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प्रश्न
The equations of the two lines of regression are 2x + 3y − 6 = 0 and 5x + 7y − 12 = 0. Identify the regression lines
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उत्तर
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" + 2`
Comparing it with Y = bYX X + a, we get
bYX = `(-2)/3`
Now, the other equation 5x + 7y − 12 = 0 is the regression equation of X on Y.
∴ The equation becomes 5X = − 7Y + 12
i.e., X = `(-7)/5 "Y" + 12/5`
Comparing it with X = bXY Y+ a', we get
bxy = `(-7)/5`
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संबंधित प्रश्न
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Find the equation of the regression line of y on x, if the observations (x, y) are as follows :
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(a) regression coefficients byx and bxy
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From the data of 20 pairs of observations on X and Y, following results are obtained.
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| Y | 10 | 10 | 18 | 20 | 11 | 15 | 12 | 15 | 17 | 19 | 13 | 16 |
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Choose the correct alternative:
The slope of the line of regression of y on x is called the ______
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State whether the following statement is True or False:
bxy is the slope of regression line of y on x
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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`
∴ regression equation of Y on :
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`x-barx=b_(xy)(y-bary)` `x-barx=square(y-bary)`
