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Correlation

Correlation shows the strength of the relationship between two variables.

Correlation

Pearson correlation measures the linear relationship of two variables between -1 and 1: 1 is perfectly positive, -1 perfectly negative, 0 no linear relationship.

boy = np.array([160, 170, 180, 190])
kilo = np.array([55, 65, 72, 85])
print(np.corrcoef(boy, kilo)[0, 1])   # 0.99...

np.corrcoef returns a matrix; the diagonal is always 1 and [0, 1] is the value between the two variables.

Limits of correlation

Correlation only captures linear relationships. For a symmetric relationship like y = x², the correlation can be 0 even though there is full dependence:

x = np.array([-2, -1, 0, 1, 2])
print(np.corrcoef(x, x ** 2)[0, 1])   # 0.0

Correlation also isn't causation: ice-cream sales and drownings rise together because both are caused by hot weather.

Practice Compute the correlation

Compute the correlation between calisma (hours) and not_ with np.corrcoef, round it to 3 digits and print it.

Starter code

model.py
import numpy as np

calisma = np.array([1, 2, 3, 4, 5])
not_ = np.array([50, 55, 65, 70, 80])

# buraya yaz

Sample solution

model.py
import numpy as np

calisma = np.array([1, 2, 3, 4, 5])
not_ = np.array([50, 55, 65, 70, 80])

r = np.corrcoef(calisma, not_)[0, 1]
print(round(r, 3))

Expected output

0.993

Questions and answers

Review the lesson questions together with their answers. To test yourself, solve the lesson interactively.

1 What can be said if the correlation is -0.95?

  • There is a weak positive relationship
  • As one rises, the other falls strongly Correct answer
  • There is no relationship
  • One causes the other

Explanation: The sign gives the direction, the magnitude the strength; correlation doesn't prove causation.

2 Take the correlation between the two variables.

Question 
r = np.corrcoef(a, b)[____]
Answer 
r = np.corrcoef(a, b)[0, 1]

Explanation: The off-diagonal element is the correlation of the two variables.

3 Match the values with their meanings.

Term Meaning
1 Perfect positive linear
-1 Perfect negative linear
0 No linear relationship
0.3 Weak positive

All lessons in Beginner

1 What is ML?

  1. What is machine learning?
  2. Supervised and unsupervised
  3. Data and model
  4. Training and testing
  5. Feature and label notation
  6. Summary - ML fundamentals

2 NumPy basics

  1. What is NumPy?
  2. Creating arrays
  3. Array properties
  4. Array indexing
  5. Reshaping arrays
  6. Summary - NumPy basics

3 Pandas basics

  1. What is Pandas?
  2. Creating a DataFrame
  3. Column operations
  4. Selecting and filtering data
  5. Viewing first rows
  6. Summary - Pandas basics

4 Data preprocessing

  1. Data cleaning
  2. Missing data
  3. Data types
  4. Label encoding
  5. Data splitting
  6. Summary - Data preprocessing

5 Statistics basics

  1. Mean
  2. Median
  3. Standard deviation
  4. Variance
  5. Correlation
  6. Summary - Statistics

6 Linear algebra

  1. Vectors
  2. Matrices
  3. Matrix multiplication
  4. Transpose
  5. Identity matrix
  6. Summary - Linear algebra

7 Project: Data analysis

  1. Loading data
  2. Cleaning data
  3. Computing statistics
  4. Printing results

8 Regression

  1. What is regression?
  2. Linear regression
  3. Model training
  4. Prediction
  5. Error measurement
  6. Summary - Regression

9 KNN

  1. What is KNN?
  2. The K parameter
  3. Distance measurement
  4. Classification
  5. Model training
  6. Summary - KNN

10 Decision trees

  1. What is a decision tree?
  2. Splitting criterion
  3. Depth
  4. Classification
  5. Overfitting
  6. Summary - Decision trees

11 Classification

  1. What is classification?
  2. Binary classification
  3. Multi-class
  4. Accuracy
  5. Confusion matrix
  6. Summary - Classification

12 Model evaluation

  1. Train-test split
  2. Accuracy
  3. Precision
  4. Recall
  5. F1 score
  6. Summary - Model evaluation

13 Project: Classification

  1. Preparing data
  2. Training model
  3. Prediction
  4. Evaluation

14 Scaling

  1. What is scaling?
  2. StandardScaler
  3. MinMaxScaler
  4. When to use?
  5. Pipeline
  6. Summary - Scaling

15 Feature engineering

  1. What is a feature?
  2. Feature selection
  3. Feature extraction
  4. Categorical features
  5. Numerical features
  6. Summary - Feature engineering

16 Model selection

  1. What is model selection?
  2. Cross-validation
  3. Grid search
  4. Score comparison
  5. Hyperparameter
  6. Summary - Model selection

17 Project: Regression

  1. Preparing data
  2. Training model
  3. Prediction
  4. Error measurement

18 Metrics

  1. What is a metric?
  2. Accuracy
  3. Precision
  4. Recall
  5. F1 score
  6. Summary - Metrics

19 Data visualization

  1. What is visualization?
  2. Scatter plot
  3. Histogram
  4. Line plot
  5. Box plot
  6. Summary - Visualization

20 Beginner final

  1. Challenge 1
  2. Challenge 2
  3. Challenge 3
  4. Challenge 4