Regression predictive modeling is the task of approximating a mapping function (f) from input variables (X) to a continuous output variable (y).

A continuous output variable is a real-value, such as an integer or floating point value. These are often quantities, such as amounts and sizes.

For example, a house may be predicted to sell for a specific dollar value, perhaps in the range of $100,000 to $200,000.

- A regression problem requires the prediction of a quantity.
- A regression can have real valued or discrete input variables.
- A problem with multiple input variables is often called a multivariate regression problem.
- A regression problem where input variables are ordered by time is called a time series forecasting problem.

Because a regression predictive model predicts a quantity, the skill of the model must be reported as an error in those predictions.

There are many ways to estimate the skill of a regression predictive model, but perhaps the most common is to calculate the root mean squared error, abbreviated by the acronym RMSE.

For example, if a regression predictive model made 2 predictions, one of 1.5 where the expected value is 1.0 and another of 3.3 and the expected value is 3.0, then the RMSE would be:

RMSE = sqrt(average(error^2))

RMSE = sqrt(((1.0 - 1.5)^2 + (3.0 - 3.3)^2) / 2)

RMSE = sqrt((0.25 + 0.09) / 2)

RMSE = sqrt(0.17)

RMSE = 0.412

A benefit of RMSE is that the units of the error score are in the same units as the predicted value.

An algorithm that is capable of learning a regression predictive model is called a regression algorithm.

Some algorithms have the word “regression” in their name, such as linear regression and logistic regression, which can make things confusing because linear regression is a regression algorithm whereas logistic regression is a classification algorithm.