[Python] Why does my logistic curve_fit prediction return huge values although R² ≈ 0.99?

I’m trying to fit a logistic function to GDP data (China GDP dataset) using scipy.optimize.curve_fit. The fitting looks very good (R² ≈ 0.99, curve matches the data), but when I try to predict a single value for a given year, the result is extremely large (≈ 1e24) while the real value is only ≈ 9e10.

Here is a simplified version of my code:

import numpy as np
import pandas as pd
from scipy.optimize import curve_fit
from scipy.special import expit

df = pd.read_csv("china_gdp.csv")
msk = np.random.rand(len(df)) < 0.8
x = df['Year'].values.astype(float)
y = df['Value'].values.astype(float)

# normalize x, y to [0,1]
x_s = (x - x.min()) / (x.max() - x.min())
y_s = (y - y.min()) / (y.max() - y.min())

def logistic(x, B1, B2, B3, B4):
return B3 + B4 * expit(B1*(x - B2))

# initial guess and bounds
p0 = (5.0, 0.5, 0.0, 1.0)
bounds = ([0.0, 0.0, -np.inf, 0.0], [np.inf, 1.0, np.inf, np.inf])

popt, pcov = curve_fit(logistic, x_s, y_s, p0=p0, bounds=bounds)
print(dict(zip(['B1','B2','B3','B4'], popt)))

# check fit
import matplotlib.pyplot as plt
xx = np.linspace(0, 1, 300)
yy = logistic(xx, *popt)
plt.scatter(x_s, y_s, s=15, label='data')
plt.plot(xx, yy, label='fit')
plt.legend(); plt.show()

from sklearn.metrics import r2_score
xtest = x_s[~msk]
ytest = y_s[~msk]
ypred = logistic(xtest, *popt)
print(r2_score(ytest, ypred))

x_in = 1970
rs = logistic((x_in - x.min()) / (x.max() - x.min()), *popt)
r = rs * (y.max() - y.min()) + y.min()
print(r)


Output:

0.9985891574981185
192285528141.3661


But the real GDP value for 1970 is 91506211306.3745.

Am I mis-scaling my input/output, or is there an issue with how I define the logistic function / initial parameters?

I expected the prediction to be close to the real GDP values since the fit looks good and the R² score is high. I suspect I'm doing something wrong with scaling or with the logistic function parameters.

Dataset link

Continue reading...