# 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 librariesimport pandas as pdimport 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. 