The Pearson correlation coefficient, or PCC, is the standard statistical method for computing pairwise or bivariate correlation in Pandas. It’s so commonly used in statistics, that it is often referred to simply as “the correlation coefficient.” Pearson correlation coefficient is exactly the same thing as Pearson’s r, and the Pearson product moment correlation coefficient (PPMCC), it just has several names.
As with other correlation coefficients, Pearson correlation is used to compute the strength of linear correlation between two variables in a dataset. It’s basically the ratio between the covariance of the variables and the product of their standard deviations, and gives a normalised measure of covariance that returns a value between 1 and 1. A value of 1 indicates a perfect positive linear relationship, a value of 1 indicates a perfect negative linear relationship, and a value of 0 indicates no linear relationship.
By interpreting the result of the Pearson correlation coefficient you can tell whether one variable is associated with a change in the other. For example, the price of new cars might be positively correlated with top speed, since most very expensive new cars are supercars or hypercars.
In this tutorial, I’ll explain Pearson correlation and show how you can use it to spot correlations between variables in your dataset using the Pandas corr()
function.
The Pearson correlation coefficient can be easily calculated in Pandas using corr()
. The corr()
function is used to compute pairwise correlation coefficients on Pandas dataframe values, and can either calculate them as individual pairs (i.e. top speed and price), or as pairs across an entire dataframe.
Since Pearson correlation coefficient is so widely used by statisticians and data scientists, the corr()
function is preconfigured with default values to return the Pearson correlation coefficient. However, you can change this to use the similar Spearman rank correlation (or Spearman’s r), or the Kendall Tau correlation coefficient, if you think they better suit your data.
The corr()
function takes three arguments, all of which are optional. Here’s a quick summary of what they do.
Parameter  Description 

method 
The method parameter defines which of the three correlation coefficient methods to use. The default is pearson , which is the Pearson productmoment correlation coefficient. The other two methods are kendall , for the Kendall Tau correlation coefficient, and spearman for the Spearman's rank correlation coefficient. 
min_periods 
The min_periods parameter defines the minimum number of observations required to calculate the correlation coefficient. If there are fewer than min_periods observations, the correlation coefficient will be set to NaN . This currently only works when the method parameter is set to pearson or spearman . 
numeric_only 
The numeric_only parameter was new in Pandas 1.5.0, so it won't work on earlier releases of Pandas. This parameter defines whether to only calculate the correlation coefficient on numeric columns. If set to True , only numeric columns will be used to calculate the correlation coefficient. If set to False , all columns will be used to calculate the correlation coefficient. The default is True . In a future release, the value of numeric_only will change to False , so if you don't set it you'll currently get this warning:
"FutureWarning: The default value of numeric_only in DataFrame.corr is deprecated. In a future version, it will default to False. Select only valid columns or specify the value of numeric_only to silence this warning." Passing numeric_only=True will fix it.

When using corr(method='pearson')
, or just corr()
, since method='pearson'
is the default, the resulting correlation matrix will have a value for every pair of columns in the original DataFrame.
The value will be a number between 1 and 1, where 1 is a perfect positive linear relationship, 0 is no linear relationship, and 1 is a perfect negative linear relationship. Different authors use slightly different interpretations of the coefficients, but they’re generally very similar to the ones below.
Pearson's r value  Strength of relationship 

0  No linear relationship 
0.1 to 0.3  Weak linear relationship 
0.3 to 0.5  Moderate linear relationship 
0.5 to 0.7  Strong linear relationship 
0.7 to 1  Very strong linear relationship 
0.1 to 0.3  Weak negative linear relationship 
0.3 to 0.5  Moderate negative linear relationship 
0.5 to 0.7  Strong negative linear relationship 
0.7 to 1  Very strong negative linear relationship 
To get started, open a new Jupyter notebook and import the Pandas library. You only need this to calculate correlation coefficients in Pandas, but to cover some more advanced topics we’ll also import the Matplotlib and Seaborn data visualisation packages, and the Scipy statistical analysis package.
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
from scipy.stats import pearsonr
Then, either create a dummy dataset of data with linear relationships between the variables, or import a dataset into Pandas from a CSV file. I’m using a house price dataset, as this contains several correlated variables.
df = pd.read_csv('https://raw.githubusercontent.com/flyandlure/datasets/master/housing.csv')
df.head().T
0  1  2  3  4  

