Explanation
To find the values of x and y, as well as the coefficient of correlation, we can use the given regression equations:
1. Regression equation of X on Y: 10x - 2y = 4
2. Regression equation of Y on X: 2y - 5x = 8
We can solve this system of linear equations to find the values of x and y.
Let's first solve for y in terms of x using the equation (1):
10x - 2y = 4
-2y = 4 - 10x
y = (10x - 4) / 2
y = 5x - 2
Now, substitute this expression for y into the equation (2):
2(5x - 2) - 5x = 8
10x - 4 - 5x = 8
5x - 4 = 8
5x = 8 + 4
5x = 12
x = 12 / 5
x = 2.4
Now that we have found the value of x, we can find the value of y using the equation for y:
y = 5x - 2
y = 5 * 2.4 - 2
y = 12 - 2
y = 10
So, the values of x and y are:
x = 2.4
y = 10
Now, to find the coefficient of correlation (r), we can use the relationship between the regression coefficients:
r = ± √(bxy * byx)
Where bxy is the regression coefficient of X on Y and byx is the regression coefficient of Y on X.
From the given equations:
- Regression equation of X on Y: bxy = 10
- Regression equation of Y on X: byx = 5
Now, calculate the coefficient of correlation:
r = ± √(10 * 5) = ± √50 ≈ ± 7.07 (rounded to two decimal places)
So, the coefficient of correlation (r) is approximately ±7.07, indicating a strong positive linear correlation between X and Y. The positive or negative sign depends on the direction of the correlation.