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Chapter 6 Statistics
Example
The data set Puromycin has 23 rows representing the measurement
of initial velocity of a biochemical reaction for 6 different
concentrations of substrate and two different cell treatments. The
section Nonlinear Regression describes these data in detail and
discusses a theoretical model for the data. Before fitting a theoretical
model, we can use the Local (Loess) Regression dialog to fit
nonparametric smooth curves to the data.
Our model consists of a separate curve for each treatment group. We
predict the response conc by the variables vel and state. Since
state is a factor, this fits a separate smooth curve in vel for each
level of state.
1. Open the Local (Loess) Regression dialog.
2. Type Puromycin in the Data Set field.
3. Type conc~vel+state in the Formula field. Alternatively,
select conc as the Dependent variable and CTRL-click to
select vel and state as the Independent variables. As a
third way of generating a formula, click the Create Formula
button, select conc as the Response variable, and CTRL-click
to select vel and state as the Main Effects. You can use the
Create Formula button to create complicated linear models
and learn the notation for model specifications. The on-line
help discusses formula creation in detail.
4. On the Plot page of the dialog, select Cond. Plots of Fitted
vs Predictors. This type of plot displays a separate plot in
one variable for different subsets of another variable. In our
case, it plots a separate curve for each level of state.
5. Click OK.
A summary of the loess model is presented in the Report window,
and a Graph window displays the conditional plot.
Nonlinear
Regression
296
Nonlinear regression uses a specific nonlinear relationship to predict a
continuous variable from one or more predictor variables. The form
of the nonlinear relationship is usually derived from an applicationspecific theoretical model.