Notation:

*x ^{(i)}*: input variables/features

*y ^{(i)}*: output/target variables

*(x ^{(i)}, y^{(i)})*: training example (pair)

**training set** - a list of training examples

**superscripted (i)** - an index into the training set (not an exponentiation)

Given a training set, we want to learn a function h_{θ}(x) so that it is a good predictor for each value of x's corresponding y. This function is called a **hypothesis function**.

*e.g.,* given a set of square feet and costs of houses, you could create a scatter plot of data

**supervised learning** - given the "right answer" for each example in the training set for the data

**regression problem** - given square feet of a living area, we want to predict a real-valued output (the price)

**classification problem** - given square feet of a living area, we want to predict a discrete value (if it's a house or apartment)

**x**: input, square feet of a living area

**y**: output, estimated price

**h _{θ}(x)**: hypothesis function that maps from x to y

Take the training set and put it through the learning algorithm.

We represent our hypothesis function with:
h_{θ}(x) = θ_{0} + θ_{1}x

This is univariate (x) linear regression.

θ_{0} and θ_{1} are the parameters of the model.

We compute these parameters using the **cost function**.