Track C — Chapter 15 Problem Set (Correlation)

This problem set gives practice with correlation, including:

  • Pearson correlation (r) and interpretation

  • Correlation matrices

  • The third-variable problem

  • Partial correlation (controlling for a third variable)

Prerequisite

Complete the Chapter 15 lab first:

How to run

From the repository root:

python -m scripts.psych_ch15_problem_set

Run a single exercise:

python -m scripts.psych_ch15_problem_set --exercise 1
python -m scripts.psych_ch15_problem_set --exercise 2
python -m scripts.psych_ch15_problem_set --exercise 3

What you should submit

For each exercise:

  1. Report Pearson r, degrees of freedom, and p-value.

  2. Report and interpret the 95% CI for r.

  3. Write a short interpretation (2–4 sentences): - direction and strength, - what the scatterplot would look like, - whether the relationship is practically meaningful.

For Exercise 3: - Explain why correlation does not imply causation (third-variable problem). - Report the partial correlation controlling for Z and interpret the difference.

Exercises

Exercise 1 — Strong positive correlation

A dataset with a clear positive linear relationship.

Goal: - large positive r and a highly significant p-value.

Exercise 2 — Near-zero correlation

A dataset where x and y are unrelated.

Goal: - r close to 0 and typically non-significant.

Exercise 3 — Third-variable problem (partial correlation)

x and y share a common cause z, producing a strong raw correlation.

Goal: - strong raw correlation for x–y, - partial correlation controlling z near zero.