A partial residual plot is useful for identifying outliers, as well as determining whether a linear model is the correct type of model to use (vs. nonlinear).

A residual is the difference between an actual observed value of y and the predicted value (y-hat) for a given x value, based on the regression model.

Scatter Plot
A graph plots the costs, in dollars, and their distances from the predicted line, below the line at 500, slightly above at 1000, above at 1750, and slightly below at 3000.
Residual Plot
A graph plots the residuals, less than negative 50 at 500, between 0 and 50 at 1000, just less than 100 at 1750, and just less than negative 50 at 3000.

A scatter plot of residuals can reveal whether a linear model is appropriate based on whether there is a discernible pattern in the residuals. If there is no pattern, then a linear model is preferred. If there is a pattern, a linear relationship is likely not the correct choice for the plotted variable.

Residual Plot - No Clear Pattern
A graph of residuals vary between negative 1 and 1.
Residual Plot - U-Shaped Pattern
A graph of residuals fall from around 7 at x = 0 to around negative 2 at x = 5, then rise to around 4 at x = 9.

Residual plots are also useful in identifying outliers. An outlier will have a residual value either well above or well below the others since the actual value of an outlier is much different than the value predicted by the model. Outliers should be evaluated, and if they are due to a collection or calculation error, they should be removed from the study.