Model Representation
Recall that in regression problems, we are taking input variables and trying to map the output onto a continuous expected result function.
Linear regression with one variable is also known as "univariate linear regression."
Univariate linear regression is used when you want to predict a single output value from a single input value. We're doing supervised learning here, so that means we already have an idea what the input/output cause and effect should be.
The Hypothesis Function
Our hypothesis function has the general form:
hθ(x)=θ0+θ1x
We give to hθ values for θ0 and θ1 to get our output 'y.' In other words, we are trying to create a function called hθ that is able to reliably map our input data (the x's) to our output data (the y's).
Example:
| x (input) | y (output) |
| 0 | 4 |
| 1 | 7 |
| 2 | 7 |
| 3 | 8 |
Now we can make a random guess about our hθ function: θ0=2 and θ1=2. The hypothesis function becomes hθ(x)=2+2x.
So for input of 1 to our hypothesis, y will be 4. This is off by 3.
