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A matrix is an array of numbers arranged in rows and columns

Correlation Matrix

A matrix is an array of numbers arranged in rows and columns.

A correlation matrix is simply a table showing the correlation coefficients between variables.

Here, the variables are represented in the first row, and in the first column:

The table above has used data from the full health data set.

Observations:

  • We observe that Duration and Calorie_Burnage are closely related, with a correlation coefficient of 0.89. This makes sense as the longer we train, the more calories we burn
  • We observe that there is almost no linear relationships between Average_Pulse and Calorie_Burnage (correlation coefficient of 0.02)
  • Can we conclude that Average_Pulse does not affect Calorie_Burnage? No. We will come back to answer this question later!

    • Correlation Matrix in Python

    We can use the corr() function in Python to create a correlation matrix. We also use the round() function to round the output to two decimals:

    Example

    Corr_Matrix = round(full_health_data.corr(),2)
    print(Corr_Matrix)

    Output:

    Using a Heatmap

    We can use a Heatmap to Visualize the Correlation Between Variables:

    The closer the correlation coefficient is to 1, the greener the squares get.

    The closer the correlation coefficient is to -1, the browner the squares get.

    Use Seaborn to Create a Heatmap

    We can use the Seaborn library to create a correlation heat map (Seaborn is a visualization library based on matplotlib):

    Example

    import matplotlib.pyplot as plt
    import seaborn as sns

    correlation_full_health = full_health_data.corr()

    axis_corr = sns.heatmap(
    correlation_full_health,
    vmin=-1, vmax=1, center=0,
    cmap=sns.diverging_palette(50, 500, n=500),
    square=True
    )

    plt.show()

    Example Explained:

  • Import the library seaborn as sns.
  • Use the full_health_data set.
  • Use sns.heatmap() to tell Python that we want a heatmap to visualize the correlation matrix.
  • Use the correlation matrix. Define the maximal and minimal values of the heatmap. Define that 0 is the center.
  • Define the colors with sns.diverging_palette. n=500 means that we want 500 types of color in the same color palette.
  • square = True means that we want to see squares.

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