In this article
Linear Regression is one of a number of statistical tools that are used to understand how an objective is driven by other variables; for example how "employee satisfaction" depends on salary, relationship with boss, levels of training etc. Perhaps in the example a manager would like to find out which of the variables has the greatest effect on employee satisfaction so that he/she can implement changes to improve the working environment in the company. The stronger the effect a variable has on the objective, the more “important” the variable is, and the analysis will allow the user to model the impact that changes in the variables will have on the objective.
Regression calculations are performed dynamically, based on any filter settings and/or report base settings in preview/view mode in Reportal. If the number of data rows available for the calculation exceeds the system limit (10.000), the “Case selection” setting for the regression run will be employed and 10.000 cases will be used in the calculation.
Linear Regression has two methods:
- Simple Regression (using just two variables)
- Multiple Regression (using several variables)
Note: The variables used in a Linear Regression must be Numeric variables or variables that contain a scale. Loop questions cannot be used in linear regression.
This type of analysis is also known as root cause analysis or driver analysis.
Note: Linear Regression results (the linear regression runs) can be accessed using scripting. Refer to the Forsta Scripting documentation for further details.
Note: If a report includes Linear Regression statistics and/or charts, these will be included in the export file if the report definition is exported (go to Exporting a Report Definition for more information) or if the report is exported to Excel or PowerPoint (2003 or 2007) (go to Exporting a Report for more information).
Two-Variable Regression
The Simple Regression analysis uses just two variables, a "dependent variable" and an "independent variable", where the hypothesis is that changes to the independent variable will directly effect the dependent variable in a linear relationship. These variables are plotted against each other on a chart, and a "best fit" linear relationship equation is derived which may have several coefficients. In the chart, the closer the data points are to the line, the better is the "fit" and the more important is the independent variable to the dependent variable (go to Linear Regression Example for more information).
Multiple Regression
The purpose of multiple regression is to learn more about the relationship between several independent variables and a dependent variable.
For example, a manager might use multiple regression procedures to determine the basic compensation for company employees. An analyst would identify a number of factors or dimensions such as "the amount of responsibility" or "number of people to supervise" that are believed to contribute to the value of a job, and would then usually conduct a salary survey among comparable companies, recording the salaries and respective characteristics (i.e. the values on dimensions) for different positions. This information can then be combined and used in a multiple regression analysis to build a regression equation, resulting in for example:
Salary = (0.5 * Responsibility) + (0.8 * No_Supervised)
Once this regression equation has been determined, the analyst can easily construct a graph of the expected (predicted) salaries for similar positions in similar companies, and the actual salaries of employees in the subject company. The analyst is then able to determine which positions are underpaid (below the regression line) or overpaid (above the regression line), or paid fairly. In this case, because multiple variables impact the regression, a direct linear relationship chart is not available.
The general expression is of the form:
Y = a + (b1* X1) + (b2* X2) + ... + (bp* Xp)
In this equation, the regression coefficients (or B coefficients) represent the independent contributions of each independent variable to the prediction of the dependent variable. The higher the B-coefficient, the greater the impact the variable has on the dependent variable. See the circled values in the illustration below here.
Figure 1 - Example of the results from a multiple regression run
To create a multiple regression model, add multiple variables in the Independent Variables field, separated by comma (e.g. q3,q4,q5,q6 etc.) - see above.