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,..., x_n):

y = β₀ + β₁x₁ + β₂x₂ + … + β_nx_n.

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,...,x_n). The degree d of the polynomial has to be selected beforehand:

y = β₀ + β₁₁x₁ + ... + β_n1x_n + ... + β_d1x₁^d ... + β_ndx_n^d.

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

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.

Except where otherwise noted, content on this site is licensed under the Development License Agreement.