Prove that correlation coefficient is the geometric mean of regression coefficient

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journal article

Query: The Geometric Mean Functional Relationship

Biometrics

Vol. 36, No. 3 (Sep., 1980)

, pp. 547-550 (4 pages)

Published By: International Biometric Society

https://doi.org/10.2307/2530224

https://www.jstor.org/stable/2530224

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Journal Information

Biometrics is a scientific journal emphasizing the role of statistics and mathematics in the biological sciences. Its object is to promote and extend the use of mathematical and statistical methods in pure and applied biological sciences by describing developments in these methods and their applications in a form readily assimilable by experimental scientists. JSTOR provides a digital archive of the print version of Biometrics. The electronic version of Biometrics is available at http://www.blackwell-synergy.com/servlet/useragent?func=showIssues&code;=biom. Authorized users may be able to access the full text articles at this site.

Publisher Information

The International Biometric Society is an international society for the advancement of biological science through the development of quantitative theories and the application, development and dissemination of effective mathematical and statistical techniques. The Society welcomes as members biologists, mathematicians, statisticians, and others interested in applying similar techniques.

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Prove that correlation coefficient is the geometric mean of regression coefficient

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If one of the two regression coefficients is negative, then the variables are negatively correlated.

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If both the coefficient of regression is positive, then the coefficient of correlation is positive or negative?

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If the two coefficients of regression are negative, what will be the sign of the value of coefficient of correlation?

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Mean of x= 53 <br> Mean of y = 28 <br> Regression coefficient of y on x = - 1.2 <br> Regression coefficient of x on y= - 0.3 <br> `r = square`

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If the sign of the correlation coefficient is negative, then the sign of the slope of the respective regression line is _____

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सहसम्बन्ध गुणांक समाश्रयण गुणांकों का ....... होता है।

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Prove that correlation coefficient is the geometric mean of regression coefficient

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What is the correlation coefficient is the geometric mean between the regression coefficient?

Answer: The correlation coefficient is the Geometric Mean between the Regression Coefficients i.e., r2= bxy byx b. The sign to be taken before the square root is same as that of regression coefficients.

Is the geometric mean of two regression coefficients *?

The geometric mean between the two regression coefficients is equal to the coefficient of correlation, r = .

What is the geometric mean of two regression coefficients BXY and Byx?

Geometric mean between two regression coefficients is equal to coefficient of correlation. r=bxy×byx.

What are the differences between correlation and regression?

Correlation stipulates the degree to which both variables can move together. However, regression specifies the effect of the change in the unit in the known variable(p) on the evaluated variable (q). Correlation helps to constitute the connection between the two variables.