Factor Analysis Example

Factor Analysis Example

Problem Statement

We have collected data on several different models of cars with respect to several parameters. Determine which factors can be treated together using Factor Analysis.

How to perform analysis

Step 1: Open Sigma Magic
  1. Click on the Sigma Magic button on the Excel toolbar.
  2. Click on the New button to create a new project.
Step 2: Add the analysis template
  1. Click on the Tool Wizard to add the analysis template.
  2. Click on Analytics and then on Factor Analysis.

                                                                                                                                                                                 
Step 3: Specify analysis options
A new worksheet will be added to your workbook. Analysis Setup will be automatically opened, in the setup tab specify the survey results.


Click on Data to specify the data required for this analysis.



Click the Verify tab to ensure all the inputs are okay and shown in a green checkmark.


Step 4: Generate analysis result
Click OK and then click Compute Outputs to get the final results.


Interpretation of Results

  • The Scree Plot and Eigenvalues suggest selecting 2 or 3 factors, as the elbow point occurs around the second or third component.
  • The Eigenvalues > 1 rule supports retaining 3 factors, as seen in the table.
  • The factor loadings table indicates how strongly each variable correlates with the extracted factors.
  • Factor 1: Gear (0.92), AM (0.85), and Drat (0.79) strongly load onto this factor.
  • Factor 2: HP (0.77), Cyl (0.74), and Disp (0.58) dominate this factor.
  • Factor 3: Carb (0.65), HP (0.45), and WT (0.54) contribute here.
  • Varimax Rotation is used to simplify factor structure by reducing cross-loadings.
  • This helps in achieving clearer groupings for easier interpretation.
  • Factor 1 relates to transmission and efficiency (Gear, AM, Drat).
  • Factor 2 represents engine power and performance (HP, Cyl, Disp).
  • Factor 3 seems to capture weight and fuel-related aspects (Carb, WT, HP).
  • The factor scores (Regression method) allow ranking observations based on their factor influences.
  • Can be used in clustering, predictive modeling, or segmentation.
  • Identifies key groups affecting vehicle performance.
  • Helps optimize vehicle design by focusing on distinct categories.
  • Useful for market research, customer segmentation, and automotive analysis. 

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