dx= ( x - x̅ ) and dy = (y - y ) r is free from origin r is free from unit of measurement - ≤r≤+ Direct Method: N ∑ dxdy − ( ∑ dx ) ( ∑ dy ) N ∑ dx − ( ∑ dx ) N ∑ dy − ( ∑ dy ) Example : Calculate Karl Pearson’s Coefficient of correlation from the following data and interpret its value: Price :X Supply:Y Solution: Let us take Price as X and supply as Y Computation of Pearson’s Correlation Coefficient Price: X Supply: Y XY X Y ∑x = ∑y = ∑xy = ∑x = ∑y =11685 r = N ∑ XY − ( ∑ X) ( ∑ Y) N ∑ X − ( ∑ X) N ∑ Y − ( ∑ Y) r = ( x ) − ( x ) ( x ) − ( ) 5x11685 − ( ) - - Introduction to Statistical Methods and Econometrics r = , − , × r = =+ . . Price of the product and supply for the product is positively correlated. When price of the product increases then the supply for the product also increases.
Actual Mean Method: Ex- : Estimate the coefficient of correlation with actualmean method for the following data. Age of Cars in years Cost of Annual Maintains (in ₹) Solution: r = ∑xy ∑x ∑y