Create a correlation Matrix using Python

A correlation matrix is a table containing correlation coefficients between variables. Each cell in the table represents the correlation between two variables. The value lies between -1 and 1. A correlation matrix is used to summarize data, as a diagnostic for advanced analyses and as an input into a more advanced analysis. The two key components of the correlation are:

• Magnitude: larger the magnitude, stronger the correlation.
• Sign: if positive, there is a regular correlation. If negative, there is an inverse correlation.

A correlation matrix has been created using the following two libraries:

1. Numpy Library
2. Pandas Library

Method 1: Creating a correlation matrix using Numpy library

Numpy library make use of corrcoef() function that returns a matrix of 2×2. The matrix consists of correlations of x with x (0,0), x with y (0,1), y with x (1,0) and y with y (1,1). We are only concerned with the correlation of x with y i.e. cell (0,1) or (1,0). See below for an example.

Example 1: Suppose an ice cream shop keeps track of total sales of ice creams versus the temperature on that day.

Output

[[1.         0.95750662]
 [0.95750662 1.        ]]

From the above matrix, if we see cell (0,1) and (1,0) both have the same value equal to 0.95750662 which lead us to conclude that whenever the temperature is high we have more sales.

Example 2: Suppose we are given glucose level in boy respective to age. Find correlation between age(x) and glucose level in body(y).

Output

[[1.        0.5298089]
 [0.5298089 1.       ]]

From the above correlation matrix, 0.5298089 or 52.98% that means the variable has a moderate positive correlation.

Method 2: Creating correlation matrix using Pandas library 

In order to create a correlation matrix for a given dataset, we use corr() method on dataframes.

Example 1:

 Output:

Dataframe is : 
    x   y   z
0  45  38  10
1  37  31  15
2  42  26  17
3  35  28  21
4  39  33  12
Correlation matrix is :
          x         y         z
x  1.000000  0.518457 -0.701886
y  0.518457  1.000000 -0.860941
z -0.701886 -0.860941  1.000000

Example 2:

CSV File used:

Output:

Correlation Matrix is : 
                     AVG temp C  Ice Cream production
AVG temp C              1.000000              0.718032
Ice Cream production    0.718032              1.000000