Impara What is Correlation? | Covariance and Correlation

Correlation is a statistical measure that quantifies the relationship between two variables. It is determined as the scaled covariation and due to this scale, we can determine the measure of dependencies in addition to their direction.
Correlation ranges between -1 and 1, where:

If the correlation is +1 then values have a perfect positive linear relationship. As one variable increases, the other variable increases proportionally;
If the correlation is -1 then values have a perfect negative linear relationship. As one variable increases, the other variable decreases proportionally;
If the correlation coefficient is close to 0 then there is no linear relationship between the variables.

To calculate the correlation we can follow the same steps as to calculate covariance and use np.corrcoef(x, y)[0, 1].


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import matplotlib.pyplot as plt
import numpy as np

# Create a figure with three subplots
fig, axes = plt.subplots(1, 3)
fig.set_size_inches(10, 5)

# Positive linear dependence
x = np.random.rand(100) * 10  # Generate random x values
y = x + np.random.randn(100)  # Generate y values with added noise
axes[0].scatter(x, y)  # Scatter plot of x and y
axes[0].set_title('Correlation is '+ str(round(np.corrcoef(x, y)[0, 1], 3) ))  # Set title with correlation coefficient

# Negative linear dependence
x = np.random.rand(100) * 10  # Generate random x values
y = -x + np.random.randn(100)  # Generate y values with added noise
axes[1].scatter(x, y)  # Scatter plot of x and y
axes[1].set_title('Correlation is '+ str(round(np.corrcoef(x, y)[0, 1], 3) ))  # Set title with correlation coefficient

# Independent
np.random.seed(0)  # Set random seed for reproducibility
x = np.random.rand(200)  # Generate random x values
y = np.random.rand(200)  # Generate random y values
axes[2].scatter(x, y)  # Scatter plot of x and y
axes[2].set_title('Correlation is '+ str(round(np.corrcoef(x, y)[0, 1], 3) ))  # Set title with correlation coefficient

plt.show()  # Display the plot

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Sezione 5. Capitolo 2

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If the correlation is +1 then values have a perfect positive linear relationship. As one variable increases, the other variable increases proportionally;
If the correlation is -1 then values have a perfect negative linear relationship. As one variable increases, the other variable decreases proportionally;
If the correlation coefficient is close to 0 then there is no linear relationship between the variables.

To calculate the correlation we can follow the same steps as to calculate covariance and use np.corrcoef(x, y)[0, 1].


              123456789101112131415161718192021222324252627
            
import matplotlib.pyplot as plt
import numpy as np

# Create a figure with three subplots
fig, axes = plt.subplots(1, 3)
fig.set_size_inches(10, 5)

# Positive linear dependence
x = np.random.rand(100) * 10  # Generate random x values
y = x + np.random.randn(100)  # Generate y values with added noise
axes[0].scatter(x, y)  # Scatter plot of x and y
axes[0].set_title('Correlation is '+ str(round(np.corrcoef(x, y)[0, 1], 3) ))  # Set title with correlation coefficient

# Negative linear dependence
x = np.random.rand(100) * 10  # Generate random x values
y = -x + np.random.randn(100)  # Generate y values with added noise
axes[1].scatter(x, y)  # Scatter plot of x and y
axes[1].set_title('Correlation is '+ str(round(np.corrcoef(x, y)[0, 1], 3) ))  # Set title with correlation coefficient

# Independent
np.random.seed(0)  # Set random seed for reproducibility
x = np.random.rand(200)  # Generate random x values
y = np.random.rand(200)  # Generate random y values
axes[2].scatter(x, y)  # Scatter plot of x and y
axes[2].set_title('Correlation is '+ str(round(np.corrcoef(x, y)[0, 1], 3) ))  # Set title with correlation coefficient

plt.show()  # Display the plot

Tutto è chiaro?

Grazie per i tuoi commenti!

Sezione 5. Capitolo 2

What is Correlation?

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What is Correlation?