Regression Coefficient


Definition:
The Regression Coefficient is the constant ‘b’ in the regression equation that tells about the change in the value of dependent variable corresponding to the unit change in the independent variable.

If there are two regression equations, then there will be two regression coefficients:

  • Regression Coefficient of X on Y: The regression coefficient of X on Y is represented by the symbol bxy that measures the change in X for the unit change in Y. Symbolically, it can be represented as:Regression coefficient-1The bxy can be obtained by using the following formula when the deviations are taken from the actual means of X and Y:Regression coefficient-2When the deviations are obtained from the assumed mean, the following formula is used:Regression coefficient-3
  • Regression Coefficient of Y on X: The symbol byx is used that measures the change in Y corresponding to the unit change in X. Symbolically, it can be represented as:Regression coefficient-4
    In case, the deviations are taken from the actual means; the following formula is used:Regression coefficient-5
    The byx can be  calculated by using the following formula when the deviations are taken from the assumed means:Regression coefficient-6

The Regression Coefficient is also called as a slope coefficient because it determines the slope of the line i.e. the change in the independent variable for the unit change in the independent variable.

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