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Correlation coefficient r lie between the regression coefficients byx and bxy
- a)true
- b)false
- c)both
- d)none
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Correlation coefficient r lie between the regression coefficients byx ...
Explanation:
Correlation Coefficient (r):
- The correlation coefficient (r) measures the strength and direction of a linear relationship between two variables. It ranges from -1 to 1, where 1 indicates a perfect positive linear relationship, -1 indicates a perfect negative linear relationship, and 0 indicates no linear relationship.
Regression Coefficients (byx and bxy):
- Regression coefficients byx and bxy are the slopes of the regression lines when predicting one variable from another. They represent the change in the dependent variable for a one-unit change in the independent variable.
Relationship between r, byx, and bxy:
- The correlation coefficient (r) is related to the regression coefficients byx and bxy in the following way:
- r = sqrt(|byx * bxy|)
Conclusion:
- Therefore, it is true that the correlation coefficient (r) lies between the regression coefficients byx and bxy. The relationship between these coefficients is determined by the strength and direction of the linear relationship between the variables.
Correlation Coefficient (r):
- The correlation coefficient (r) measures the strength and direction of a linear relationship between two variables. It ranges from -1 to 1, where 1 indicates a perfect positive linear relationship, -1 indicates a perfect negative linear relationship, and 0 indicates no linear relationship.
Regression Coefficients (byx and bxy):
- Regression coefficients byx and bxy are the slopes of the regression lines when predicting one variable from another. They represent the change in the dependent variable for a one-unit change in the independent variable.
Relationship between r, byx, and bxy:
- The correlation coefficient (r) is related to the regression coefficients byx and bxy in the following way:
- r = sqrt(|byx * bxy|)
Conclusion:
- Therefore, it is true that the correlation coefficient (r) lies between the regression coefficients byx and bxy. The relationship between these coefficients is determined by the strength and direction of the linear relationship between the variables.
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Correlation coefficient r lie between the regression coefficients byx and bxya)trueb)falsec)bothd)noneCorrect answer is option 'A'. Can you explain this answer?
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