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If 4y-5x is the regression line of y on x and the coefficient of correlation between x and y is 0.75 what is the value of the regression coefficient of x on y?
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If 4y-5x is the regression line of y on x and the coefficient of corre...
Understanding Regression Coefficients
To find the regression coefficient of x on y, we start by recognizing the relationship between the regression line and the coefficient of correlation.
Regression Line of y on x
- The given regression line is 4y - 5x = 0.
- This can be rearranged to express y in terms of x: y = (5/4)x.
Coefficient of Correlation
- The coefficient of correlation (r) between x and y is given as 0.75.
- This value indicates a positive relationship between the variables.
Calculating the Regression Coefficient
- The regression coefficient of y on x (denoted as b(y|x)) is the slope of the regression line.
- In this case, b(y|x) = 5/4 = 1.25.
Formula for Regression Coefficient of x on y
- The regression coefficient of x on y (denoted as b(x|y)) can be calculated using the formula:
b(x|y) = r * (sy/sx)
- Here, sy is the standard deviation of y, and sx is the standard deviation of x.
- However, a key relationship exists: b(x|y) = r * (sx/sy).
Using the Relationship
- Since we understand the correlation and the regression coefficients:
- b(x|y) = (r * sx/sy) = (1/r) * b(y|x).
Final Calculation
- Substituting the values:
b(x|y) = (1/0.75) * 1.25 = 1.67.
Conclusion
- Therefore, the regression coefficient of x on y is approximately 1.67. This indicates that for each unit increase in y, x is expected to increase by about 1.67 units.
To find the regression coefficient of x on y, we start by recognizing the relationship between the regression line and the coefficient of correlation.
Regression Line of y on x
- The given regression line is 4y - 5x = 0.
- This can be rearranged to express y in terms of x: y = (5/4)x.
Coefficient of Correlation
- The coefficient of correlation (r) between x and y is given as 0.75.
- This value indicates a positive relationship between the variables.
Calculating the Regression Coefficient
- The regression coefficient of y on x (denoted as b(y|x)) is the slope of the regression line.
- In this case, b(y|x) = 5/4 = 1.25.
Formula for Regression Coefficient of x on y
- The regression coefficient of x on y (denoted as b(x|y)) can be calculated using the formula:
b(x|y) = r * (sy/sx)
- Here, sy is the standard deviation of y, and sx is the standard deviation of x.
- However, a key relationship exists: b(x|y) = r * (sx/sy).
Using the Relationship
- Since we understand the correlation and the regression coefficients:
- b(x|y) = (r * sx/sy) = (1/r) * b(y|x).
Final Calculation
- Substituting the values:
b(x|y) = (1/0.75) * 1.25 = 1.67.
Conclusion
- Therefore, the regression coefficient of x on y is approximately 1.67. This indicates that for each unit increase in y, x is expected to increase by about 1.67 units.
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If 4y-5x is the regression line of y on x and the coefficient of correlation between x and y is 0.75 what is the value of the regression coefficient of x on y?
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If 4y-5x is the regression line of y on x and the coefficient of correlation between x and y is 0.75 what is the value of the regression coefficient of x on y? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If 4y-5x is the regression line of y on x and the coefficient of correlation between x and y is 0.75 what is the value of the regression coefficient of x on y? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 4y-5x is the regression line of y on x and the coefficient of correlation between x and y is 0.75 what is the value of the regression coefficient of x on y?.
If 4y-5x is the regression line of y on x and the coefficient of correlation between x and y is 0.75 what is the value of the regression coefficient of x on y? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If 4y-5x is the regression line of y on x and the coefficient of correlation between x and y is 0.75 what is the value of the regression coefficient of x on y? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 4y-5x is the regression line of y on x and the coefficient of correlation between x and y is 0.75 what is the value of the regression coefficient of x on y?.
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