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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.
For bivariate data. `bar x = 53, bar y = 28, "b"_"YX" = - 1.2, "b"_"XY" = - 0.3` Find estimate of X for Y = 25.
From the data of 7 pairs of observations on X and Y, following results are obtained.
∑(xi - 70) = - 35, ∑(yi - 60) = - 7,
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- The line regression of X on Y.
- The correlation coefficient between X and Y.
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| Advertisement expenditure (₹ in lakh) (X) |
Sales (₹ in lakh) (Y) | |
| Arithmetic Mean | 10 | 90 |
| Standard Mean | 3 | 12 |
Correlation coefficient between X and Y is 0.8
- Obtain the two regression equations.
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- What should be the advertising budget if the company wants to attain sales target of ₹ 120 lakh?
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bYX = 2.6 and bXY = `1/2.6`
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| Sales | Adv. Exp. | |
| Mean | 40 | 6 |
| S.D. | 10 | 1.5 |
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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:
If for a bivariate data, bYX = – 1.2 and bXY = – 0.3, then r = ______
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Choose the correct alternative:
|byx + bxy| ≥ ______
Choose the correct alternative:
bxy and byx are ______
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If r = 0.5, σx = 3, `σ_"y"^2` = 16, then byx = ______
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If r = 0.5, σx = 3, σy2 = 16, then bxy = ______
Choose the correct alternative:
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Obtain the two regression lines:
| ADVERTISEMENT (x) (₹ in lakhs) |
DEMAND (y) (₹ in lakhs) |
|
| Mean | 10 | 90 |
| Variance | 9 | 144 |
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| X | Y | |
| Mean | 13 | 17 |
| Standard Deviation | 3 | 2 |
If r = 0.6, Estimate x when y = 16 and y when x = 10
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Regression coefficient of y on x = – 1.2
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| 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` |
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