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The equations given of the two regression lines are 2x + 3y - 6 = 0 and 5x + 7y - 12 = 0.
Find:
(a) Correlation coefficient
(b) `sigma_x/sigma_y`
We assume that 2x + 3y - 6 = 0 to be the line of regression of y on x.
2x + 3y - 6 = 0
⇒ `x = - 3/2y + 3`
⇒ `"bxy" = - 3/2`
5x + 7y - 12 = 0 to be the line of regression of x on y.
5x + 7y - 12 = 0
⇒ `y = - 5/7x + 12/7`
⇒ `"byx" = - 5/7`
Now,
r = `sqrt("bxy.byx") = sqrt(15/14)`
byx = `(rσ_y)/(σ_x) = - 5/7, "bxy" = (rσ_x)/(σ_y) = - 3/2`
⇒ `(σ_x^2)/(σ_y^2) = (3/2)/(5/7)`
⇒ `(σ_x^2)/(σ_y^2) = 21/10`
⇒ `(σ_x)/(σ_y) = sqrt(21/10)`.
Concept: Lines of Regression of X on Y and Y on X Or Equation of Line of Regression
Is there an error in this question or solution?
Answer (Detailed Solution Below)
Option 3 :
Free
10 Qs. 10 Marks 10 Mins
Concept:
The line of regression of y on x is given by: where byx is called the regression coefficient of y on x.
Similarly, the line of regression of x on y is given by: wherebxy is called the regression coefficient of x on y.
The correlation coefficient r2 = byx × bxy
The two lines of regression intersect each other at
Calculation:
Given: Two regression lines are 6x + y = 30 and 3x + 2y = 25.
As we know that, the two lines of regression intersect each other at
By solving these two equations: 6x + y = 30 and 3x + 2y = 25
We get
We can write 6x + y = 30 as line of regression of x on y: ------(1)
By comparing equation (1), with line of regression of x on y which is given by: we get
Similarly, we can write 3x + 2y = 25 as line of regression of y on x: ------(2)
By comparing equation (2), with line of regression of x on y which is given by : we get
As we know that, r2 = byx × bxy
As we know that, sign of
⇒ r = - 0.5Ace your Statistics preparations for Correlation and Regression with us and master Mathematics for your exams. Learn today!
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