Residual Plots - Bivariate Data

Sometimes, it is not appropriate to use a least squares line for a set of data. Previously we used “r” to determine how well a linear model fits a set of data. You can also use residuals to further analyse the appropriateness of a linear model.

A residual is the vertical distance between an observed data value and the least squares line. These distances can be represented on a residual plot which provides a visual representation of the residuals for a set of data.

How to calculate residuals on CAS:

• Place all data on the statistics section on the class-pad.

• Press calculate, regression, linear regression.

• Turn on “copy residual” in list 3.

• Tap on “list 3” to get the residuals for each point.

How to make a residual plot on CAS:

• Click on the “graph” button and change the “y-list” to list 3.

• Click the button in the corner to graph it.

A residual plot with randomly scattered data around the x-axis shows an appropriate linear model but if the plot has a clear pattern it tells us that the model is not appropriate for a linear model.