A “**residuals and fits plot**” will be the most commonly created plot when performing a residual analysis. It’s a scatter plot that shows residuals on both the and. The definition of residuals fitted values (estimated answers) are shown on the. This plot can be used to detect outliers, unequal error variances, and non-linearity.

This plot shows that alcohol consumption and arm strength are in a declining linear relationship. The plot also indicates that there are not unusual data points within the data set. It also shows that the variance around the estimated regression line suggests that equal error variances are reasonable.

### Definition of Residual (Residual)

The definition of residuals (e _{i}), is the difference between an observed and corresponding fitted value, which is the value that the model predicts.

Residues, which are the difference between any data points and the regression line are often called “**errors**.” An error in this context does not necessarily mean that the analysis is flawed. It simply means that there is an unexplained difference. The residual, in other words is an error that cannot be explained by the regression line.

A time series model’s residuals are the amount of material left after fitting it. The residuals are equal to the difference between the observations and the corresponding fitted values:et=yt-^yt.et=yt-y^t.

It’s useful to examine residuals of scales that have been transformed if a transformation was used in the model. These are called in the definition “innovation residuals”. For example, suppose we modeled the logarithms of the data, wt=log(yt)wt=log(yt). Then the innovation residuals are given by wt-^wtwt-w^t whereas the regular residuals are given by yt-^ytyt-y^t. For more information on how to forecast using transformations. In cases where no transformation was used, the innovation residuals will be identical to regular residuals. We will refer to them as “residuals” in these cases.

### The Sum and Mean Residuals

The sum of all residuals equals zero, assuming your line is the one with the best fit. The mean number of residuals is also equal because the mean = sum of the residuals/number of items. The sum of the residuals is zero so 0/n will always be zero.