Using Principal Components Analysis (PCA) to Analyze
Latino Stress by Agricultural Season and Occupation
Wade K. Copeland
October 13, 2025
Introduction
Outline
What is PCA?
General Description
Geometric Interpretation
Application
Description
Output
Graphical Interpretation
Inference
What is PCA?
General Description Part 1
PCA is an exploratory data dimension reduction technique.
Exploratory – No a priori assumptions about the structure of the
data. Because of this, we say PCA is an unsupervised machine learning
method.
Dimension Reduction – Some data sets have a large number of
variables or features. PCA provides a way of reducing a large feature
space into a few summary variables.
General Description Part 2
PCA creates axes that explain decreasing amounts of variation in the
data.
The first PC axis (PC1) is the direction of most variation. The
second PC axis (PC2) explains the second most variation and is
orthogonal to PC1.
Orthogonality means the PC axes are uncorrelated.
There are as many PC axes as there are variables in the data.
Together, the PC axes explain 100% of the observed variation in the
data.
2-Dimensional PCA Example
Simulated Data
What is the direction of most variability for x1 and x2?
PC1
What is the direction that explains the second most amount of
variation?
