The coefficient of correlation :

The correct answer is - varies between ±1

Key Points

• Definition of the coefficient of correlation:
  • The coefficient of correlation, commonly denoted as r, measures the strength and direction of the linear relationship between two variables.
  • It is a key concept in statistics, particularly in regression and correlation analysis.
• Range of the coefficient of correlation:
  • The value of r always lies within the range of −1 to +1.
  • A value of +1 indicates a perfect positive linear relationship.
  • A value of −1 indicates a perfect negative linear relationship.
  • A value of 0 indicates no linear relationship between the variables.
• Why other options are incorrect:
  • Option 2 (has no limit): Incorrect because the coefficient of correlation is bounded by ±1.
  • Option 3 (can be less than 1): Misleading as it suggests the value can exceed ±1, which is not possible.
  • Option 4 (can be more than 1): Incorrect because the coefficient of correlation cannot exceed +1 or −1.

Additional Information

• Interpretation of the coefficient of correlation:
  • A value closer to +1 indicates a strong positive linear relationship (e.g., as one variable increases, the other also increases).
  • A value closer to −1 indicates a strong negative linear relationship (e.g., as one variable increases, the other decreases).
  • A value near 0 indicates a weak or no linear relationship.
• Types of correlation:
  • Positive correlation: Both variables move in the same direction.
  • Negative correlation: Variables move in opposite directions.
  • No correlation: No apparent relationship between the variables.
• Practical applications:
  • Used in finance to measure the relationship between stock prices or returns.
  • Applied in economics to study the relationship between demand and price or income and expenditure.
  • In social sciences, it helps study relationships between variables like education level and income.