Linear Regression - Data360_Analyze - Latest

Models data using linear regression allowing identification of data trends.

This node uses the embedded R engine to model the relationship between a dependent (response) variable and one or more independent (explanatory) variables.

The node fits the data using a linear regression model.

The node provides two summaries of the model created for the input data together with details of the regression coefficients and residual errors.

The Summary pin contains a summary of the model and includes information on:

• The call used to generate the model.
• Range and quartile values for the residual errors.
• The estimates for the coefficients of the independent variables used in the model and the estimate of the intercept, the standard error, the t-statistic value and p-value.
• Significance code indicators for the independent variables and the intercept.
• The residual standard error.
• The Multiple R-squared (coefficient of determination) value and Adjusted R-squared value.
• The F-statistic with the corresponding p-value for that test.

If the node is configured to output the serialized model to a file, the Summary pin also includes the file path to the file that contains the serialized model.

The Residuals pin contains the value of the residual error for the difference between each of the observations in the input data and the fitted values derived by the model.

The Coefficients pin contains the estimated values of the coefficients of the independent variables and the intercept for the best-fit line determined by the model.

The anovaSummary pin contains a summary table for an Analysis Of Variance performed on the regression model and includes information on:

• Details of the Degrees of Freedom, Sum of Squares, Mean of Squares, F-value and p-value for each of the independent variables in the regression model.
• The Degrees of Freedom, Sum of Squares and Mean of Squares for the Residuals.
• An indication when the model may be unbalanced.
• Significance code indicators for the independent variables.

The ModelFormula property can be used to provide fine-grain control of the specification of the variables to be included in the regression analysis.

The basic format of the model formula is:

dependent variable ~ independent variables

where the ~ indicates the dependent variable "is modeled by" or "is modeled as a function of" the independent variable.

A simple linear regression could have a model formula of:

y ~ x

Similarly, a multiple linear regression with two independent variables could use the following formula:

y ~ x + z

Note that the operators used in a model formula do not have their normal mathematical meaning. In this case, the "+" means "include this variable".

The model formula supports the use of other operators too, for example:

y ~ x * z

which indicates that in addition to including the "x" and the "z" variable in the model, the interaction between the "x" and "z" variables should also be included in the model.

The * operator can be useful in a range of scenarios, for instance, if the "z" was a categorical variable (e.g. field with a boolean or string data type) it could be used to create a model that estimated the regression coefficients for each level (category) in "z". That is, it implements a "group-by" function using the "z" variable. The coefficients generated by the node include the interaction terms for each level except the baseline factor. The lowest level (in terms of its alphanumeric value) in the categorical variable is used as the baseline factor for the interactions - the interaction coefficients for each of the other levels are then relative to the baseline coefficient. When used with the Predict Linear Regression node, the regression model can be used to predict outcomes for each level in the "group-by" variable.

Variables with alphanumeric levels are automatically considered to be categorical (factors). In the situation where a variable uses numeric values to indicate the levels (e.g. male=1, female=2) the model formula can be modified to indicate that the variable should be treated as a categorical variable when building the regression model by using the "as.factor()" function:

y ~ x * as.factor(z)

In the example given, the baseline factor level would be "1" i.e. male.

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