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If the coefficient of determination is 0.64 and the regression coefficient x on y is 4 then the regression coefficient y on x is?
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If the coefficient of determination is 0.64 and the regression coeffic...
Calculation of Regression Coefficient Y on X
Coefficient of Determination:
Regression Coefficient X on Y:
Calculation of Sy and Sx:
Formula:
Regression Coefficient Y on X:
Formula:
Final Calculation:
Conclusion:
Coefficient of Determination:
- Coefficient of Determination = r^2
- Given that, Coefficient of Determination = 0.64
- Therefore, r^2 = 0.64
- So, r = sqrt(0.64) = 0.8 (since r is positive)
Regression Coefficient X on Y:
- Regression Coefficient X on Y = bxy = r * (Sy / Sx)
- Given that, bxy = 4
Calculation of Sy and Sx:
- Sy = standard deviation of y
- Sx = standard deviation of x
- Using the formula:
Formula:
- Sy = sqrt[(∑y^2 - (∑y)^2/n)/(n-1)]
- Sx = sqrt[(∑x^2 - (∑x)^2/n)/(n-1)]
Regression Coefficient Y on X:
- Regression Coefficient Y on X = byx = r * (Sx / Sy)
- Using the formula:
Formula:
- byx = r * (Sx / Sy)
Final Calculation:
- Sy = sqrt[(∑y^2 - (∑y)^2/n)/(n-1)]
- Sy = sqrt[(∑x^2 - (∑x)^2/n)/(n-1)]
- byx = r * (Sx / Sy)
- byx = 0.8 * (Sx / Sy)
- Given that, bxy = 4
- Therefore, Sy/Sx = 0.2
- So, byx = 0.8 * 0.2 = 0.16
Conclusion:
- The regression coefficient y on x is 0.16.
Community Answer
If the coefficient of determination is 0.64 and the regression coeffic...
If coefficient of determination means r²=0.64 and regression coefficient of X on y is 4 then ... by formula r²=byx×bxy means
0.64=4×byx mean byx=0.64÷4 means byx=0.16
0.64=4×byx mean byx=0.64÷4 means byx=0.16
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If the coefficient of determination is 0.64 and the regression coefficient x on y is 4 then the regression coefficient y on x is?
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If the coefficient of determination is 0.64 and the regression coefficient x on y is 4 then the regression coefficient y on x is? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If the coefficient of determination is 0.64 and the regression coefficient x on y is 4 then the regression coefficient y on x is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the coefficient of determination is 0.64 and the regression coefficient x on y is 4 then the regression coefficient y on x is?.
If the coefficient of determination is 0.64 and the regression coefficient x on y is 4 then the regression coefficient y on x is? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If the coefficient of determination is 0.64 and the regression coefficient x on y is 4 then the regression coefficient y on x is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the coefficient of determination is 0.64 and the regression coefficient x on y is 4 then the regression coefficient y on x is?.
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