choose the appropriate answer :
Which of the following statements is false?  1. When value of correlation coefficient is one, the two regression lines coincide 2. The regression coefficients are independent of the change of origin and of scale 3. The sign of the regression coefficients are always the same 4. The square of the coefficient of correlation is called coefficient of determination 
Which of the following statements are true? a. The correlation coefficient is dependent on the choice of both origin and scale observations. b. The correlation coefficient is dependent on the units of measurements. c. The coefficient of correlation is the square root of the coefficient of determination. d. The zero value of the correlation coefficient cannot estimate the value of the dependent variable.
Which of the following statements are true?
1. The coefficient of rank correlation has the same limits as the Karl Pearson's coefficient of correlation.
2. The coefficient of correlation is independent of the change of origin but not of scale.
3. The covariance between $$X$$ and $$Y$$ is defined as $$\frac{{\sum {xy} }}{n}$$ where, $$x = \left( {X - \overline X } \right),y = \left( {Y - \overline Y } \right)$$      and $$n = $$ no. of paired observations.
4. $${b_{xy}}$$ is called regression coefficient of $$X$$ variable on $$Y$$ variable.
5. If $${b_{xy}}$$ is 0.4 and $${b_{yx}}$$ is 1.6, coefficient of determination would be 0.8.
Select the correct answer:
Consider the following statements: 1. Both the regression coefficients have the same sign. 2. If one of the regression coefficients is greater than unity, the other must be less than unity. Which of the above statements is/are correct?
An assertion and a reason are given below. Assertion: The phenomenon of nuclear fission generates great energy. Reason: The process in which a nucleus is broken into two parts is called nuclear fission. Choose the answer. A. Both Assertion and Reason are true and Reason is the correct explanation of Assertion. B. Both Assertion and Reason are true but Reason is not the correct explanation of Assertion. C. Both Assertion and Reason are false. D. Assertion is true but Reason is false.
From the given table, what is the percentage of students scoring 40 or more, but less than 70. Scores Less than 20 Less than 30 Less than 40 Less than 50 Less than 60 Less than 70 Less than 80 No. of Students 12 19 22 31 38 46 50
Consider the following statements: 1) If the correlation coefficient rxy = 0, then the two lines of regression are parallel to each other. 2) If the correlation coefficient rxy = + 1, then the two lines of regression are perpendicular to each other. Which of the above statements is/are correct?
What is/are true about ridge regression?
1. When lambda is 0, model works like linear regression model
2. When lambda is 0, model doesn't work like linear regression model
3. When lambda goes to infinity, we get very, very small coefficients approaching
04. When lambda goes to infinity, we get very, very large coefficients approaching infinity.