linearRegressionIn1Variable

Using Linear Regression for Prediction

This specific folder contains an example of using linear regression to predict future city populations. But understand that by just giving a different input TrainingSet.txt file you can easily use linear regression to predict something you want!

How To Use This Code

1. install Octave or Matlab

2. fork this repo and clone it locally!

3. navigate to the folder with the above files

4. type run in Octave or Matlab command line

5. You will see a printout of linear regression being applied to predict population size of new cities. Additionally there will be several graphs:

   • Graph of data
   • Graph of cost function
   • Graph of minimal theta values for hypothesis equation

Linear Regression In 1 Variable Review

• Linear Regression in 1 variable with training set
  • m = number of training examples
  • x's = "input" variable/feature
  • y's = "output" target variable
  • (x,y) = one training example
  • (x^(i),y^(i)) = ith training example
  • h(x) = theta_0 + theta_1 * x where h maps from x's to y's
  • WHOLE POINT: Find theta_0 & theta_1 so that h(x) is close to y for our training examples (x,y)
  • mathamatically this means we need to minimize (1/2m)(Sum from i = 1 to m of (h(x^(i))-y^(i))^2 ) where (1/2m) makes math easilier and (h(x^(i)) = theta_0 + theta_1 * x^(i)
  • math notation = minimize over theta_0, theta_1 the cost function J(theta_0, theta_1) also called the squared error function
  • WHOLE POINT explained in this picture:
    
  • Now plugging in the minimal theta_0 and theta_1 our function h(x) = theta_0 + theta_1 * x will predict h(x) = y by giving it an input x.
  • But how do we find the minimal theta_0 and theta_1?! GRADIENT DESCENT = algorithm that lets us find a minimal theta_0 and theta_1. It can also be used to minimize any arbitrary function J.
  • "Batch" Gradient Descent = each step of gradient descent uses all of the training examples.