If the two regression lines cut each other at the right angle then the value of coefficient of correlation (r) will be

The correct answer is - 0 (zero)

Key Points

• Regression Lines at Right Angle
  • When two regression lines intersect at a right angle, the angle between them is 90 degrees.
  • This occurs only if the coefficient of correlation (r) is zero.
• Coefficient of Correlation
  • The coefficient of correlation (r) measures the strength and direction of a linear relationship between two variables.
  • If r is zero, it indicates no linear relationship between the variables.

Additional Information

• Properties of Regression Lines
  • Regression lines are used to estimate the relationship between two variables.
  • The regression line of Y on X is given by Y = a + bX.
  • The regression line of X on Y is given by X = a' + b'Y.
  • If these lines are perpendicular, the product of their slopes is -1.
• Interpretation of Correlation Coefficient
  • A correlation coefficient of +1 indicates a perfect positive linear relationship.
  • A correlation coefficient of -1 indicates a perfect negative linear relationship.
  • A correlation coefficient of 0 indicates no linear relationship.
  • Values between 0 and ±1 indicate varying degrees of linear relationship strength.