np.poly1d: how to calculate R^2 - numpy

Question

I am fitting my data to a linear regression. But I want to know how to calculate the R2 values. The following is the code I have so far.
total_csv= pd.read_csv('IgG1_sigma_biospin_neg.csv',header=0).iloc[:,:]
x_values=(19,20,21,22)
y_values=IgG1_sigma_biospin_neg.loc[0, ['19-', '20-', '21-', '22-']].tolist()
my_fitting= np.polyfit(x_values,y_values,1)
my_lin_fitting = np.poly1d(my_fitting)
my_x=Symbol('x')
print('my_equation:',expand(my_lin_fitting (my_x)))
I get the equation of the linear fitting of my data 35.6499591999999*x + 6018.6395529.
In [95]:y_values
Out[95]: [6698.0902240000005, 6733.253559000001, 6757.754712999999, 6808.75637]
Do you know how to calculate R2 values?

Answer 1

To the best of my knowledege, np.polyfit does not provide a coefficient of determination (R2).
The residual that Richard mentioned in his answer is something different, named Sum of Squares Error (SSE). More info about it here:
https://365datascience.com/tutorials/statistics-tutorials/sum-squares/
Good news is, you can easily calculate R2 from SSE. First you calculate the Sum of Square Total (SST), then the R2 is merely R2 = 1 - SSE / SST. (See above link for further explanations.)
import numpy as np
# generate pseudo-data so the code can be run standalone (nicer for a mwe)
x_values = np.arange(100)
y_values = 3 * x_values + 2 + np.random.random(100)-0.5
my_fitting = np.polyfit(x_values, y_values, 1, full=True)
coeff = my_fitting[0]
### Residual or Sum of Square Error (SSE)
SSE = my_fitting[1][0]
### Determining the Sum of Square Total (SST)
## the squared differences between the observed dependent variable and its mean
diff = y_values - y_values.mean()
square_diff = diff ** 2
SST = square_diff.sum()
### Now getting the coefficient of determination (R2)
R2 = 1 - SSE/SST
print(R2)
Another approach is to use the already implemented function provided by Scikit-learn./
## Alternative using sklearn
from sklearn.metrics import r2_score
predict = np.poly1d(coeff)
R2 = r2_score(y_values, predict(x_values))
print(R2)
Both methods give me the very same answer.

Answer 2

first thing - you should be using np.polynomial.polynomial Class/methods instead of np.polyfit (see the doc's on np.polyfit, pointing people to use the newer code)
You can then use the polyfit method there. It will by default only return the coefficients. If you want the residual (R2), then specify full=True. polyfit will then also return a list, with the first element the residual (R2). See here.
The mod to your code above would be below:
import numpy.polynomial.polynomial as poly
my_fitting, stats = poly.polyfit(x_values,y_values,1, full=True)
R2 = stats[0][0]