Pearson Correlation Coefficient

Pearson correlation is a number between -1 and +1 that indicates how much 2 variables are linearly related.

Python Code to find out

We will use python code to find out Pearson correlation coefficient between two variables.

# Importing the required libraries
import pandas as pd
import pingouin as pg

#a csv file with data.
df = pd.read_csv('Assignment1_problem1_data.csv')
df.head(10)

#The file looks like this.

	x1	x2	x3
0	2.5	1.2	8
1	3.6	1.0	15
2	1.2	1.8	12
3	0.8	0.9	6
4	4.0	3.0	8
5	3.4	2.2	10

#### Simple correlation between two columns (r is the correlation coefficient)

pg.corr(x=df['x1'], y=df['x2'])

#the output is as follows

	n	r	CI95%	r2	adj_r2	p-val	BF10	power
	6	0.529748	[-0.49, 0.94]	0.280633	-0.198945	0.27971	0.814	0.199882

So the x1 and x2 are positivily correlated as the r= 0.529748, meaning when x1 increases x2 increases and vice versa.

####Now for x1 and x3

pg.corr(x=df['x1'], y=df['x3'])

#the output is as follows

	n	r	CI95%	r2	adj_r2	p-val	BF10	power
	6	0.314443	[-0.67, 0.9]	0.098875	-0.501876	0.54388	0.577	0.094945

So the x1 and x3 are positivily correlated as the r= 0.314443, meaning when x1 increases x2 increases and vice versa.

####Now for x2 and x3

pg.corr(x=df['x2'], y=df['x3'])

#the output is as follows

	n	r	CI95%	r2	adj_r2	p-val	BF10	power
	6	-0.129455	[-0.85, 0.76]	0.016759	-0.638736	0.806902	0.504	0.057173

So the x1 and x3 are negatively correlated as the r=-0.129455, meaning when x2 increases x3 decreases and vice versa.

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Finding Pearson correlations

Pearson Correlation Coefficient

Python Code to find out

Ricky D'Cruze