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Example demonstrating how gradient descent may be used to solve a linear regression problem

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## Gradient Descent Example for Linear Regression

This example project demonstrates how the gradient descent algorithm may be used to solve a linear regression problem. A more detailed description of this example can be found here.

### Code Requirements

The example code is in Python (version 2.6 or higher will work). The only other requirement is NumPy.

### Description

This code demonstrates how a gradient descent search may be used to solve the linear regression problem of fitting a line to a set of points. In this problem, we wish to model a set of points using a line. The line model is defined by two parameters - the line's slope `m`, and y-intercept `b`. Gradient descent attemps to find the best values for these parameters, subject to an error function.

The code contains a main function called `run`. This function defines a set of parameters used in the gradient descent algorithm including an initial guess of the line slope and y-intercept, the learning rate to use, and the number of iterations to run gradient descent for.

```initial_b = 0 # initial y-intercept guess
initial_m = 0 # initial slope guess
num_iterations = 1000```

Using these parameters a gradient descent search is executed on a sample data set of 100 ponts. Here is a visualization of the search running for 200 iterations using an initial guess of `m = 0`, `b = 0`, and a learning rate of `0.000005`. ### Execution

To run the example, simply run the `gradient_descent_example.py` file using Python

``````python gradient_descent_example.py
``````

The output will look like this

``````Starting gradient descent at b = 0, m = 0, error = 5565.10783448
Running...
After 1000 iterations b = 0.0889365199374, m = 1.47774408519, error = 112.614810116
``````

Example demonstrating how gradient descent may be used to solve a linear regression problem

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