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प्रश्न
Two samples from bivariate populations have 15 observations each. The sample means of X and Y are 25 and 18 respectively. The corresponding sum of squares of deviations from respective means is 136 and 150. The sum of the product of deviations from respective means is 123. Obtain the equation of the line of regression of X on Y.
उत्तर
Given, n = 15, `bar x = 25, bar y = 18`,
`sum (x_i - bar x)^2 = 136, sum(y_i - bar y)^2 = 150,`
`sum (x_i - bar x)(y_i - bar y)` = 123
Now, `"b"_"XY" = (sum (x_i - bar x)(y_i - bary))/(sum(y_i - bary)) = 123/150` = 0.82
Also, `"a"' = bar x - "b"_"XY" bar y`
= 25 - 0.82 × 18 = 25 - 14.76 = 10.24
∴ The regression equation of X on Y is
X = a' + bXY Y
∴ X = 10.24 + 0.82Y
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Mean of x = `barx = square`
Mean of y = `bary = square`
bxy = `square/square`
byx = `square/square`
Regression equation of x on y is `(x - barx) = "b"_(xy) (y - bary)`
∴ Regression equation x on y is `square`
Regression equation of y on x is `(y - bary) = "b"_(yx) (x - barx)`
∴ Regression equation of y on x is `square`
