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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.
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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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