Correlation Is Not Cause

Part of the Statistics for ML section of Coddy's Machine Learning journey. Lesson 33 of 64.

r only sees straight lines. Here y is fully decided by x, yet r is 0:

A scatter plot of y = x squared for x from -3 to 3: a perfect U of points, titled r = 0.0

The falling half cancels the rising half. An r near 0 means no straight line, not no relationship: plot before you drop a feature.

And one far point can fake a strong r, so check outliers first:

Eight blue points in a loose blob near 4 across and 5 up with r = -0.27, and one red point far away at 20 and 25. With it, r jumps to 0.95

Finally, r never proves a cause. Older children have bigger shoes and read better: age, a hidden third variable, drives both.

Challenge

Medium

A tea shop tests its cups: steep and taste for 9 cups (steeping minutes, score), sugar and score for 10 others (sugar cubes, score). The program reads one extra cup's sugar, then score.

Print the r of steep and taste.
Print the r of sugar and score, then with the extra cup added.

Round to 2 decimals, labelled as below. For another shop and extra cup 10, 2.0:

Steeping r: -0.05
Sugar r: -0.23
Sugar r with the extra cup: -0.88

Try it yourself

import numpy as np

# Steeping time in minutes and taste score of 9 cups
steep = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9])
taste = np.array([3.1, 5.0, 6.6, 7.7, 8.1, 7.6, 6.5, 5.1, 3.4])

# Sugar cubes and taste score of 10 other cups
sugar = np.array([0, 2, 1, 3, 0, 2, 1, 3, 2, 1])
score = np.array([6.5, 5.8, 7.4, 6.1, 5.9, 7.0, 6.2, 6.8, 6.4, 5.7])

# The extra cup
extra_sugar = float(input())
extra_score = float(input())

# Write your code below

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Statistics for ML

3Probability by Simulation

Probability as Frequency The Law of Large Numbers Sums of Dice Expected Value Conditional Probability Recap: Dice Stall Odds

6Relationships

Reading Scatter Plots Correlation Correlation Matrix Correlation HeatmapsCorrelation Is Not CauseRecap: Ice Cream and Sun

9Feature Scaling

Why Scale Features Min-Max Scaling Standardization StandardScaler Recap: Climbing Partners

12Final Challenges

Train Delays Air Quality Wine Chemistry Clinic Survey

Practice on your own: Online Python compiler