Non-Linear Regressions (Exponential, Quadratic, etc.)

(Video) The Basics of Nonlinear Regression

by TileStats

In this video by TileStats, you will learn about the basics of nonlinear regressions for a number of polynomials.

Non-Linear Regressions

Regressions are ways that we can predict things, like the weather or the price of your favorite video game. Regressions help us to understand relationships between different things (think: variables). There are two main types of variables we will focus on in this lesson. The first is the dependent variable, or the response variable. This is the variable we want to predict or understand. For example, it could be the height of a plant. The second is the independent variable, or the predictor variable. This is what you make to use to make the predictions. For example, it could be the amount of sunlight the plant receives.

So far, we've been talking about linear regressions. However, when two variables relate to each other, they could have a non-linear relationship.

Non-Linear Models

Sometimes, things don't follow a simple pattern, like we saw with linear models. This is where nonlinear regressions models come into play. These models can handle nonlinear relationships where the pattern curves or bends.

For example, if you were studying how the height of a plant changes with different amounts of water, you might find that after a certain point, more water doesn't help the plant grow taller - it might even hurt it! This kind of relationship can be represented with nonlinear functions, which look different from straight lines.

When we talk about fitting the data, we mean finding the best way to describe the relationship using a mathematical model. For nonlinear regression, we use nonlinear models to find the best curve that matches our data. Think back to the nonlinear models you've learned: quadratic, exponential, parametric, etc.

When we create a model, we need to find out certain values, called parameter estimates. These help to define our nonlinear model. For example, we might find specific numbers that describe how steep or flat our curve is. We may also use higher order models to better fit our data. This means using more complicated equations, like quadratics or exponentials, which can capture the curves in our data.

Looking Further

Sometimes, we have more than one independent variable. For instance, if you wanted to know how both sunlight and water affect plant heigh, you would use multiple linear regression. Even though we're talk about linear regression here, it's a step toward understanding how complex models work. You don't need to worry about this right now - you'll learn about these types of models further on in your math career!