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Question

Calculate coefficient of of correlation from the following data and interpret the result.

Number of Years of024681012Schooling of FarmersAnnual Yield per Area446101087           (in000)


Solution

Let X and Y denote number of years of schooling of farmers and annual yielding per acre respectively.

Calculation of Coefficient of Correlation

Xx=(X¯X)X2Yy=(Y¯Y)y2xy    ¯X=6    ¯Y=706364391824164391242461126001039082410396104168114126367000X=42X2=112y=49y2=38xy=42
Here, N= 7, X=42,X2=112,y=49,y2=38 and xy=42
Now, ¯X=XN=427=6 and ¯Y=YN=497=7
r=xyx2×y2=42112×38
=424256=4265.24=0.644
It shows a moderate degree of positive correlation between number of years of schooling of farmers and annual yield per acre.

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