# How do I calculate r-squared using Python and Numpy?

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I"m using Python and Numpy to calculate a best fit polynomial of arbitrary degree. I pass a list of x values, y values, and the degree of the polynomial I want to fit (linear, quadratic, etc.).

This much works, but I also want to calculate r (coefficient of correlation) and r-squared(coefficient of determination). I am comparing my results with Excel"s best-fit trendline capability, and the r-squared value it calculates. Using this, I know I am calculating r-squared correctly for linear best-fit (degree equals 1). However, my function does not work for polynomials with degree greater than 1.

Excel is able to do this. How do I calculate r-squared for higher-order polynomials using Numpy?

Here"s my function:

``````import numpy

# Polynomial Regression
def polyfit(x, y, degree):
results = {}

coeffs = numpy.polyfit(x, y, degree)
# Polynomial Coefficients
results["polynomial"] = coeffs.tolist()

correlation = numpy.corrcoef(x, y)[0,1]

# r
results["correlation"] = correlation
# r-squared
results["determination"] = correlation**2

return results
``````

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Frank Wu

Berlin | 2023-01-30

square is always a bit confusing 😭 How do I calculate r-squared using Python and Numpy? is not the only problem I encountered. I just hope that will not emerge anymore

Angelo Ungerschaft

San Francisco | 2023-01-30

Maybe there are another answers? What How do I calculate r-squared using Python and Numpy? exactly means?. I am just not quite sure it is the best method

Javier Schteiner

San Francisco | 2023-01-30

I was preparing for my coding interview, thanks for clarifying this - How do I calculate r-squared using Python and Numpy? in Python is not the simplest one. I am just not quite sure it is the best method

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