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प्रश्न
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`
उत्तर
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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| Production (X) |
Demand (Y) |
|
| Mean | 85 | 90 |
| Variance | 25 | 36 |
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The equations of the two lines of regression are 6x + y − 31 = 0 and 3x + 2y – 26 = 0. Find the value of the correlation coefficient
| 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`
