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Q.

The following information is obtained to study the relationship between average rainfall (in cm) and the yield of Maize (in quintal per hectare) in different taluka of Gujarat:

ParticularsRainfall (cm) xxYield of Maize (Quintal Per Hectare) yy
Mean82180
Variance64225

Correlation Coefficient =0.82= 0.82

Estimate the yield of Maize when the rainfall is 60 cm.

Gujarat GsebGujarat Board (GSEB) HSC Commerce Board 2026Subjective· 3mImportance★★★★★
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byx=rSySx=1.5375b_{yx}=r\tfrac{S_y}{S_x}=1.5375; y^=180+1.5375(60−82)=146.18\hat y=180+1.5375(60-82)=146.18.

Standard deviations: Sx=64=8, Sy=225=15S_x=\sqrt{64}=8,\ S_y=\sqrt{225}=15. Regression coefficient of yield YY on rainfall XX:

byx=r SySx=0.82×158=1.5375.b_{yx}=r\,\frac{S_y}{S_x}=0.82\times\frac{15}{8}=1.5375.

Regression line of YY on XX through (xˉ,yˉ)=(82,180)(\bar x,\bar y)=(82,180):

y^=yˉ+byx(x−xˉ)=180+1.5375(x−82).\hat y=\bar y+b_{yx}(x-\bar x)=180+1.5375(x-82). …

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