past 10 years data on rainfall and output of wheat in a certain village offered the following results. av. wheat output- 25qtl av. rainfall 20cms , variance of wheat output- 3qtl , variance of rainfall- 5 cms, r- 0.65, find the most likely wheat output per acre when rainfall is 35 cms Related: Correlation And Regression (Part - 1)?

Question

past 10 years data on rainfall and output of wheat in a certain village offered the following results. av. wheat output- 25qtl av. rainfall 20cms , variance of wheat output- 3qtl , variance of rainfall- 5 cms, r- 0.65, find the most likely wheat output per acre when rainfall is 35 cms Related:  Correlation And Regression (Part - 1)?

Answer

Calculation of Regression Equation

Regression equation: Y = a + bX

Where Y is the dependent variable (wheat output) and X is the independent variable (rainfall)

a = Y - bX

b = r * (SDy/SDx)

SDy = square root of variance of wheat output = square root of 3 = 1.73

SDx = square root of variance of rainfall = square root of 5 = 2.24

r = 0.65

a = 25 - 0.65 * (1.73/2.24) * 20 = 18.81

b = 0.65 * (1.73/2.24) = 0.50

Regression equation: Y = 18.81 + 0.50X

Prediction of Wheat Output

Given rainfall = 35 cms

Using regression equation: Y = 18.81 + 0.50 * 35 = 35.31

Therefore, the most likely wheat output per acre when rainfall is 35 cms is 35.31 quintals

Interpretation of Results

The regression equation indicates that there is a positive linear relationship between rainfall and wheat output in the village

For every one unit increase in rainfall, there is an expected increase of 0.50 quintals in wheat output

The coefficient of determination (r-squared) can be calculated as r^2 = 0.65^2 = 0.42

This means that 42% of the variation in wheat output can be explained by the variation in rainfall

However, it should be noted that there may be other factors that influence wheat output in the village, which are not accounted for in this analysis

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