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If the lines of regression in a bivariate distribution are given by x 2y =5 and 2x 3y=8, then the coefficient of correlation is:?
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If the lines of regression in a bivariate distribution are given by x ...
Calculation of Coefficient of Correlation in Bivariate Distribution
Given:
- Lines of regression: x/2 + y/5 = 1 and x/4 + y/8 = 1
To find:
- Coefficient of correlation
Solution:
Let x and y be the two variables in the bivariate distribution. Then,
- Equation of line of regression of x on y: x/2 + y/5 = 1
- Equation of line of regression of y on x: x/4 + y/8 = 1
By comparing the above equations with the general equation of a straight line, y = mx + c, we get:
- Line of regression of x on y: y = (-2/5)x + 2/5
- Line of regression of y on x: y = (-1/2)x + 1
Let the means of x and y be denoted by x̄ and ȳ respectively. Then,
- Slope of line of regression of x on y: bxy = (-2/5)(σx/σy)
- Slope of line of regression of y on x: byx = (-1/2)(σy/σx)
Where σx and σy are the standard deviations of x and y respectively.
Now, the coefficient of correlation (r) can be calculated using the formula:
r = ±√(bxy × byx)
Calculation:
- σx = √5/2, σy = √80/2
- bxy = (-2/5)(√5/2/√80/2) = -1/4
- byx = (-1/2)(√80/2/√5/2) = -2/√5
- r = ±√((-1/4) × (-2/√5)) = ±√(1/10) = ±0.316
Answer:
The coefficient of correlation in the given bivariate distribution is ±0.316.
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If the lines of regression in a bivariate distribution are given by x 2y =5 and 2x 3y=8, then the coefficient of correlation is:?
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If the lines of regression in a bivariate distribution are given by x 2y =5 and 2x 3y=8, then the coefficient of correlation 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 lines of regression in a bivariate distribution are given by x 2y =5 and 2x 3y=8, then the coefficient of correlation is:? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the lines of regression in a bivariate distribution are given by x 2y =5 and 2x 3y=8, then the coefficient of correlation is:?.
If the lines of regression in a bivariate distribution are given by x 2y =5 and 2x 3y=8, then the coefficient of correlation 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 lines of regression in a bivariate distribution are given by x 2y =5 and 2x 3y=8, then the coefficient of correlation is:? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the lines of regression in a bivariate distribution are given by x 2y =5 and 2x 3y=8, then the coefficient of correlation is:?.
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