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प्रश्न
If for bivariate data `bar x = 10, bar y = 12,` v(x) = 9, σy = 4 and r = 0.6 estimate y, when x = 5.
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उत्तर
Given, `bar x = 10, bar y = 12,` v(x) = 9, σy = 4, r = 0.6
∴ σx = 3
To estimate y, we should first find the regression equation of Y on X.
∴ `"b"_"YX" = "r" sigma_y/sigma_x = 0.6 xx 4/3 = 0.8`
Also, `"a" = bar "y" - "b"_"YX" bar"x"`
= 12 - 0.8(10) = 12 - 8 = 4
The regression equation of Y on X is
Y = a + bYX X
∴ Y = 4 + 0.8 X
For X = 5,
Y = 4 + 0.8 (5) = 4 + 4 = 8
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For a bivariate data `barx = 10`, `bary = 12`, V(X) = 9, σy = 4 and r = 0.6
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`
