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Question
The regression equation of y on x is 2x – 5y + 60 = 0
Mean of x = 18
`2 square - 5 bary + 60` = 0
∴ `bary = square`
`sigma_x : sigma_y` = 3 : 2
∴ byx = `square/square`
∴ byx = `square/square`
∴ r = `square`
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Solution
The regression equation of y on x is 2x – 5y + 60 = 0.
Mean of x = 18
`2barx - 5bary + 60` = 0
`2 xx 8 - 5bary + 60` = 0
∴ `5 bary` = 36 + 60
∴ `5 bary` = 96
∴ `bary` = 19.2
`sigma_x : sigma_y` = 3 : 2
2x – 5y + 60 = 0 ⇒ y = 0.4x + 12
∴ byx = `2/5`
∴ byx = `("r"sigma_y)/sigma_`
∴ 0.4 = `"r"xx 2/3`
∴ r = `0.4 xx 3/2`
∴ r = 0.6
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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`
Mean of x = 25
Mean of y = 20
`sigma_x` = 4
`sigma_y` = 3
r = 0.5
byx = `square`
bxy = `square`
when x = 10,
`y - square = square (10 - square)`
∴ y = `square`
| 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`
