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If the regression equations are 8x – 10y + 66 = 0 and 40x – 18y = 214, the mean value of y is ______

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If the regression equations are 8x – 10y + 66 = 0 and 40x – 18y = 214, the mean value of y is ______

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Chapter 2.3: Linear Regression - Q.3

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The regression equation of x on y is 40x – 18y = 214  ......(i)

The regression equation of y on x is 8x – 10y + 66 = 0  ......(ii)

Solving equations (i) and (ii),

`barx = square`

`bary = square`

∴ byx = `square/square`

∴ bxy = `square/square`

∴ r = `square`

Given variance of x = 9

∴ byx = `square/square`

∴ `sigma_y = square`


Complete the following activity to find, the equation of line of regression of Y on X and X on Y for the following data:

Given:`n=8,sum(x_i-barx)^2=36,sum(y_i-bary)^2=40,sum(x_i-barx)(y_i-bary)=24`

Solution:

Given:`n=8,sum(x_i-barx)=36,sum(y_i-bary)^2=40,sum(x_i-barx)(y_i-bary)=24`

∴ `b_(yx)=(sum(x_i-barx)(y_i-bary))/(sum(x_i-barx)^2)=square`

∴ `b_(xy)=(sum(x_i-barx)(y_i-bary))/(sum(y_i-bary)^2)=square`

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Out of the two regression lines x + 2y – 5 = 0 and 2x + 3y = 8, find the line of regression of y on x.


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