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प्रश्न
For a certain bivariate data of a group of 10 students, the following information gives the internal marks obtained in English (X) and Hindi (Y):
| 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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उत्तर
Given, `barx` = 13, `bary` = 17, `sigma_x` = 3, `sigma_y` = 2, r = 0.6
byx = `"r" sigma_y/sigma_x = 0.6 xx 2/3` = 0.4
bxy = `"r" sigma_x/sigma_y = 0.6 xx 3/2` = 0.9
The regression equation of X on Y is given by `("X" - barx) = "b"_(xy) ("Y" - bary)`
(X – 13) = 0.9(Y – 17)
X – 13 = 0.9Y – 15.3
X = 0.9Y – 15.3 + 13
X = – 2.3 + 0.9Y ......(i)
For Y = 16, from equation (i) we get
X = – 2.3 + (0.9)(16)
= – 2.3 + 14.4
= 12.1
The regression equation of Y on X is given by `("Y" - bary) = "b"_(yx) ("X" - barx)`
(Y – 17) = 0.4(X – 13)
Y – 17 = 0.4X – 5.2
Y = 0.4X – 5.2 + 17
Y = 11.8 + 0.4X .....(ii)
For X = 10, from equation (ii) we get
Y = 11.8 + 0.4(10)
= 11.8 + 4
= 15.8
संबंधित प्रश्न
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]
Obtain
- The line of regression of Y on X.
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- The correlation coefficient between X and Y.
You are given the following information about advertising expenditure and sales.
| 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.
- What is the likely sales when the advertising budget is ₹ 15 lakh?
- What should be the advertising budget if the company wants to attain sales target of ₹ 120 lakh?
For a certain bivariate data
| X | Y | |
| Mean | 25 | 20 |
| S.D. | 4 | 3 |
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| X | Y | |
| Mean | 85 | 90 |
| S.D. | 5 | 6 |
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For certain bivariate data the following information is available.
| X | Y | |
| Mean | 13 | 17 |
| S.D. | 3 | 2 |
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Variance of X = 9
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8x − 10y + 66 = 0
and 40x − 18y = 214.
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- The mean values of X and Y.
- Correlation coefficient between X and Y.
- Standard deviation of Y.
Find the line of regression of X on Y for the following data:
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The following results were obtained from records of age (X) and systolic blood pressure (Y) of a group of 10 men.
| X | Y | |
| Mean | 50 | 140 |
| Variance | 150 | 165 |
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If bYX = − 0.6 and bXY = − 0.216, then find correlation coefficient between X and Y. Comment on it.
Choose the correct alternative:
If for a bivariate data, bYX = – 1.2 and bXY = – 0.3, then r = ______
Choose the correct alternative:
Find the value of the covariance between X and Y, if the regression coefficient of Y on X is 3.75 and σx = 2, σy = 8
Choose the correct alternative:
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State whether the following statement is True or False:
If byx = 1.5 and bxy = `1/3` then r = `1/2`, the given data is consistent
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If u = x – a and v = y – b then bxy = buv
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|bxy + byx| ≥ ______
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If u = `(x - 20)/5` and v = `(y - 30)/4`, then byx = ______
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`sigma_x : sigma_y` = 3 : 2
∴ byx = `square/square`
∴ byx = `square/square`
∴ r = `square`
| 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` |
bxy = `square/square`
byx = `square/square`
∴ Regression equation of x on y is `square`
∴ Regression equation of y on x is `square`
bXY . bYX = ______.
The following results were obtained from records of age (x) and systolic blood pressure (y) of a group of 10 women.
| x | y | |
| Mean | 53 | 142 |
| Variance | 130 | 165 |
`sum(x_i - barx)(y_i - bary)` = 1170
For a bivariate data:
`sum(x - overlinex)^2` = 1200, `sum(y - overliney)^2` = 300, `sum(x - overlinex)(y - overliney)` = – 250
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