Let x and y be the rainfall and production given:
x̄ = 30; ȳ = 40, = σ2x =25
∴ σx = 5 σ2y = 64
∴ σ2y =8; γ = 0.6
1. To find y when x = 50; we need the regression equation of y on x:
(y – ȳ) = byx (x – x̄)
2. To find x when y = 45, we need the regression equation of x on y: (x – x̄) = b × y (y – ȳ)
X = 1.875+ 30 = 31.875 cms rainfall.