# Statistical meaning of pearsonr() output in Python

I have calculated the Pearson correlation by using

pearsonr(var1, var2)


I understand that the first number is the Pearson correlation and the second number is the significance.

I have a few questions:

• Above which value can we consider significant correlation?
• Is the R-square only R**2?
• How do I calculate the adjusted R square?

2. Yes, for a simple linear regression with one predictor and an intercept, $$r * r$$ is really an estimate of $$R^2$$. Of course, your code is not explicitly fitting a model or anything but there is a link between the Pearson product-moment correlation, this simple linear model and different other tests. It becomes more complicated if the model includes several predictors (see Regression $R^2$ and correlations).
3. Adjusted $$R^2$$ is adjusted to take the number of parameters into account (a model with more parameters can be expected to better predict the data in the sample even if the additional variables aren't really useful). There is a formula in Wikipedia and several earlier questions on this: How to choose between the different Adjusted $R^2$ formulas?, Why is adjusted R-squared less than R-squared if adjusted R-squared predicts the model better?. If you read more on that, you will notice that there is in fact quite a lot of discussion on how to adjust $$R^2$$ and the usefulness of these coefficients in practice.
You can apparently get an adjusted $$R^2$$ directly in Python/SciPy using the ols.ols() function, see http://wiki.scipy.org/Cookbook/OLS