Tamil Nadu Board of Secondary EducationHSC Commerce Class 11th

# 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 - Business Mathematics and Statistics

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.

#### 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

Concept: Regression Analysis
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