# linear regression

## premise

- $X$ is a
`matrix`

which has`m`

rows and`n`

columns, that means it is a $m \times n$ matrix, represents for training set. - $\theta$ is a $1 \times n$
`vector`

, stands for hypothesis parameter. - $y$ is a $m \times 1$
`vector`

, stands for real value of training set. - $\alpha$ named
`learning rate`

for defining learning or descending speed. - $S(X_j)$ means to get standard deviation of the j feature from training set.

# 1. Hypothesis

Draw hypothesis of a pattern.

# 2. Cost

Calculate the Cost for single training point.

# 3. Cost function

Draw cost function for iterating whole training set.

# 4. Get optimized parameter

Learn from training set to get optimized parameter for proposed algorithm.

### Gradient Descend

Complicate to implement.

suitable for any senario.

### Normal equation

Convenient, but performance bad while

`m`

grow large than 100000.

Unable to conquer non-invertable matrix.

## Feature scaling

Use feature scaling to optimize training set.

Make gradient descend converge much faster.