Dimension reduction methods have the goal of using the correlation structure among the predictor variables to accomplish which of the following:
a. To reduce the number of predictor components
b. To help ensure that these components are dependent
c. To provide a framework for interpretability of the results
d. To help ensure that these components are independent
e. To increase the number of predictor components
Choose the correct answer from the options given below:
✅ Correct answer: a, c and d only
✅ Explanation:
Dimension reduction methods (like Principal Component Analysis (PCA), Factor Analysis, etc.) aim to simplify high-dimensional data by leveraging the correlation structure among predictor variables. Let’s examine each statement:
🔹 a. To reduce the number of predictor components ✅
✔ True
This is the main purpose of dimension reduction — reducing a large set of variables to a smaller set of representative components, while retaining the most important information.
🔹 b. To help ensure that these components are dependent ❌
✘ False
Dimension reduction methods (especially PCA) aim to produce independent or uncorrelated components, not dependent ones.
🔹 c. To provide a framework for interpretability of the results ✅
✔ True
By simplifying the data into fewer dimensions, it becomes easier to interpret patterns, relationships, and clusters in the data.
🔹 d. To help ensure that these components are independent ✅
✔ True
Especially in PCA, the resulting principal components are orthogonal (i.e., uncorrelated), ensuring statistical independence.
🔹 e. To increase the number of predictor components ❌
✘ False
The goal is the opposite — to reduce, not increase, the number of components.
✅ Final Answer: a, c and d only ✅