Let’s consider the China’s GDP Kaggle Dataset to test the non-linear regression algorithm

Import and install libraries

import numpy as np
import pandas as pd

!pip install wget

Read the csv file

df = pd.read_csv(“YourPath/china_gdp.csv”)
df.head(10)

Let’s plot the data

import matplotlib.pyplot as plt
%matplotlib inline
plt.figure(figsize=(8,5))
x_data, y_data = (df[“Year”].values, df[“Value”].values)
plt.plot(x_data, y_data, ‘ro’)
plt.ylabel(‘GDP’)
plt.xlabel(‘Year’)
plt.show()

Let’s introduce the non-linear sigmoid function

X = np.arange(-5.0, 5.0, 0.1)
Y = 1.0 / (1.0 + np.exp(-X))

plt.plot(X,Y)
plt.ylabel(‘Dependent Variable’)
plt.xlabel(‘Indepdendent Variable’)
plt.show()

def sigmoid(x, Beta_1, Beta_2):
y = 1 / (1 + np.exp(-Beta_1*(x-Beta_2)))
return y

beta_1 = 0.10
beta_2 = 1990.0

logistic function

Y_pred = sigmoid(x_data, beta_1 , beta_2)

Let’s plot initial prediction against datapoints

plt.plot(x_data, Y_pred*15000000000000.)
plt.plot(x_data, y_data, ‘ro’)

Lets normalize our data

xdata =x_data/max(x_data)
ydata =y_data/max(y_data)

Let’s perform non-linear curve fitting

from scipy.optimize import curve_fit
popt, pcov = curve_fit(sigmoid, xdata, ydata)

And print the final parameters

print(” beta_1 = %f, beta_2 = %f” % (popt[0], popt[1]))

beta_1 = 690.451712, beta_2 = 0.997207

x = np.linspace(1960, 2015, 55)
x = x/max(x)
plt.figure(figsize=(8,5))
y = sigmoid(x, *popt)
plt.plot(xdata, ydata, ‘ro’, label=’data’)
plt.plot(x,y, linewidth=3.0, label=’fit’)
plt.legend(loc=’best’)
plt.ylabel(‘GDP’)
plt.xlabel(‘Year’)
plt.show()

Let’s split data into the train and test sets

msk = np.random.rand(len(df)) < 0.8
train_x = xdata[msk]
test_x = xdata[~msk]
train_y = ydata[msk]
test_y = ydata[~msk]

Let’s build the model using the train set

popt, pcov = curve_fit(sigmoid, train_x, train_y)

Predict using test set

y_hat = sigmoid(test_x, *popt)

Perform evaluation

print(“Mean absolute error: %.2f” % np.mean(np.absolute(y_hat – test_y)))
print(“Residual sum of squares (MSE): %.2f” % np.mean((y_hat – test_y) ** 2))
from sklearn.metrics import r2_score
print(“R2-score: %.2f” % r2_score(y_hat , test_y) )

Mean absolute error: 0.03
Residual sum of squares (MSE): 0.00
R2-score: 0.96

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