Segmented regression

Segmented regression analysis can also be performed on multivariate data by partitioning the various independent variables.

The breakpoint can be interpreted as a critical, safe, or threshold value beyond or below which (un)desired effects occur.

The breakpoint can be important in decision making [1] The figures illustrate some of the results and regression types obtainable.

The least squares method applied separately to each segment, by which the two regression lines are made to fit the data set as closely as possible while minimizing the sum of squares of the differences (SSD) between observed (y) and calculated (Yr) values of the dependent variable, results in the following two equations: where: The data may show many types or trends,[2] see the figures.

[5] The coefficient of determination for all data (Cd), that is to be maximized under the conditions set by the significance tests, is found from: where Yr is the expected (predicted) value of y according to the former regression equations and Ya is the average of all y values.