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प्रश्न
For bivariate data. `bar x = 53, bar y = 28, "b"_"YX" = - 1.2, "b"_"XY" = - 0.3` Find Correlation coefficient between X and Y.
उत्तर
Here, `bar x = 53, bar y = 28, "b"_"YX" = - 1.2, "b"_"XY" = - 0.3`
r = `+-sqrt("b"_"XY" * "b"_"YX")`
`= +- sqrt((- 0.3)(- 1.2))`
`= +- sqrt0.36 = +- 0.6`
Since bYX and bXY both are − negative,
r is also negative.
∴ r = −0.6
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संबंधित प्रश्न
For bivariate data. `bar x = 53, bar y = 28, "b"_"YX" = - 1.2, "b"_"XY" = - 0.3` Find estimate of X for Y = 25.
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| Arithmetic Mean | 10 | 90 |
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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 |
| 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`
Mean of x = 53
Mean of y = 28
Regression coefficient of y on x = – 1.2
Regression coefficient of x on y = – 0.3
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b. When x = 50,
`y - square = square (50 - square)`
∴ y = `square`
c. When y = 25,
`x - square = square (25 - square)`
∴ x = `square`
bxy . byx = ______.
If byx > 1 then bxy is _______.
|bxy + byz| ≥ ______.
