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# Regression analysis

## 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. 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.

## Example: Does the employee count predict sales?

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. In this example, we chose the following settings: The results of the regression analysis are shown in the table below.The evaluation '* * ***' in column H shows that 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. Confluence Op Regression.gzip

This operator performs a multiple linear regression analysis.

### Columns of input table

ParameterValueOpt.DescriptionExample
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.-

### Parameter

ParameterValueOpt.DescriptionExample
Coefficients

System.Double

-If an estimated coefficient in the absolute value is larger or smaller than the defined value, a * is appended to the description string. Otherwise a - is appended.-
p-Value variables

System.Double

-If the p-value for an independent variable is greater than or equal to the specified value, a * sign will be appended to the description string, otherwise a - will be appended.-
@RSQUARED

System.Double

-If R² is greater than or equal to the specified value, a * sign will be appended to the description string, otherwise a - will be appended.-

System.Double

-If the adjusted R² is greater than or equal to the specified value, a * sign will be appended to the description string, otherwise a ! will be appended.-
ANOVA p-value

System.Double

-If the p-value of the ANOVA is less than or equal to the specified value, a * sign will be appended to the description string, otherwise a - will be appended.-
Select all numeric columns

System.Boolean

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

System.Boolean

-If selected, estimated values for the dependent variable above the arithmetic means and/or medians of the individual dependent variables are calculated and shown.-
Coefficients (i. v.)

System.Boolean

-The coefficients of the independent variables calculated in the regression analysis are shown in the result.-
p values (ind. var.)

System.Boolean

-The p-values of the independent variables are shown in the result.-
Statistics (ind. var.)

System.Boolean

-Arithmetic mean, median, standard deviation, variance, skew and kurtosis of the data for independent variables are shown.-
Min/Max/Quantile (ind. var.)

System.Boolean

-Minima, maxima and various quantiles (10%, 25%, 50%, 75%, 90%) of the data for the independent variables are shown.-
Statistics (dep. var.)

System.Boolean

-Arithmetic mean, median, standard deviation, variance, skew and kurtosis of the data for dependent variables are shown. Additionally, the number of observations and the p-value from the Anderson-Darling test on normal distribution are output.-
Min/Max/Quantile (dep. var.)

System.Boolean

-Minimum, maximum and various quantiles (10%, 25%, 50%, 75%, 90%) of the data for the dependent variables are shown.-
R² / p-value ANOVA

System.Boolean

-R-squared R² ANOVA p-value are shown in the result.-

System.Boolean

-The modified R-squared is shown in the result.-
Evaluation

System.Boolean

-Show description string-

### Example 2: Multivariate linear regression

Situation The company from example 1 provides a training for their employees, and assumes that it has a positive effect on the resulting sales. Therefore, the number of employees, their training status (yes/no), and sales figures are measured in different regions. We now want to calculate a regression model which includes only significant predictors of the sales figures. Furthermore, we want to estimate the average sales in case the significant factors are increased by one. In this example, we chose the following settings: The table below shows the results of the regression analysis.For the variable "Training", p-value was > 0.1 (our limit chosen in the settings), and it was therefore excluded from the regression model automatically.Based on the results, the sales figures are predicted to increase from 101.7 (Sales Median in column J) to 104 (Sales estimated in column K) if an additional employee is hired. ProblemFrequent CausesSolutions
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 messageIf 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.