# 19 Non-linear Models

## Overview

Here we’ll explore the logistic regression model and a function for least-squares fitting of arbitrary non-linear functions.

Objectives

Upon completion of this lesson, you should be able to:

- Recognize when a logistic model would be appropriate
- Fit a logistic model to proportion (group) data
- Fit a logistic model to binary (individual) data
- Interpret coefficients of the logistic model
- Fit arbitrary non-linear models using
`nls()`

## Data and R Code Files

The R code file and data files for this lesson can be found on the Essential R - Notes on learning R page.

## 19.1 A Brief Definition of the Logistic Model

Here we’ll discuss the baxic background assumptions of the logistic regression model.

## 19.2 Fitting a Logistic Model

In this video, we’ll examine a data set which shows group proportions (so any value between 0 and 1 is possible) and fit a logistic regression to the data.

## 19.3 Interpreting the Coefficients of the Logistic Model I

Now we’ll interpret the coefficients of the model we fit in the last video.

## 19.4 Interpreting the Coefficients of the Logistic Model II

In this video, we’ll plot our regression model over the data and add our midpoint as calculated from the coefficients.

## 19.5 Logistic Regression on Individual Data I

We’ll try a different data set now, where each case is binary (either “a” or “b”), but we’ll see we can still fit a logistic regression.

## 19.6 Logistic Regression on Individual Data II

We’ll wind up our discussion of logistic regression by examining the model we fit in the last video.

## 19.7 Other Non-linear Models Using `nls()`

Now we can move on to introduce `nls()`

for fitting “non-linear least squares” models. We’ll demonstrate with some data for enzyme kinetics that exhibit Michaelis-Menten dynamics.

## 19.8 Interpreting an `nls()`

Model

Here we’ll examine the object created by `nls()`

.

## 19.9 Using `anova()`

on `nls()`

Models

Finally we’ll demonstrate the use of `anova()`

for comparison of nested `nls()`

models.