Like exponential and logarithmic growth, logistic growth increases over time. One of the most notable differences with logistic growth models is that, at a certain point, growth steadily slows and the function approaches an upper bound, or limiting value. Because of this, logistic regression is best for modeling phenomena where there are limits in expansion, such as availability of living space or nutrients.

It is worth pointing out that logistic functions actually model resource-limited exponential growth. There are many examples of this type of growth in real-world situations, including population growth and spread of disease, rumors, and even stains in fabric. When performing logistic regression analysis, we use the form most commonly used on graphing utilities:

Recall that:

• [latex]\frac{c}{1+a}[/latex] is the initial value of the model.
• when b > 0, the model increases rapidly at first until it reaches its point of maximum growth rate, [latex]\left(\frac{\mathrm{ln}\left(a\right)}{b},\frac{c}{2}\right)[/latex]. At that point, growth steadily slows and the function becomes asymptotic to the upper bound y = c.
• c is the limiting value, sometimes called the carrying capacity, of the model.