By fitting a linear equation to the observed data, linear regression models try to represent the relationship between two variables. These models are an effective way to describe complex relationships between variables. The first variable is the explanatory variable, with the second as the dependent variable.

A simple example of how one might use linear regression models is to relate the mass of a vehicle to its length. While a model may demonstrate that there is a statistically significant relationship between two variables, it does not mean that this relationship is causal. For example, larger seed size does not cause a larger plant to grow.

Types of Linear Regression Models

When constructing linear regression models and the relationship between the variables, it is best to base your design on theory. You should test for a relationship between the variables that you are considering for inclusion in your model--one way to do so is with a scatter plot. If no relationship is found between the variables, then these data are not likely to create a useful model.

A second method to construct your model is data mining. Rather than start with a theoretical basis, this method lets the data dictate the structure of the model. While this is useful in some circumstances, it is recommended that you focus on theory-based models.