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Question
You are given the following data:
| Details | X | Y |
| Arithmetic Mean | 36 | 85 |
| Standard Deviation | 11 | 8 |
If the Correlation coefficient between X and Y is 0.66, then find
- the two regression coefficients,
- the most likely value of Y when X = 10.
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Solution
`bar"X"` = 36, `bar"Y"` = 85, σx = 11, σy = 8, r = 0.66
(i) The two regression coefficients are,
byx = `"r"(sigma_"y")/(sigma_"x") = 0.66 xx 8/11` = 0.48
bxy = `"r"(sigma_"x")/(sigma_"y") = 0.66 xx 11/8` = 0.9075 = 0.91
(ii) Regression equation of X on Y:
`"X" - bar"X" = "b"_"xy"("Y" - bar"Y")`
X – 36 = 0.91(Y – 85)
X – 36 = 0.91Y – 77.35
X = 0.91Y – 77.35 + 36
X = 0.91Y – 41.35
Regression line of Y on X:
`"Y" - bar"Y" = "b"_"yx"("X" - bar"X")`
Y – 85 = 0.48(X – 36)
Y = 0.48X – 17.28 + 85
Y = 0.48X + 67.72
The most likely value of Y when X = 10
Y = 0.48(10) + 67.72 = 72.52
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