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प्रश्न
If the two regression lines for a bivariate data are 2x = y + 15 (x on y) and 4y = 3x + 25 (y on x), find
- `bar x`,
- `bar y`,
- bYX
- bXY
- r [Given `sqrt0.375` = 0.61]
उत्तर
Given,
regression equation of X on Y is 2x = y + 15,
i.e., 2x - y = 15 …(i)
regression equation of Y on X is 4y = 3x + 25,
i.e., - 3x + 4y = 25 …(ii)
By (i) × 4 + (ii) we get
8x - 4y = 60
+ - 3x + 4y = 25
5x = 85
∴ x = 17
Substituting the value of x = 17 in (i), we get
2(17) – y = 15
∴ 34 y = 15
∴ y = 34 – 15 = 19
Since the point of intersection of two regression lines is `(bar x, bar y)`,
(i) `bar x` = 17
(ii) `bar y` = 19
(iii) Regression equation of Y on X is 4y = 3x + 25
i.e., 4Y = 3X + 25
i.e., Y = `3/4 "X" + 25/4`
Comparing it with Y = bYX X + a, we get
`"b"_"YX" = 3/4`
(iv) Regression equation of X on Y is 2x = y + 15
i.e., 2X = Y + 15
i.e., X = `"Y"/2 + 15/2`
Comparing it with X = bXY Y + a' we get,
`"b"_"XY" = 1/2`
(v) r = `+-sqrt("b"_"XY" * "b"_"YX")`
`= +- sqrt((1/2) * (3/4)) = +- sqrt0.375 = +- 0.61`
Since bYX and bXY both are positive,
r is also positive.
∴ r = 0.61
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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
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- 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.
- 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?
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| X | Y | |
| Mean | 13 | 17 |
| S.D. | 3 | 2 |
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Cov(x, x) = Variance of x
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when x = 10,
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