Least Squares Regression

least_squares_regression.cpp

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+#include <bits/stdc++.h>
+
+using namespace std;
+
+
+void regression(vector<float> x, vector<float> y)
+{
+    int n = x.size();
+    float mx = accumulate(x.begin(), x.end(), 0)/n;
+    float my = accumulate(y.begin(), y.end(), 0)/n;
+
+    float sx = accumulate(x.begin(), x.end(), 0);
+    float sy = accumulate(y.begin(), y.end(), 0);
+    float sx_sy = 0;
+    float sx_x = 0;
+    for(int i =0; i<n; i++)
+    {
+        sx_sy += x[i]*y[i];
+        sx_x += x[i]*x[i];
+    }
+    float b = (n*sx_sy-sx*sy)/(n*sx_x-sx*sx);
+
+    float a = my - b*mx;
+
+    printf("y= %.3f + %.3f*x", a, b);
+}
+
+int main(void)
+{
+    vector<float> x = { 5, 7, 12, 16, 20 };
+    vector<float> y = { 40, 120, 180, 210, 240 };
+    regression(x,y);
+    return 0;
+}

polynomial_regression.py

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+import numpy as np
+import matplotlib.pyplot as plt
+
+def calculate_matrix(x, n):
+    m = len(x)
+    matrix = np.zeros((n+1, n+1))
+    for i in range(n+1):
+        for j in range(n+1):
+            matrix[i][j] = np.sum(x**(i+j))
+    return matrix
+
+def calculate_vector(x, y, n):
+    m = len(x)
+    vector = np.zeros(n+1)
+    for i in range(n+1):
+        vector[i] = np.sum(y * x**i)
+    return vector
+
+def calculate_b(x, y, n):
+    k = calculate_matrix(x, n)
+    l = calculate_vector(x, y, n)
+    return np.linalg.solve(k, l)
+
+if __name__ == "__main__":
+    X = np.array([1, 2, 3, 4, 5, 6, 7])
+    Y = np.array([45000, 50000, 60000, 80000, 110000, 150000, 200000])
+
+    n = 3  # Adjust the degree of polynomial as needed
+    b_coeffs = calculate_b(X, Y, n)
+    x_vals = np.linspace(1, 7, 100)
+    y_vals = sum(b_coeffs[i] * x_vals**i for i in range(n+1))
+    plt.scatter(X, Y, color='blue')
+    plt.plot(x_vals, y_vals, label='Polynomial Regression')
+    plt.xlabel('x')
+    plt.ylabel('y')
+    plt.title('Plot of Polynomial Regression')
+    plt.legend()
+    plt.grid(True)
+    plt.show()