The Hypothesis Function
Our hypothesis function has the general form:
The hypothesis function is sometimes simply denoted as .
Note that this is like the equation of a straight line. We give to values for and to get our estimated output .
We try to find proper values for and which provide the best possible "fit" or the most representative "straight line" through the data points mapped on the x-y plane.
A list of m training examples — — is called a training set. Our goal is, given a training set, to learn a hypothesis function h : X → Y so that h(x) is a “good” predictor for the corresponding value of y.
We will also use X to denote the space of input values, and Y to denote the space of output values. In this example, .