Linear regression is one of the oldest and most fundamental types of statistical analysis. A linear regression model is a type of generalized linear model (as are logistic regression, log-linear models, and multinomial response models). It shows the relationships between a set of observed variables.
When a linear regression model is adequate, it is better than a more sophisticated model like a decision tree.
There is a rich set of statistics available to explore the nature of any linear regression model.
By transforming a variable—for example, by taking its exponent, log, or square—and building a linear regression model, you might be able answer questions like these:
- Is there a linear relationship between each observed variable and the variable to predict?
- If not, is there another type of relationship that does?
- Which variables help predict the target dependent variable?
Sometimes you can create an essentially nonlinear model by using linear regression on transformed data. For example, piecewise linear regression, a sophisticated form of regression, builds nonlinear models of nonlinear phenomena.