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Coefficient of determination (R2) and Adjusted R2

  • Coefficient of determination(R2) can also be used to test the significance of the coefficients collectively apart from using F-test


  • The drawback of using Coefficient of determination is that the value of the coefficient of determination always increases as the number of independent variables are increased even if the marginal contribution of the incoming variable is statistically insignificant
  • To take care of the above drawback, coefficient of determination is adjusted for the number of independent variables taken. This adjusted measure of coefficient of determination is called adjusted R2
  • Adjusted R2 is given by the following formula:
  • Where:
    • n = Number of Observations
    • k = Number of Independent Variables
    • = Adjusted R2

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