Summary

This operator performs a multiple linear regression analysis.

Method

Regression analysis is a statistical process for estimating the relationships among variables. Specifically, it is estimated, how the value of a criterion variable (dependent variable) changes when a predictor (independent variable) is varied. The estimation target is a function of the independent variables called the regression function. For more information see for example Wikipedia Regression Analysis.

Linear regression.svg

Source: https://en.wikipedia.org/wiki/Regression_analysis#/media/File:Linear_regression.svg

The operation "Regression Analysis" produces estimates for the coefficients of the independent variables, and an evaluation of the regression in form of a string. Additionally, it is possible to display different statistical measures regarding the regression analysis and plot the data.

Configuration

Input settings of existing table

Parameter

Value

Opt.

Description

Example

Identifier

System.Object

opt.

Observations will be grouped by the specified columns. For each group a regression analysis will be computed.

-

Independent variables (ind. var.)

System.Object

opt.

Columns, which contain the data for the independent variables. At most one of those columns may have a non-numeric type and must contain exactly two distinct values. The two values will be encoded 0-1.

-

Dependent variables (dep. var.)

System.Double

-

Numeric column, which contains the data for the dependent variable.

-

Inactive variables

System.Object

opt.

Inactive variables are removed from the regression model without modifying the structure of the event table. In this ways, operators or templates that build on this table structure continue to work even after the regression model has been modified.

-

Settings

Parameter

Value

Opt.

Description

Example

All numeric columns as independent variables

System.Boolean

-

All numeric columns (except the columns for the dependent variables and identifiers) are selected as independent variables.

-

System.Boolean

-

If selected, independent variables which don't have significant influence on the dependent variable are excluded via backward elimination. Whether variable has significant influence or not depends on its p-value and the limit specified under 'p-value variables'.

-

Show coefficients

System.Boolean

-

The coefficients of the independent variables calculated in the regression analysis are shown in the result.

-

Show p-values

System.Boolean

-

The p-values of the independent variables are shown in the result.

-

Show R² / ANOVA p-value

System.Boolean

-

Coefficient of determination R² and ANOVA p-value are shown in the result table

-

Show adjusted R²

System.Boolean

-

The adjusted R² is shown in the result table.

-

Show AIC

System.Boolean

-

The Akaike information criterion is shown in the result table.

-

Show BIC

System.Boolean

-

The Bayesian information criterion (BIC) is shown in the result table.


Want to learn more?

Examples

Situation

A company expects a linear relation between the number of employees and sales. Therefore, they measure the number of employees and the sales figures in different regions. 

This assumption shall be examined by calculating a linear regression analysis.

Settings

In this example, we chose the following settings:

Result

  • The results of the regression analysis are shown in the table below.
  • The absolute value of the coefficient "Employees" is greater or equal 1, and that the variable "Employees" has a significant effect on "Sales".
  • Therefore, also R², Adj. R², and the p-value of ANOVA fall into the ranges specified by us in the operation.
  • Based on these results, we assume a linear relationship between the number of employees and sales figures.
  • The coefficient "c Employees" in column C means that it is estimated that 1.637 additional units of sales are to be expected per additional employee.

Project File

-

Troubleshooting

Problem

Frequent Causes

Solutions

Error message or "n. def."

1. There are too few values to estimate this figure.


Create larger groups, or categories (= less differentiation by identifier categories).


2. An independent variable shows only one value and does not vary. No calculation is possible.


Do not use this independent variable, since it does not vary (requirement for regression analysis).


3. Two or more variables are linearly dependent. E.g.,

  • TOTAL = A + B
  • A = 3*B - TOTAL

Using A,B, and TOTAL as independent variables does not allow to distinguish between the effects of each single variable. 

Do not use any of these variables (only independent variables).

Error message

If the option "Select all numeric columns is set", the semantics of each column needs to be set to "Number"

Use the operator Format columns and change the semantics.


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