e-Statistics

Residual Plot

The standard assumption of regression model is that the random error terms $\epsilon_1,\ldots,\epsilon_n$ are iid normally distributed random variables with mean 0 and common variance $\sigma^2$ . Thus, the statistical model for the simple linear regression is given by $Y_i \sim N(\beta_0 + \beta_1 x_i, \sigma^2)$ for $i=1,\ldots,n$ .

The data set consists of

explanatory variable for 's;
dependent variable for 's.

For each value

of the independent variable, the prediction equation provides a fitted value $\hat{y}_i = \hat{\beta}_0 + \hat{\beta}_1 x_i$ . Then we can plot the fitted value $\hat{Y}_i$ against the standardized residuals $\dfrac{Y_i - \hat{y}_i}{\hat{\sigma}}$ .

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