Regression
The Regression method calculates parameters for functional dependencies of a Dependent Time Series (explained variable or regressand) and an Independent Time Series or several Independent Time Series (explanatory variables or regressors).
According to your assumption, you choose whether the functional relationship to be determined is a linear, polynomial, or exponential dependence (see following table).
| Functional Correlation | Function to Be Adapted | Calculated Parameters |
|---|---|---|
| Linear | \(y(x_1, ..., x_n)=a_0+a_1x_1+...+a_nx_n\) | \(a_0, a_1, ..., a_n\) |
| Polynomial | \(y(x_1, ..., x_n)=P(x_1, ..., x_n)\) | Coefficients of the polynomial \(P\) |
| Exponential | \(y(x)=a⋅exp(bx)\) | \(a,b\) |
Here \(P\) is a polynomial of a given degree. Exponential correlation can only be calculated for an independent time series, because the functional correlation is transferred into a linear regression model by logarithmizing.
The mean squared difference between the dependent time series and the selected function, applied to the independent time series, is minimized.
One of the two result time series demonstrates the parameters for the function. In linear regression, it contains the regression line.
The second result time series represents the difference between the given (e.g., measured) data and the values lying on the regression curve.
The equation for calculating the regression from the parameters of the function is displayed in a results window and in the Properties window of the result time series under Data Source. These specifications can be copied from the Properties window and used for further calculations.
The following figure illustrates schematically how the regression is determined.
Applying the Method
To start the method, select Methods → Analyze time series → Regression from the menu bar or the context menu of the time series in the Project Explorer (see the following figure).
In the window that opens (see figure below), select the Dependent Time Series, the Independent Time Series, and the type of Functional Relation.
For the Polynomial Dependence, Degree bounds must also be applied by selecting a Minimum and a Maximum, and it must be determined whether to Include mixed terms (see following figure).
Examples
The following example shows the regression of the Dependent Time Series Heat Demand and the Independent Time Series Air Temperature 2011 assuming a Linear Dependence.
In the Result window the equation for the linear regression is displayed (see second figure in the previous slider). This information can be copied from the Properties window (see third figure in the previous slider) for further processing.
The result time series, which contains the linear regression line, is given the suffix _Regression_linear by default. The result time series, which contains the deviation, receives the suffix _Error_linear by default.
The following example shows the result time series of a linear regression in Plot Window 1 and the corresponding Result window.
The following example shows the two result time series of a polynomial regression in Plot Window 1 and the corresponding Result window.
For polynomial models, if the Degree bounds are too generous or if the selected model approach does not fit the data, the following warning appears.
