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The regression coefficients are zero if r is equal to?
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The regression coefficients are zero if r is equal to?
Regression Coefficients and Correlation Coefficient
Regression analysis is a statistical technique that is used to model the relationship between dependent and independent variables. It helps to determine the strength and direction of the relationship between variables. Whereas, Correlation coefficient measures the strength of the linear relationship between two variables.
Regression Coefficients and Correlation Coefficient Relationship
The regression coefficients are related to the correlation coefficient by the following formula:
r = bxy / (sx * sy)
Where,
- r is the correlation coefficient
- bxy is the regression coefficient
- sx is the standard deviation of the independent variable
- sy is the standard deviation of the dependent variable
Regression Coefficients are zero if r is equal to
When the correlation coefficient is equal to zero, it indicates that there is no linear relationship between the independent and dependent variables. In this case, the regression coefficients will be zero. This means that the independent variable has no effect on the dependent variable and therefore, the regression line will be a horizontal line passing through the mean value of the dependent variable.
It is important to note that even though the regression coefficients are zero when the correlation coefficient is zero, it is possible that there may still be a non-linear relationship between the variables. Therefore, it is important to also examine the scatter plot of the variables to determine the nature of the relationship.
Conclusion
The regression coefficients are related to the correlation coefficient and are zero when there is no linear relationship between the variables. It is important to examine both the correlation coefficient and the scatter plot of the variables to determine the nature of the relationship.
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The regression coefficients are zero if r is equal to?
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The regression coefficients are zero if r is equal to? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The regression coefficients are zero if r is equal to? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The regression coefficients are zero if r is equal to?.
The regression coefficients are zero if r is equal to? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The regression coefficients are zero if r is equal to? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The regression coefficients are zero if r is equal to?.
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