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प्रश्न
| x | y | xy | x2 | y2 |
| 6 | 9 | 54 | 36 | 81 |
| 2 | 11 | 22 | 4 | 121 |
| 10 | 5 | 50 | 100 | 25 |
| 4 | 8 | 32 | 16 | 64 |
| 8 | 7 | `square` | 64 | 49 |
| Total = 30 | Total = 40 | Total = `square` | Total = 220 | Total = `square` |
bxy = `square/square`
byx = `square/square`
∴ Regression equation of x on y is `square`
∴ Regression equation of y on x is `square`
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उत्तर
| x | y | xy | x2 | y2 |
| 6 | 9 | 54 | 36 | 81 |
| 2 | 11 | 22 | 4 | 121 |
| 10 | 5 | 50 | 100 | 25 |
| 4 | 8 | 32 | 16 | 64 |
| 8 | 7 | 56 | 64 | 49 |
| Total = 30 | Total = 40 | Total = 214 | Total = 220 | Total = 340 |
From the table, we have
n = 5, ∑x = 30, ∑y = 40, ∑xy = 214, ∑x2 = 220, ∑y2 = 340
`barx = (sumx_"i")/"n" = 30/5` = 6
`bary = (sumy_"i")/"n" = 40/5` = 8
bxy = `(sumxy - "n" bar(x) bar(y))/(sumy^2 - "n" bary^2)`
= `(214 - 5 xx 6 xx 8)/(340 - 5(8)^2`
= `(214 - 240)/(340 - 320)`
= `(-26)/20`
bxy = `(-13)/10`
byx = `(sumxy - "n" bar(x) bar(y))/(sumx^2 - "n" barx^2)`
= `(214 - 5 xx 6 xx 8)/(220 - 5(6)^2`
= `(214 - 240)/(220 - 180)`
= `(-26)/40`
byx = `(-13)/20`
∴ Regression equation of x on y is x = – 1.3y + 16.4
∴ Regression equation of y on x is y = – 0.65x + 11.9
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a. r = `square`
b. When x = 50,
`y - square = square (50 - square)`
∴ y = `square`
c. When y = 25,
`x - square = square (25 - square)`
∴ x = `square`
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byx = `square`
bxy = `square`
when x = 10,
`y - square = square (10 - square)`
∴ y = `square`
