Properties of the Regression Line

Regression is concerned with the study of the relationship among variables. The aim of regression (or regression analysis) is to make models for prediction and for making other inferences. Two or more variables may be treated by regression. The regression line is usually written as \widehat Y = a + bX. The general properties of the regression line \widehat Y = a + bX are given below:

  • We know that \overline Y = a + b\overline X . This shows that the line passes through the means \overline X and \overline Y .
  • The sum of errors is equal to zero. The regression equation is \widehat Y = a + bX and the sum of derivatives of observed Y from estimated \widehat Y is

\sum \left( {Y - \widehat Y} \right) = \sum \left( {Y - a - bX} \right) = \sum Y - na - b\sum X = 0

\left[ {\sum Y = na + b\sum X} \right]

When \sum \left( {Y - \widehat Y} \right) = 0, it means that \sum Y = \sum \widehat Y.