Added README file for regression toolkit

linear-regression-toolkit-py/README.md

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+# Linear Regression Toolkit
+
+**Description:**
+
+This toolkit library provides a set of functions for implementing simple linear regression. Linear regression is a widely used method for modeling the relationship between a dependent variable (target) and one or more independent variables (features). This library is focused on simple linear regression, which deals with a single independent variable and a single dependent variable. It includes functions for making predictions, computing the cost function, and performing gradient descent to optimize model parameters.
+
+**Table of Contents:**
+
+- [Usage](#usage)
+- [Functions](#functions)
+- [Example Usage](#example-usage)
+- [Notes](#notes)
+
+## Usage
+
+This library contains the following functions:
+
+1. `compute_dep_var(x, w, b)`
+
+   This function computes the dependent variable's predicted values based on the input independent feature data `x`, weight parameter `w`, and bias parameter `b`. It returns an array of predicted values.
+
+2. `compute_cost_fn(x, y, w, b)`
+
+   This function calculates the cost function, which represents the error in the model's predictions. It uses the sum of squared errors between predicted and actual dependent variable values.
+
+3. `compute_deriv_fn(x, y, w, b)`
+
+   This function computes the derivatives of the weight and bias parameters, which are used in gradient descent to update the model parameters.
+
+4. `compute_gradient_descent(x, y, n, a, w, b)`
+
+   This function performs gradient descent to optimize the weight and bias parameters for the linear regression model. It returns the final optimized weight and bias, as well as a history of cost function values over iterations.
+
+## Example Usage
+
+Here's an example of how you can use these functions to perform linear regression:
+
+```python
+import numpy as np
+
+# Sample data
+x = np.array([1, 2, 3, 4, 5])
+y = np.array([2, 4, 5, 4, 5])
+
+# Initial weight and bias
+w_initial = 1
+b_initial = 0
+
+# Number of iterations and learning rate
+iterations = 100
+learning_rate = 0.01
+
+# Perform gradient descent
+final_w, final_b, cost_history = compute_gradient_descent(x, y, iterations, learning_rate, w_initial, b_initial)
+
+print("Optimized weight:", final_w)
+print("Optimized bias:", final_b)