Add: Ordinary Least Squares Regression Algorithm

DIRECTORY.md

@@ -715,6 +715,7 @@
   * [Mfcc](machine_learning/mfcc.py)
   * [Mini Batch Gradient Descent](machine_learning/mini_batch_gradient_descent.py)
   * [Multilayer Perceptron Classifier](machine_learning/multilayer_perceptron_classifier.py)
+  * [Ordinary Least Squares Regression](machine_learning/ordinary_least_squares_regression.py)
   * [Polynomial Regression](machine_learning/polynomial_regression.py)
   * [Principle Component Analysis](machine_learning/principle_component_analysis.py)
   * [Q Learning](machine_learning/q_learning.py)

machine_learning/ordinary_least_squares_regression.py

@@ -0,0 +1,80 @@
+"""
+Ordinary Least Squares Regression (OLSR):
+
+Ordinary Least Squares Regression (OLSR) is a statistical method for
+estimating the parameters of a linear regression model.
+It is the most commonly used regression method,
+and it is based on the principle of minimizing
+the sum of the squared residuals.
+
+Below is a simple implementation of OLSR
+without using any external libraries.
+
+WIKI: https://en.wikipedia.org/wiki/Ordinary_least_squares
+"""
+
+import numpy as np
+
+
+def ols_regression(x_point: np.ndarray, y_point: np.ndarray) -> tuple:
+    """
+    Performs Ordinary Least Squares Regression (OLSR) on the given data.
+
+    Args:
+        x: The independent variable.
+        y: The dependent variable.
+
+    Returns:
+        a (float): The intercept of the regression line.
+        b (float): The slope of the regression line.
+
+    Examples:
+    >>> x = np.array([1, 2, 3, 4, 5])
+    >>> y = np.array([2, 4, 6, 8, 10])
+    >>> a, b = ols_regression(x, y)
+    >>> float(a)  # Intercept should be 0.0
+    0.0
+    >>> float(round(b, 2))  # Slope should be 2.0
+    2.0
+    """
+
+    # Calculate the mean of the independent variable and
+    # the dependent variable.
+    x_mean = np.mean(x_point)
+    y_mean = np.mean(y_point)
+
+    # Calculate the slope of the regression line.
+    slope = np.sum((x_point - x_mean) * (y_point - y_mean)) / np.sum(
+        (x_point - x_mean) ** 2
+    )
+
+    # Calculate the intercept of the regression line.
+    intercept = y_mean - slope * x_mean
+
+    return intercept, slope
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+
+    # Load the data
+    x_points = np.array([1, 2, 3, 4, 5])
+    y_points = np.array([2, 4, 6, 8, 10])
+
+    # Perform OLS regression
+    intercept, slope = ols_regression(x_points, y_points)
+
+    # Intercept (a) and slope (b) of the regression line
+    print("Intercept:", intercept)
+    print("Slope:", slope)
+
+    # Predict the target variable for a new data point with
+    # an independent variable value of 6
+    x_new = 6
+
+    # Make a prediction
+    y_pred = intercept + slope * x_new
+
+    print("Prediction:", y_pred)