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If the relationship between two variables x and y in given by 2x+3y+4=0 then the value of the correlation coefficient between x and y is?
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If the relationship between two variables x and y in given by 2x+3y+4=...
y = -2/3 x - 4/3 .. (1) which is regression equation of y on x and
x = -3/2 y -2 ...(2) which is regression of x on y. From (1), regression coefficient of y on x i.e. b (yx) = -2/3 & from (2) regression coefficient of x on y i.e. b (xy) = -3/2
We know, b(yx) * b (xy) = r^2 where r is the correlation coefficient of x & y. Hence r^2 = 1 Or, r = +/ - 1
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If the relationship between two variables x and y in given by 2x+3y+4=...
Find the Correlation Coefficient between x and y
1. Given Equation: 2x + 3y + 4 = 0
2. Correlation Coefficient Formula:
The correlation coefficient (r) is calculated using the formula:
r = -2 * (covariance(x, y) / (σx * σy))
3. Convert Given Equation to Slope-Intercept Form:
3y = -2x - 4
y = (-2/3)x - 4/3
4. Calculate Covariance:
Covariance(x, y) = E[(x - μx)(y - μy)]
where E denotes expectation, and μx and μy are the means of x and y, respectively.
5. Calculate Standard Deviations (σx and σy):
σx = sqrt(Var(x))
σy = sqrt(Var(y))
where Var(x) and Var(y) are the variances of x and y, respectively.
6. Substitute Values into the Correlation Coefficient Formula:
r = -2 * (covariance(x, y) / (σx * σy))
7. Interpretation:
- If r is close to 1, it indicates a strong positive correlation.
- If r is close to -1, it indicates a strong negative correlation.
- If r is close to 0, it indicates a weak or no correlation between x and y.
By following these steps and calculations, you can determine the correlation coefficient between variables x and y based on the given equation.
1. Given Equation: 2x + 3y + 4 = 0
2. Correlation Coefficient Formula:
The correlation coefficient (r) is calculated using the formula:
r = -2 * (covariance(x, y) / (σx * σy))
3. Convert Given Equation to Slope-Intercept Form:
3y = -2x - 4
y = (-2/3)x - 4/3
4. Calculate Covariance:
Covariance(x, y) = E[(x - μx)(y - μy)]
where E denotes expectation, and μx and μy are the means of x and y, respectively.
5. Calculate Standard Deviations (σx and σy):
σx = sqrt(Var(x))
σy = sqrt(Var(y))
where Var(x) and Var(y) are the variances of x and y, respectively.
6. Substitute Values into the Correlation Coefficient Formula:
r = -2 * (covariance(x, y) / (σx * σy))
7. Interpretation:
- If r is close to 1, it indicates a strong positive correlation.
- If r is close to -1, it indicates a strong negative correlation.
- If r is close to 0, it indicates a weak or no correlation between x and y.
By following these steps and calculations, you can determine the correlation coefficient between variables x and y based on the given equation.
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If the relationship between two variables x and y in given by 2x+3y+4=0 then the value of the correlation coefficient between x and y is?
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If the relationship between two variables x and y in given by 2x+3y+4=0 then the value of the correlation coefficient between x and y 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 relationship between two variables x and y in given by 2x+3y+4=0 then the value of the correlation coefficient between x and y is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the relationship between two variables x and y in given by 2x+3y+4=0 then the value of the correlation coefficient between x and y is?.
If the relationship between two variables x and y in given by 2x+3y+4=0 then the value of the correlation coefficient between x and y 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 relationship between two variables x and y in given by 2x+3y+4=0 then the value of the correlation coefficient between x and y is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the relationship between two variables x and y in given by 2x+3y+4=0 then the value of the correlation coefficient between x and y is?.
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