Correlation | Class 11 Economics Notes

Karl Pearson's Coefficient of Correlation

Karl Pearson's coefficient of correlation (r) is a precise numerical measure of the degree and direction of linear relationship between two variables X and Y. It is also called the product moment correlation coefficient or simple correlation coefficient. The coefficient r ranges between -1 and +1. A value of +1 indicates perfect positive linear correlation, -1 indicates perfect negative linear correlation, and 0 indicates no linear correlation. The coefficient is calculated using deviations of each variable from their means, their variances, and covariance. The formula can be expressed in multiple equivalent forms involving sums of products of deviations, sums of squares, or raw scores. It is important to verify linearity through scatter diagrams before calculating r, as non-linear relationships can give misleading results. The coefficient is dimensionless and unaffected by changes in origin or scale of measurement. Interpretation of r involves understanding both its sign (direction) and magnitude (strength).

📊 Diagram: Scatter diagrams illustrating perfect positive correlation (points on an upward line), perfect negative correlation (points on a downward line), and no correlation (random scatter).

🔗 Connection: Prepares for worked examples calculating r and understanding its properties.