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.

Answer 1

`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