Linear Regression

• calculation of least squares estimator
  b <- (sum(x*y) - n*mean(y)*mean(x)) / (sum(x*x) - n*mean(x)*mean(x))
a <- mean(y) - b*mean(x)
• predicted value of Y for any value of X
  a + b * x
• total dispersion of yi
• SQT
  sum((y - mean(y)) * (y - mean(y)))
• SQE
  sum((Y - mean(y)) * (Y - mean(y)))
• SQR
  sum((y - Y) * (y - Y))
• coefficient of determination R² as a measure for the quality of the model
  SQE / SQT
• Alternative Formula
  1 - (SQR / SQT)

• Properties of the coefficient of determination

  R² = 0 explained dispersion zero -> regression model is extremely bad R² = 1 explained dispersion = total dispersion -> regression model is perfectly fitted to data

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