主成分分析是否需纳入因变量？R语言降维场景下的GPA取舍疑问

Question 1: Should the dependent variable be included when performing PCA? #

Short answer: No, you should not include the dependent variable in your PCA analysis.

PCA is an unsupervised dimensionality reduction technique—it focuses on identifying patterns and variance within the set of predictor (independent) variables alone, without considering their relationship to a dependent variable. Including the dependent variable would skew the principal components to account for variance tied to the outcome you're ultimately trying to predict, which defeats the purpose of using PCA to simplify your predictor set. The goal here is to capture the underlying structure in your predictors, not mix that with variation specific to the response.

Question 2: For your GPA dataset, should we keep or remove GPA from the CSV when running PCA in R? #

Following the logic above, you must remove the GPA column from your dataset before performing PCA. GPA is your dependent variable, and including it would contaminate the principal components with variance linked to the outcome you care about, rather than focusing on the structure of your predictors (饮酒量, 学习时长, IQ, SAT分数).

Here's a straightforward example of how to handle this in R:

# Load your dataset
student_data <- read.csv("student_data.csv")

# Subset to retain only independent variables for PCA
predictor_data <- student_data[, c("饮酒量", "学习时长", "IQ", "SAT分数")]

# Run PCA (scaling is critical here—variables are on different scales!)
pca_output <- prcomp(predictor_data, scale. = TRUE)

# Review summary of the principal components
summary(pca_output)

A quick reminder: Using scale. = TRUE is non-negotiable here. PCA is highly sensitive to variable scales—for example, IQ (0-160) and SAT (400-1600) operate on very different ranges. Scaling ensures each variable contributes equally to the variance calculation, so your principal components aren't dominated by the largest-scale variable.

内容的提问来源于stack exchange，提问作者JungleDiff