Question

Consider the two regression lines 3x+2y=26 and 6x+y=31,
(a) Find the mean value and correlation coefficient between x and y.
(b) If the variance of y is 4, find the S.D. of x.​

Answer 1

Answer:

so this question answer is given up

Answer 2

Given: Two regression lines are 3x+2y=26 and 6x+y=31

Required: The mean value and correlation coefficient between x and y.

Solution:

The first step is to check which line is x on y and which one is y on x.

So we start with 3x+2y=26 and 6x+y=31 and solve simultaneously to get x and y. By doing so, we get x= 4 and y=7

Let us assume 3x+2y=26 is y on x so we write it as 2y= 26-3x =

y= 26/2-3x/2 so Byx= -3/2

So, 6x+y= 31 will be the x on y regression line so X= 31/6- Y/6

So Bxy= -1/6

correlation coefficient between x and y= $\sqrt{Bxy*Byx$= $\sqrt{-1/6*-3/2$

= 1/4= 0.25.

a) Mean values are 4 and 7

correlation coefficient between x and y= 0.25

Variance is 4

Variance= square of S.D.= 4*4 =16

B) The s.d. is 16