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प्रश्न
The equations of the two lines of regression are 6x + y − 31 = 0 and 3x + 2y – 26 = 0. Identify the regression lines
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उत्तर
Let 3x + 2y – 26 = 0 be the regression equation of Y on X
∴ The equation becomes 2Y = −3X + 26
i.e., Y = `(-3)/2 "X" + 26/2`
Comparing it with Y = bYX X + a, we get
bYX = `(-3)/2`
Now, the other equation 6x + y − 31 = 0 is the regression equation of X on Y.
∴ The equation becomes 6X = − Y + 31
i.e., X = `(-1)/6 "Y" + 31/6`
Comparing it with X = bXY Y+ a', we get
bxy = `(-1)/6`
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संबंधित प्रश्न
Identify the regression equations of X on Y and Y on X from the following equations :
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Find:
- The line of regression of Y on X.
- The line of regression of X on Y.
- Correlation coefficient between X and Y.
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If for bivariate data `bar x = 10, bar y = 12,` v(x) = 9, σy = 4 and r = 0.6 estimate y, when x = 5.
The equation of the line of regression of y on x is y = `2/9` x and x on y is x = `"y"/2 + 7/6`.
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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),
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`bary = square`
∴ byx = `square/square`
∴ bxy = `square/square`
∴ r = `square`
Given variance of x = 9
∴ byx = `square/square`
∴ `sigma_y = square`
For certain bivariate data on 5 pairs of observations given:
∑x = 20, ∑y = 20, ∑x2 = 90, ∑y2 = 90, ∑xy = 76 then bxy = ______.
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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`
∴ regression equation of Y on :
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Estimate y when x = 5
Solution: Line of regression of Y on X is
`"Y" - bary = square ("X" - barx)`
∴ Y − 12 = `r.(σ_y)/(σ_x)("X" - 10)`
∴ Y − 12 = `0.6 xx 4/square ("X" - 10)`
∴ When x = 5
Y − 12 = `square(5 - 10)`
∴ Y − 12 = −4
∴ Y = `square`
