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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
For bivariate data. `bar x = 53`, `bar y = 28`, byx = −1.2, bxy = −0.3. Find the correlation coefficient between x and y.
You are given the following information about advertising expenditure and sales.
| Advertisement expenditure (₹ in lakh) (X) |
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| 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?
Bring out the inconsistency in the following:
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∑ x = 8500, ∑ y = 9600, σX = 60, σY = 20, r = 0.6
Estimate the expenditure on food and entertainment when expenditure on accommodation is Rs 200.
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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Estimate the likely sales for a proposed advertisement expenditure of ₹ 10 crores.
The following data about the sales and advertisement expenditure of a firms is given below (in ₹ Crores)
| Sales | Adv. Exp. | |
| Mean | 40 | 6 |
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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 |
and `sum (x_i - bar x)(y_i - bar y) = 1120`. Find the prediction of blood pressure of a man of age 40 years.
Choose the correct alternative:
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Choose the correct alternative:
bxy and byx are ______
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State whether the following statement is True or False:
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State whether the following statement is True or False:
Regression coefficient of x on y is the slope of regression line of x on y
If the sign of the correlation coefficient is negative, then the sign of the slope of the respective regression line is ______
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The geometric mean of negative regression coefficients is ______
byx is the ______ of regression line of y on x
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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)`
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Mean of x = 25
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`sigma_x` = 4
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byx = `square`
bxy = `square`
when x = 10,
`y - square = square (10 - square)`
∴ y = `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 = ______.
For a bivariate data:
`sum(x - overlinex)^2` = 1200, `sum(y - overliney)^2` = 300, `sum(x - overlinex)(y - overliney)` = – 250
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- bxy
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