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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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San Francisco | 2023-01-30

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