How do we find the best fit line through a scatter? Typically, with ordinary least squares (OLS). Although we have other methods. The OLS finds the line that minimizes the residual sum of squares (RSS); i.e., the sum of the square of vertical distance between observed Y and predicted Y. Why not just minimize the sum of residuals instead of the squared residuals? To “penalize” larger residuals.

The residual plot illustrates at least two properties of the classical linear regression model (CLRM):

• The expected (average) residual is zero,
• Homoscedastic residuals; e.g., we don’t expect to see the dispersion of the residuals exhibiting some patter as we move from left to right along the independent variable
• Also, we can visually (sort of) confirm that the residuals are not correlated with the independent variable X. In short, the residual plot should be centered at zero but otherwise without meaningful, obvious pattern (bias)

Briefcast:

Comments

1. Abel 02 Jan 2010

   Classic

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