The two regression equations are 2x + 3y+18 = 0 x + 2y - 25 0 find the value of y if x = 9

hello here we have been given the two lines of regression R this and the variance of X is 12 to find variance of Y and coefficient of correlation to solve this question will first list for write the given things that is being that is equals to minus of half and xy that is equals to minus 3 by 2 from these lines because it can be written as y equals to minus half of X + 5 by 2 and X is equals to minus 3 by 2 X + 8 by to from here we got these so also we can write as we why x.bf why root we will get to be under root 3 by 4 that is equals to my iron mines of fruit that is less than one now

therefore we can write a is equals to minus root 3 by 2 is the both terms hard negative value so I had to be negative so we can now write Sigma X that is equal to under root of which will lead to root 3 also we know device is our times of signal that is minus half will be minus root 3 by 2 Sigma bye-bye 2 root 3 from here we get the value of Y is equals to the value is to show the we got this gets cancelled vs cancelled from here so without oven is equal to four so coefficient of correlation coefficient of correlation

will be minus of root 3 by 2 these are required answer thank you

The given regression equations are
2x + 3y – 6 = 0 and 2x + 2y – 12 = 0

(i) Let 2x + 3y – 6 = 0 be the regression equation of Y on X

∴ The equation becomes 3Y = – 2X + 6

i.e., Y = `(-2)/3 "X" + 6/3`

Comparing it with Y = bYX X + a, we get

`"b"_"YX" = - 2/3`

Now, the other equation, i.e., 2x + 2y – 12 = 0 is the regression equation of X on Y.

∴ The equation becomes 2X = –2Y + 12

i.e., X = `- 2/2 "Y" + 12/2`

Comparing it with X = bXY Y + a' we get

`"b"_"XY" = - 2/2 = - 1`

∴ r = `+-sqrt("b"_"XY" * "b"_"YX")`

`= +- sqrt(-1 * (- 2/3)) = +-sqrt(2/3) = +- 0.82`

since bXY and bYX are negative,

r is also negative.

∴ r = - 0.82

(ii) `"b"_"XY" = "r" sigma_"X"/sigma_"Y"`

∴ `- 1 = - 0.82 xx sigma_"X"/sigma_"Y"`

∴ `sigma_"X"/sigma_"Y" = (- 1)/- 0.82`

∴ `sigma_"X"/sigma_"Y"` = 1.22