## Regression Basics

Regression is a statistical technique used to predict the value of a dependent variable based on the value of one or more independent variables. In other words, a regression can be used to find the relationship between variables. The two main types of regression are linear and nonlinear.

### What is regression?

Regression is a statistical tool used to understand the relationship between variables. In its simplest form, regression allows you to estimate how a dependent variable (usually denoted by Y) changes as an independent variable (usually denoted by X) changes.

For example, you could use regression to estimate how GPA changes as class size increases. However, regression can be used to estimate the relationship between two variables even if cause and effect cannot be assumed. In this case, GPA and class size would be considered simultaneously.

There are two main types of regression: linear and nonlinear. Linear regression estimates the relationship between two variables by fitting a straight line, or linear equation, to the data. Nonlinear regression estimates the relationship between two variables by fitting a curved line, or nonlinear equation, to the data.

### Types of regression

There are two main types of regression: linear and nonlinear. Linear regression produces a straight line on a graph, while nonlinear regression produces a curve. The type of regression you use will depend on the type of data you have and the results you are hoping to achieve.

## Regression Properties

In statistics, regression is a mathematical model that predicts a dependent variable based on an independent variable. The two main types of regression are linear and nonlinear. Linear regression is when the dependent variable is a linear function of the independent variable. Nonlinear regression is when the dependent variable is a nonlinear function of the independent variable.

### Linearity

One important property of linear regression is that it is linear in its parameters. This means that if we have a model with two parameters, w_1 and w_2, then the model will be of the form:

y = w_1 * x_1 + w_2 * x_2

where y is the dependent variable, x_1 and x_2 are the independent variables, and w_1 and w_2 are the model parameters.

Another important property of linear regression is that it is additive. This means that if we have a model with two independent variables, x_1 and x_2, then the effect of x_1 on the dependent variable y will be independent of the value of x_2. In other words, the effect of x_1 on y will be the same whether x_2 is 0 or 1.

### Additivity

In regression, additivity is the property that the response variable is a linear combination of the predictor variables. In other words, the response variable can be decomposed into a sum of contributions, each of which is associated with a particular predictor variable. Additivity is a strong simplifying assumption that makes regression easier to understand and interpret. It also makes it easier to fit models to data, because many statistical software packages assume additivity when fitting models.