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Question
| x | y | `x - barx` | `y - bary` | `(x - barx)(y - bary)` | `(x - barx)^2` | `(y - bary)^2` |
| 1 | 5 | – 2 | – 4 | 8 | 4 | 16 |
| 2 | 7 | – 1 | – 2 | `square` | 1 | 4 |
| 3 | 9 | 0 | 0 | 0 | 0 | 0 |
| 4 | 11 | 1 | 2 | 2 | 4 | 4 |
| 5 | 13 | 2 | 4 | 8 | 1 | 16 |
| Total = 15 | Total = 45 | Total = 0 | Total = 0 | Total = `square` | Total = 10 | Total = 40 |
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`
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Solution
| x | y | `x - barx` | `y - bary` | `(x - barx)(y - bary)` | `(x - barx)^2` | `(y - bary)^2` |
| 1 | 5 | – 2 | – 4 | 8 | 4 | 16 |
| 2 | 7 | – 1 | – 2 | 2 | 1 | 4 |
| 3 | 9 | 0 | 0 | 0 | 0 | 0 |
| 4 | 11 | 1 | 2 | 2 | 4 | 4 |
| 5 | 13 | 2 | 4 | 8 | 1 | 16 |
| Total = 15 | Total = 45 | Total = 0 | Total = 0 | Total = 20 | Total = 10 | Total = 40 |
Mean of x = `barx = (sumx)/"n"` = 3
Mean of y = `bar = (sumy)/"n"` = 9
bxy = `(sum(x - barx)(y - bary))/(sum(y - bary)^2) = 20/40 = 1/2`
byx = `(sum(x - barx)(y - bary))/(sum(x - barx)^2) = 20/10` = 2
Regression equation of x on y is `(x - barx) = "b"_(xy) (y - bary)`
i.e., `("X" - 3) = 1/2 ("Y" - 9)`
∴ Regression equation x on y is 2X – Y + 3 = 0
Regression equation of y on x is `(y - bary) = "b"_(yx) (x - barx)`
i.e., (Y – 9) = 2(X – 3)
∴ Regression equation of y on x is 2X – Y + 3 = 0
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|
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The regression equation of y on x is 2x – 5y + 60 = 0
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∴ `bary = square`
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∴ byx = `square/square`
∴ byx = `square/square`
∴ r = `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`
If byx > 1 then bxy is _______.
