Lowess exercise in Minitab
You can use Minitab to plot a LOWESS function through a set of data; LOWESS plotting is also available in Splus using either lowess or scatter.smooth. For more advanced smoothing methods, investigate loess in Splus, which creates a more sophisticated data object and incorporates models with multiple independent variables.
From Minitab, open the worksheet coredata.mtw in directory student1. The response variable is %mud in a core sample and the independent variable is the depth of the core sample. Options for LOWESS are in the Plot... dialog box under the Graphics menu. We usually like to superimpose the LOWESS curve over a scatterplot of the data. To do so, click under Display in Row 2 and select Lowess from the Display menu. Choose Graph under the For each menu. Click on Edit Attributes... and enter .8 in the Degree of Smoothing box. Does the subsequent plot look oversmoothed? If so, redo the plot with the default value of .5 for the degree of smoothing. Find a value so that the plot looks undersmoothed. What value did you use?
Note that the Edit Attributes... menu also allows you to store fits and residuals which can then be examined using the residual diagnostics you have used for regression. You may want to examine residuals for your plots, particularly the oversmoothed LOWESS curve to see if you can detect the bias in the LOWESS curve.