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प्रश्न
For bivariate data, the regression coefficient of Y on X is 0.4 and the regression coefficient of X on Y is 0.9. Find the value of the variance of Y if the variance of X is 9.
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उत्तर
Given: bYX = 0.4, bXY = 0.9,
var(x) = 9; var(y) =?
r = `+-sqrt("b"_"YX"."b"_"XY")`
= `+-sqrt(0.4 xx 0.9)`
= `+-sqrt0.36`
r = 0.6
∵ `"b"_"YX" - "b"_"XY" > 0`
var(x) = 9
`sigma_"X" = sqrt("var(x)")`
= `sqrt9 = 3`
Now, `"b"_"YX" = "r" xx sigma_"Y"/sigma_"X"`
∴ `0.4 = 0.6 xx sigma_"Y"/3`
∴ `0.4 = 0.2 xx sigma_"Y"`
∴ `sigma_"Y" = 0.4/0.2 = 2`
var(y) = `sigma_"y"^2`
= 22 = 4
∴ `sigma^2` = 4
∴ The value of variance of Y is 4.
संबंधित प्रश्न
For bivariate data. `bar x = 53, bar y = 28, "b"_"YX" = - 1.2, "b"_"XY" = - 0.3` Find estimate of Y for X = 50.
From the data of 7 pairs of observations on X and Y, following results are obtained.
∑(xi - 70) = - 35, ∑(yi - 60) = - 7,
∑(xi - 70)2 = 2989, ∑(yi - 60)2 = 476,
∑(xi - 70)(yi - 60) = 1064
[Given: `sqrt0.7884` = 0.8879]
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Bring out the inconsistency in the following:
bYX = 1.9 and bXY = - 0.25
Given the following information about the production and demand of a commodity obtain the two regression lines:
| X | Y | |
| Mean | 85 | 90 |
| S.D. | 5 | 6 |
The coefficient of correlation between X and Y is 0.6. Also estimate the production when demand is 100.
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The following data about the sales and advertisement expenditure of a firms is given below (in ₹ Crores)
| Sales | Adv. Exp. | |
| Mean | 40 | 6 |
| S.D. | 10 | 1.5 |
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The following data about the sales and advertisement expenditure of a firms is given below (in ₹ Crores)
| Sales | Adv. Exp. | |
| Mean | 40 | 6 |
| S.D. | 10 | 1.5 |
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The equations of two regression lines are
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For a bivariate data, `bar x = 53`, `bar y = 28`, byx = −1.5 and bxy = −0.2. Estimate y when x = 50.
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Choose the correct alternative:
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Choose the correct alternative:
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If byx = 1.5 and bxy = `1/3` then r = `1/2`, the given data is consistent
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Mean of x = 53
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| x | y | |
| Mean | 53 | 142 |
| Variance | 130 | 165 |
`sum(x_i - barx)(y_i - bary)` = 1170
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