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Question
Given the following information about the production and demand of a commodity.
Obtain the two regression lines:
| Production (X) |
Demand (Y) |
|
| Mean | 85 | 90 |
| Variance | 25 | 36 |
Coefficient of correlation between X and Y is 0.6. Also estimate the demand when the production is 100 units.
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Solution
Given, `bar(x)` = 85, `bar(y)` = 90, `sigma_x^2` = 25, `sigma_y^2` = 36, r = 0.6
∴ `sigma_x` = 5, `sigma_y` = 6
byx = `"r" sigma_y/sigma_x = 0.6 xx 6/5` = 0.72
bxy = `"r" sigma_x/sigma_y = 0.6 xx 5/6` = 0.5
The regression equation of Y on X is given by `("Y" - bary) = "b"_(xy) ("X" - barx)`
(Y – 90) = 0.72(X – 85)
Y – 90 = 0.72X – 61.2
Y = 0.72X – 61.2 + 90
Y = 28.8 + 0.72X ......(i)
The regression equation of X on Y is given by `("X" - barx) = "b"_(xy) ("Y" - bary)`
(X – 85) = 0.5(Y – 90)
X – 85 = 0.5Y – 45
X = 0.5Y – 45 + 85
X = 40 + 05Y ......(ii)
For X = 100, from equation (i) we get
Y = 28.8 + 0.72(100)
= 28.8 + 72
= 100.8
∴ The production is 90 when demand is 100.
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