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Chapter 5: Bivariate Data
Definition: Residual
A residual or an error is the difference between an actual, observed y value
and a corresponding y value predicted by the model.
Thus, the error for any observation is given by
Plots of residuals may display patterns that would give some idea about the
appropriateness of the model. If the functional form of the regression model
is incorrect, the residual plots constructed by using the model will often
display a distinct pattern. The pattern can then be used to propose a more
appropriate mathematical model.
Illustration 1:
Consider the scatter plot given in
Figure 5-22
.
The plot displays a linear relationship between the
and
values.
Suppose instead of using the simple linear regression model
, we incorrectly use the model
. By using this
model, then the least square estimate of
is
= mean of the
values.
Thus the predicted values will be along the horizontal line in
Figure 5-22
.