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प्रश्न
If n = 6, Σx = 36, Σy = 60, Σxy = –67, Σx2 = 50, Σy2 =106, Estimate y when x is 13
उत्तर
In order to estimate y, we have to find the regression equation of Y on X.
n = 6, Σx = 36, Σy = 60, Σxy = – 67, Σx2 = 50, Σy2 =106
∴ `barx = (sumx)/"n" = 36/6` = 6
`bary = (sumy)/"n" = 60/6` = 10
Now,
byx = `(sumxy - "n"bar(x) bar(y))/(sumx^2 - "n"x^(-2))`
= `(-67 - 6 xx 6 xx +10)/(50 - 6 xx (6)^2`
= `(-67 - 360)/(-166)`
= `427/166`
= 2.57
Also, a = `bary - "b"_(yx) barx`
= 10 – 2.57 × 6
= – 5.42
∴ The regression equation of Y on X is Y = a + byx X
∴ Y = – 5.42 + 2.57X
For X = 13,
Y = – 5.42 + 2.57(13)
= 27.99
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