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Question
The following information is given.
| Details | X (in ₹) | Y (in ₹) |
| Arithmetic Mean | 6 | 8 |
| Standard Deviation | 5 | `40/3` |
Coefficient of correlation between X and Y is `8/15`. Find
- The regression Coefficient of Y on X
- The most likely value of Y when X = ₹ 100.
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Solution
Given `bar"X"` = 6, `bar"Y"` = 8
σX = 5, σY = `40/3`
and r(X, Y) = `8/15`
Regression coefficient of Y on X
byx = `"r".(sigma_"X")/(sigma_"Y") = 8/15(40/(3 xx 5))`
= `320/225`
= 1.422
byx = 1.422
∴ Regression line of Y on X is
`"Y" - bar"Y" = "b"_"yx"("X" - bar"X")`
Y − 8 = 1.422 (X − 6)
Y − 8 = 1.422X − 8.532
Y = 1.422X − 0.532
When X = ₹ 100
Y = 1.422(100) − 0.532
= 142.2 − 0.532
Y = 141.67
∴ When X = ₹ 100, Y = ₹ 141.67
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