longitude  122.23  122.22  122.24  122.25  122.25 
latitude  37.88  37.86  37.85  37.85  37.85 
housing_median_age  41.0  21.0  52.0  52.0  52.0 
total_rooms  880.0  7099.0  1467.0  1274.0  1627.0 
total_bedrooms  129.0  1106.0  190.0  235.0  280.0 
population  322.0  2401.0  496.0  558.0  565.0 
households  126.0  1138.0  177.0  219.0  259.0 
median_income  8.3252  8.3014  7.2574  5.6431  3.8462 
median_house_value  452600.0  358500.0  352100.0  341300.0  342200.0 
ocean_proximity  NEAR BAY  NEAR BAY  NEAR BAY  NEAR BAY  NEAR BAY 
To calculate the Pearson correlation for a pair of columns, you can append the .corr()
method to the first column and pass the second column as an argument. If we do this for the median_income
and median_house_value
columns we get back a PCC or r of 0.6880, which according to our interpretation in the lookup table denotes a strong linear correlation. That means, samples with a higher median_income
generally had a higher median_house_value
.
df['median_income'].corr(df['median_house_value'])
0.688075207958548
To calculate the Pearson correlation coefficient for every pair of values in the dataframe, you can simply append the corr()
method to the end of the dataframe object. The resulting dataframe, or matrix, will have the correlation coefficient for every pair of columns in the dataframe. To avoid getting a FutureWarning
, you’ll want to set numeric_only=True
in the corr()
method.
df.corr(numeric_only=True)
longitude  latitude  housing_median_age  total_rooms  total_bedrooms  population  households  median_income  median_house_value  

longitude  1.000000  0.924664  0.108197  0.044568  0.069608  0.099773  0.055310  0.015176  0.045967 
latitude  0.924664  1.000000  0.011173  0.036100  0.066983  0.108785  0.071035  0.079809  0.144160 
housing_median_age  0.108197  0.011173  1.000000  0.361262  0.320451  0.296244  0.302916  0.119034  0.105623 
total_rooms  0.044568  0.036100  0.361262  1.000000  0.930380  0.857126  0.918484  0.198050  0.134153 
total_bedrooms  0.069608  0.066983  0.320451  0.930380  1.000000  0.877747  0.979728  0.007723  0.049686 
population  0.099773  0.108785  0.296244  0.857126  0.877747  1.000000  0.907222  0.004834  0.024650 
households  0.055310  0.071035  0.302916  0.918484  0.979728  0.907222  1.000000  0.013033  0.065843 
median_income  0.015176  0.079809  0.119034  0.198050  0.007723  0.004834  0.013033  1.000000  0.688075 
median_house_value  0.045967  0.144160  0.105623  0.134153  0.049686  0.024650  0.065843  0.688075  1.000000 
When examining a dataset it’s often easier to visualise the correlations using Seaborn, or a similar data visualisation library. Visualising the correlations via a heatmap is my preferred technique and is easily done by using just a Seaborn function and a Matplotlib function to adjust the figure size.
plt.figure(figsize=(14,8))
sns.heatmap(df.corr(numeric_only=True), annot=True, cmap='Blues')
<AxesSubplot:>
There are various ways to visualise correlations between pairs of variables. A quick way to view the correlations of a single pair is to use the Seaborn regplot()
function. This takes three arguments comprising the x
and y
columns you want to plot, and the data
from the dataframe.
plt.figure(figsize=(14,8))
sns.regplot(x='median_income', y='median_house_value', data=df)
plt.title('Median Income vs Median House Value')
Text(0.5, 1.0, 'Median Income vs Median House Value')
To determine whether the correlation coefficient is statistically significant or not you can use the pearsonr()
method from scipy.stats
. This returns does much the same as the Pandas corr()
function, in that it also returns the correlation coefficient, but crucially, it provides the pvalue that Pandas does not.
The pvalue is the probability that the correlation coefficient is not statistically significant. If the pvalue is less than 0.05 then the correlation coefficient is statistically significant. We get a very low p value, so the correlation coefficient is statistically significant.
pearsonr(df['median_income'], df['median_house_value'])
(0.6880752079585477, 0.0)
By contrast, if you use Scipy to calculate the Pearson correlation coefficient and p value of the housing_median_age
and median_house_value
columns you get back a higher p value, indicating that the result is not statistically significant.
pearsonr(df['housing_median_age'], df['median_house_value'])
(0.10562341249320992, 2.7618606761502365e52)
Matt Clarke, Sunday, November 20, 2022