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Sum

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.

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#### Solution

`bar"X"` = 25, σ_{x} = 3, `bar"Y"` = 40, σ_{y} = 6, r = 0.8

b_{yx} = `"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

Concept: Regression Analysis

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