Given information
- Equations of two lines of regression: 4x - 3y + 7 = 0 and 3x - 4y + 8 = 0
- We need to find the correlation coefficient between x and y

Finding slope of regression lines
- Slope of the regression line of x on y is given by b₁ = r * (Sx / Sy)
- Slope of the regression line of y on x is given by b₂ = r * (Sy / Sx)
- Here, Sx and Sy are the standard deviations of x and y respectively
- From the given equations of regression lines, we can write them in the form of y = mx + c
- Comparing the equations with y = mx + c, we get the slopes of the regression lines as follows:
- Slope of regression line of x on y: m₁ = 4/3
- Slope of regression line of y on x: m₂ = 3/4

Finding correlation coefficient
- We know that the correlation coefficient between x and y is given by r = √((SSₓᵧ) / (SSₓ * SSᵧ))
- Here, SSₓᵧ is the covariance between x and y, SSₓ is the variance of x, and SSᵧ is the variance of y
- We need to find these values to calculate r

Finding SSₓᵧ
- SSₓᵧ = Σ((xᵢ - x̄) * (yᵢ - ȳ))
- From the given equations of the regression lines, we can write:
- x̄ = (3/4)y - 2
- ȳ = (4/3)x - 7/3
- Substituting these values, we get:
- SSₓᵧ = Σ((xᵢ - (3/4)y + 2) * (yᵢ - (4/3)x + 7/3))
- Simplifying, we get:
- SSₓᵧ = Σ((4xᵢ - 3yᵢ - 10) / 3)
- SSₓᵧ = (4/3)Σ(xᵢ) - (3/3)Σ(yᵢ) - (10/3)n
- SSₓᵧ = (4/3)(n(̄x)) - (3/3)(n(̄y)) - (10/3)n
- Here, n is the number of observations, and (̄x) and (̄y) are the means of x and y respectively
- Substituting the values, we get:
- SSₓᵧ = (4/3)(-8) - (3/3)(7) - (10/3)5
- SSₓᵧ = -32/3 - 7 - 50/3
- SSₓᵧ = -89/3

Finding SSₓ
- SSₓ = Σ(xᵢ - x̄)²
- Substituting the value