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If x and y are two correlated variables with same variance and their correlation coefficient is r, find the regression coefficient of x on (x y) and that of (x y) on x. Hence find the correlation coefficient between x and (x y).?
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If x and y are two correlated variables with same variance and their c...
Regression Coefficients and Correlation Coefficient Between Two Correlated Variables
Given Information:
- x and y are two correlated variables with the same variance.
- The correlation coefficient between x and y is r.
Finding the Regression Coefficients:
Regression Coefficient of x on (x y):
The regression coefficient of x on (x y) is the slope of the line of best fit when x is the independent variable and (x y) is the dependent variable. This can be found using the formula:
bx(x y) = r * (σy / σx)
where:
- bx(x y) is the regression coefficient of x on (x y)
- r is the correlation coefficient between x and y
- σy is the standard deviation of y
- σx is the standard deviation of x
Substituting the Given Values:
Since x and y have the same variance, σx = σy.
Therefore, bx(x y) = r
Regression Coefficient of (x y) on x:
The regression coefficient of (x y) on x is the slope of the line of best fit when (x y) is the independent variable and x is the dependent variable. This can be found using the formula:
b(x y)x = r * (σx / σy)
where:
- b(x y)x is the regression coefficient of (x y) on x
- r is the correlation coefficient between x and y
- σy is the standard deviation of y
- σx is the standard deviation of x
Substituting the Given Values:
Since x and y have the same variance, σx = σy.
Therefore, b(x y)x = r
Calculating the Correlation Coefficient:
The correlation coefficient between x and (x y) is given by:
rx(x y) = √(1 - r2)
Substituting the Given Values:
rx(x y) = √(1 - r2) = √(1 - r2) = √(1 - r2)
Conclusion:
- The regression coefficient of x on (x y
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If x and y are two correlated variables with same variance and their correlation coefficient is r, find the regression coefficient of x on (x y) and that of (x y) on x. Hence find the correlation coefficient between x and (x y).?
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If x and y are two correlated variables with same variance and their correlation coefficient is r, find the regression coefficient of x on (x y) and that of (x y) on x. Hence find the correlation coefficient between x and (x y).? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about If x and y are two correlated variables with same variance and their correlation coefficient is r, find the regression coefficient of x on (x y) and that of (x y) on x. Hence find the correlation coefficient between x and (x y).? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If x and y are two correlated variables with same variance and their correlation coefficient is r, find the regression coefficient of x on (x y) and that of (x y) on x. Hence find the correlation coefficient between x and (x y).?.
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