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Question
Given the following data, what will be the possible yield when the rainfall is 29.
| Details | Rainfall | Production |
| Mean | 25`` | 40 units per acre |
| Standard Deviation | 3`` | 6 units per acre |
Coefficient of correlation between rainfall and production is 0.8.
Solution
`bar"X"` = 25, σx = 3, `bar"Y"` = 40, σy = 6, r = 0.8
byx = `"r"(sigma_"y")/(sigma_"x") = 0.8 xx 6/3` = 1.6
`"Y" - bar"Y" = "b"_"yx"("X" - bar"X")`
Y − 40 = 1.6 (X − 25)
Y − 40 = 1.6X − (1.6)(25)
Y − 40 = 1.6X − 40
∴ Y = 1.6X
To find the yield when the rainfall is 29″
Put X = 29 in the above equation we get yield,
Y = 1.6 × 29 = 46.4 units/acre
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