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# Performance (Regression) (RapidMiner Studio Core)

## Synopsis

This operator is used for statistical performance evaluation of regression tasks and delivers a list of performance criteria values of the regression task.## Description

This operator should be used for performance evaluation of regression tasks only. Many other performance evaluation operators are also available in RapidMiner e.g. the Performance operator, Performance (Binominal Classification) operator, Performance (Classification) operator etc. The Performance (Regression) operator is used with regression tasks only. On the other hand, the Performance operator automatically determines the learning task type and calculates the most common criteria for that type. You can use the Performance (User-Based) operator if you want to write your own performance measure.

Regression is a technique used for numerical prediction and it is a statistical measure that attempts to determine the strength of the relationship between one dependent variable ( i.e. the label attribute) and a series of other changing variables known as independent variables (regular attributes). Just like Classification is used for predicting categorical labels, Regression is used for predicting a continuous value. For example, we may wish to predict the salary of university graduates with 5 years of work experience, or the potential sales of a new product given its price. Regression is often used to determine how much specific factors such as the price of a commodity, interest rates, particular industries or sectors influence the price movement of an asset. For evaluating the statistical performance of a regression model the data set should be labeled i.e. it should have an attribute with *label* role and an attribute with *prediction* role. The *label* attribute stores the actual observed values whereas the *prediction* attribute stores the values of *label* predicted by the regression model under discussion.

## Input

- labeled data
This input port expects a labeled ExampleSet. The Apply Model operator is a good example of such operators that provide labeled data. Make sure that the ExampleSet has the label and prediction attribute. See the Set Role operator for more details regarding the label and prediction roles of attributes.

- performance
This is an optional parameter. It requires a Performance Vector.

## Output

- performance
This port delivers a Performance Vector (we call it output-performance-vector for now). The Performance Vector is a list of performance criteria values. The Performance vector is calculated on the basis of the label and prediction attribute of the input ExampleSet. The output-performance-vector contains performance criteria calculated by this Performance operator (we call it calculated-performance-vector here). If a Performance Vector was also fed at the performance input port (we call it input-performance-vector here), the criteria of the input-performance-vector are also added in the output-performance-vector. If the input-performance-vector and the calculated-performance-vector both have the same criteria but with different values, the values of the calculated-performance-vector are delivered through the output port. This concept can be easily understood by studying the Example Process of the Performance (Classification) operator.

- example set (IOObject)
The ExampleSet that was given as input is passed without changing to the output through this port. This is usually used to reuse the same ExampleSet in further operators or to view the ExampleSet in the Results Workspace.

## Parameters

- main_criterionThe main criterion is used for comparisons and needs to be specified only for processes where performance vectors are compared, e.g. attribute selection or other meta optimization process setups. If no
*main criterion*is selected, the first criterion in the resulting performance vector will be assumed to be the*main criterion*. Range: - root_mean_squared_errorThe averaged root-mean-squared error. Range: boolean
- absolute_errorThe average absolute deviation of the prediction from the actual value. The values of the
*label*attribute are the actual values. Range: boolean - relative_errorThe average relative error is the average of the absolute deviation of the prediction from the actual value divided by actual value. Values of the
*label*attribute are the actual values. Range: boolean - relative_error_lenientThe average lenient relative error is the average of the absolute deviation of the prediction from the actual value divided by the maximum of the actual value and the prediction. The values of the
*label*attribute are the actual values. Range: boolean - relative_error_strictThe average strict relative error is the average of the absolute deviation of the prediction from the actual value divided by the minimum of the actual value and the prediction. The values of the
*label*attribute are the actual values. Range: boolean - normalized_absolute_errorThe absolute error divided by the error made if the average would have been predicted. Range: boolean
- root_relative_squared_errorThe averaged root-relative-squared error. Range: boolean
- squared_errorThe averaged squared error. Range: boolean
- correlationReturns the correlation coefficient between the
*label*and*prediction*attributes. Range: boolean - squared_correlationReturns the squared correlation coefficient between the
*label*and*prediction*attributes. Range: boolean - prediction_averageReturns the average of all the predictions. All the predicted values are added and the sum is divided by the total number of predictions. Range: boolean
- spearman_rhoThe rank correlation between the actual and predicted
*labels*, using Spearman's rho. Spearman's rho is a measure of the linear relationship between two variables. The two variables in this case are the*label*and the*prediction*attribute. Range: boolean - kendall_tauThe rank correlation between the actual and predicted
*labels*, using Kendall's tau-b. Kendall's tau is a measure of correlation, and so measures the strength of the relationship between two variables. The two variables in this case are the*label*and the*prediction*attribute. Range: boolean - skip_undefined_labelsIf set to true, examples with undefined
*labels*are skipped. Range: boolean - comparator_classThis is an expert parameter. Fully qualified
*classname*of the*PerformanceComparator*implementation is specified here. Range: string - use_example_weightsThis parameter allows example
*weights*to be used for statistical performance calculations if possible. This parameter has no effect if no attribute has the*weight*role. In order to consider*weights*of examples the ExampleSet should have an attribute with the*weight*role. Several operators are available that assign*weights*e.g. the Generate Weights operator. Study the Set Roles operator for more information regarding the*weight*role. Range: boolean

## Tutorial Processes

### Applying the Performance (Regression) operator on the Polynomial data set

The 'Polynomial' data set is loaded using the Retrieve operator. The Filter Example Range operator is applied on it. The first example parameter of the Filter Example Range parameter is set to 1 and the last example parameter is set to 100. Thus the first 100 examples of the 'Polynomial' data set are selected. The Linear Regression operator is applied on it with default values of all parameters. The regression model generated by the Linear Regression operator is applied on the last 100 examples of the 'Polynomial' data set using the Apply Model operator. Labeled data from the Apply Model operator is provided to the Performance (Regression) operator. The absolute error and prediction average parameters are set to true. Thus the Performance Vector generated by the Performance (Regression) operator has information regarding the absolute error and prediction average in the labeled data set. The absolute error is calculated by adding the difference of all the predicted values from actual values of the label attribute, and dividing this sum by the total number of predictions. The prediction average is calculated by adding all the actual label values and dividing this sum by the total number of examples. You can verify this from the results in the Results Workspace.