e-Statistics

Residual Analysis

The data set consists of

  1. Response (dependent variable) for $ Y_j$'s;
  2. 1st predictor (1st explanatory variable) for $ x_{1j}$'s;
  3. 2nd predictor (2nd explanatory variable) for $ x_{2j}$'s.

The prediction equation provides a fitted value

$\displaystyle \hat{y}_j = \hat{\beta}_0 + \hat{\beta}_1 x_{1j} + + \hat{\beta}_2 x_{2j}
$

Then we can plot the fitted value $ \hat{Y}_i$ against the standardized residuals $ \frac{Y_i - \hat{y}_i}{\hat{\sigma}}$.

In model validation we look for a pattern, the indication of which suggests that the regression of choice is not a good model.