Correlation

Correlation measures the relationship between two variables.

We mentioned that a function has a purpose to predict a value, by converting input (x) to output (f(x)). We can say also say that a function uses the relationship between two variables for prediction.

Correlation Coefficient

The correlation coefficient measures the relationship between two variables.

The correlation coefficient can never be less than -1 or higher than 1.

• 1 = there is a perfect linear relationship between the variables (like Average_Pulse against Calorie_Burnage)
• 0 = there is no linear relationship between the variables
• -1 = there is a perfect negative linear relationship between the variables (e.g. Less hours worked, leads to higher calorie burnage during a training session)

Example of a Perfect Linear Relationship (Correlation Coefficient = 1)

We will use scatterplot to visualize the relationship between Average_Pulse and Calorie_Burnage (we have used the small data set of the sports watch with 10 observations).

This time we want scatter plots, so we change kind to "scatter":

Example

import matplotlib.pyplot as plt

health_data.plot(x ='Average_Pulse', y='Calorie_Burnage', kind='scatter')
plt.show()

Output:

As we saw earlier, it exists a perfect linear relationship between Average_Pulse and Calorie_Burnage.

Example of a Perfect Negative Linear Relationship (Correlation Coefficient = -1)

We have plotted fictional data here. The x-axis represents the amount of hours worked at our job before a training session. The y-axis is Calorie_Burnage.

If we work longer hours, we tend to have lower calorie burnage because we are exhausted before the training session.

The correlation coefficient here is -1.

Example

import pandas as pd
import matplotlib.pyplot as plt

negative_corr = {'Hours_Work_Before_Training': [10,9,8,7,6,5,4,3,2,1],
'Calorie_Burnage': [220,240,260,280,300,320,340,360,380,400]}
negative_corr = pd.DataFrame(data=negative_corr)

negative_corr.plot(x ='Hours_Work_Before_Training', y='Calorie_Burnage', kind='scatter')
plt.show()

Example of No Linear Relationship (Correlation coefficient = 0)

Here, we have plotted Max_Pulse against Duration from the full_health_data set.

As you can see, there is no linear relationship between the two variables. It means that longer training session does not lead to higher Max_Pulse.

The correlation coefficient here is 0.

Example

import matplotlib.pyplot as plt

full_health_data.plot(x ='Duration', y='Max_Pulse', kind='scatter')
plt.show()