The following results are obtained from the information of average rai

1.	The following results are obtained from the information of average rain and yield of a crop per acre in the last ten years of an arid region:particularsRainfall (cm)Yield of crop (kg)Mean18970standard Deviation238Correlation Coefficient = 0.6Estimate the yield of the crop if it rains 20 cms.
Answer» Here, X = Rainfall and Y = Yield of crop ∴ x̄ = 18 cm; ȳ = 970 kg, S_x = 2, S_y = 38, r = 0.6. \(Now, b = r .\frac{S_y}{S_x}\) ∴ b = 0.6 × \(\frac{38}{2}\) = 11.4 a = ȳ – bx̄ ∴ a = 970 – 11.4 (18) = 970 – 205.2 = 764.8 The regression line of yield of crop (Y) on rainfall (X) : Putting a = 764.8 and b = 11.4 in ŷ = a + bx, we get ŷ = 764.8 + 11.4x Estimate of yield of crop (Y) if rainfall X = 20 cms : Putting x = 20 in ŷ = 764.8 + 11.4x, we get ŷ = 764.8 + 11.4 (20) = 764.8 + 228 = 992.8 Hence, the estimate of yield of crop obtained is 992.8 kg.

The following results are obtained from the information of average rain and yield of a crop per acre in the last ten years of an arid region:particularsRainfall (cm)Yield of crop (kg)Mean18970standard Deviation238Correlation Coefficient = 0.6Estimate the yield of the crop if it rains 20 cms.

Answer»

Here, X = Rainfall and Y = Yield of crop
∴ x̄ = 18 cm;

ȳ = 970 kg,

S_x = 2,

S_y = 38,

r = 0.6.

\(Now, b = r .\frac{S_y}{S_x}\)

∴ b = 0.6 × \(\frac{38}{2}\)

= 11.4

a = ȳ – bx̄
∴ a = 970 – 11.4 (18)
= 970 – 205.2
= 764.8

The regression line of yield of crop (Y) on rainfall (X) :

Putting a = 764.8 and b = 11.4 in ŷ = a + bx, we get
ŷ = 764.8 + 11.4x

Estimate of yield of crop (Y) if rainfall X = 20 cms :

Putting x = 20 in ŷ = 764.8 + 11.4x, we get
ŷ = 764.8 + 11.4 (20)
= 764.8 + 228
= 992.8

Hence, the estimate of yield of crop obtained is 992.8 kg.