Question

# Calculate coefficient of of correlation from the following data and interpret the result. Number of Years of024681012Schooling of FarmersAnnual Yield per Area446101087           (in′000)

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=70−6364−39182−4164−39124−246−1126001039082410396104168114126367000∑X=42∑X2=112∑y=49∑y2=38∑xy=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=∑xy√∑x2×∑y2=42√112×38 =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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