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Question
Find the line of regression of X on Y for the following data:
n = 8, `sum(x_i - bar x)^2 = 36, sum(y_i - bar y)^2 = 44, sum(x_i - bar x)(y_i - bar y) = 24`
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Solution
Given, n = 8, `sum(x_i - bar x)^2 = 36`
`sum(y_i - bar y)^2 = 44, sum(x_i - bar x)(y_i - bar y) = 24`
∴ `"b"_"XY" = (sum(x_i - bar x)(y_i - bar y))/(sum(y_i - bar y)^2) = 24/44 = 6/11`
Now, the regression equation of X on Y is
`("X" - bar x) = "b"_"XY" ("Y" - bar y)`
i.e., `("X" - bar x) = 6/11 ("Y" - bar y)`
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| 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 |
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Mean of y = `bary = square`
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