Trend Prediction Service - Basics - Developer Documentation - Developer Documentation

# Trend Prediction Service – Basics¶

This section explains the regression algorithms used by the Trend Prediction Service.

## Linear Regression¶  Linear regression assumes a linear dependence between a single target variable (y) and one or more independent variables (x1, x2,..., xn):

y = β0 + β1x1 + β2x2 + … + βnxn.

For a single independent variable x, the model is given by y = β0 + β1x.

While not very complex, the approach has proven to be a powerful method for early detection of the potential faults. The results produced by the algorithm are both easy to interpret and to visualize.

When using multivariate input, the algorithm expects that all independent variables are available at any time.

## Polynomial Regression¶  Polynomial regression assumes a polynomial dependence between a single target variable (y) and one or more independent input variables (x1,x2,...,xn). The degree d of the polynomial has to be selected beforehand:

y = β0 + β11x1 + ... + βn1xn + ... + βd1x1d ... + βndxnd.

For a single independent variable x, the relationship is given by y = β0 + β1x + β2x2 + … + βnxn.

This approach can capture more complex relationships between the variables than a linear model at the expense of an increased computational complexity and the need for specifying the degree of the polynomial to be fitted.

In the case of the multivariate input, the algorithm expects that all independent variables are available at any time.

Last update: December 1, 2023