Correlation

• Meaning and Definition
  • Correlation: Statistical technique measuring relationship between two or more variables.
  • Covariation: Change in one variable results in corresponding change in other.
  • Examples: Price and demand, Height and weight.
• Types of Correlation
  • Based on Direction
    • Positive (Direct) Correlation: Variables move in the same direction (e.g., Price and Supply).
    • Negative (Inverse) Correlation: Variables move in opposite directions (e.g., Price and Demand).
  • Based on Number of Variables
    • Simple Correlation: Relationship between two variables.
    • Multiple Correlation: Relationship among three or more variables.
    • Partial Correlation: Relationship between two variables keeping others constant.
  • Based on Degree of Linear Relationship
    • Perfect Correlation: Coefficient ($r$) = +1 or -1.
    • High Degree: $r$ is close to +1 or -1.
    • Moderate Degree: $r$ is around ±0.5.
    • Low Degree: $r$ is closer to 0.
    • Zero (No) Correlation: $r$ = 0 (No relationship).
• Degree of Correlation: Karl Pearson's Coefficient ($r$)
  • Range: Lies strictly between -1 and +1.
  • Interpretation of Values
    • $r = +1$: Perfect positive correlation.
    • $r = -1$: Perfect negative correlation.
    • $r = 0$: Absence of correlation.
• Methods of Measuring Correlation
  • Scatter Diagram Method
    • Graphical representation of bivariate data.
    • Simple, visual, but non-mathematical.
  • Karl Pearson’s Coefficient of Correlation ($r$)
    • Algebraic/Mathematical method.
    • Measures linear relationship.
    • Formula uses mean and standard deviation.
    • Assumption: Normal population distribution.
  • Spearman’s Rank Correlation Coefficient ($R$)
    • Used for qualitative data (beauty, honesty, intelligence).
    • Based on ranks assigned to variables.
    • Formula includes adjustment for equal ranks (tie correction).
• Utility and Limitations
  • Uses in Economics & Business
    • Helps in forecasting and policy formulation.
    • Identifies cause-and-effect trends.
  • Limitations
    • Does not imply causation (Correlation $\neq$ Causation).
    • Affected by extreme values (outliers).
    • Assumes linear relationship mostly.