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Explained and unexplained variation

  • TSS = Total sum of squares
    • Measures the variation of the yi values around their mean y
  • RSS = Residual sum of squares
    • Variation attributable to factors other than the relationship between x and y
  • ESS = Explained sum of squares
    • Explained variation attributable to the relationship between x and y
  • Total variation is made up of two parts:

  • Where:
    •   = Average value of the dependent variable
    •  y = Observed values of the dependent variable
    •     = Estimated value of y for the given x value

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