Free statistics calculators designed for data scientists.
This Correlation Coefficient Calculator:
- Calculates Correlation Coefficient
- Evaluates Variation explained
- Saves & Recycles Data
Using The Correlation Coefficient Calculator
To use the calculator, enter the X values into the left box and the
associated Y values into the right box, separated by commas or
new line characters. Hit calculate. It will calculate the correlation
coefficient and generate an r-squared goodness of fit test result.
For easy entry, you can copy and paste your data into the
entry box from Excel. You can save your data for use with
this calculator and other calculators on this site. Just hit
the "save data" button. It will save the data in your browser
(not on our server, it remains private). Saved data sets will
appear on the list of saved datasets below the data entry panel.
To retrieve it, click the "load data" button next to it.
Interpreting Correlation Coefficient Results
The Pearson product moment correlation coefficient measures the
degree to which variation in one variable can be associate with
variation in another. For purposes of this calculator, we refer
to the first (our X values) as the independent variable and the
associated Y values as the dependent variable. When we calculate
the correlation between the two, we are evaluating the extent to
which they change together.
A strong positive correlation coefficient indicates that the two
tend to increase and decrease alongside each other, in similar
proportion. Strongly negatively correlated variables will move
in opposite directions. It should be noted that unlike the
coefficients of a linear regression equation, where you can
estimate the value of one variable given the other, the scale
of the correlation coefficient is independent of any differences
in the scale of the underlying variables. We are analyzing the
covariance of the two, divided by the product of their variance.
Thus, we analyze the relative change rather than the absolute
magnitude of the change.
We include a second statistic, the r-squared value, as a means of
evaluating the consistency of this trend. A high R-squared value
indicates the data points consistently move together in
accordance with the trend denoted in their correlation coefficient.
A low r-Squared value indicates there's a lot of noise in the system
and only a portion of the variation in dependent variable can be
explained by changes in the independent variable. Look at your
r-squared value to assess your confidence in in the correlation.
As always, use common sense in interpreting these results. Correlation
in data doesn't necessarily indicate causation or predict replication
in the real world. Given a large enough pile of data to go shopping in,
you will inevitably find a few spurious correlations to capture your
imagination. This is where holding back a validation sample can keep
you honest - look skeptically at any trend that doesn't replicate in
your holdout sample. Similarly, look for opportunities to A/B test your
proposed changes on a small sample before ramping them to full volume.