santifoo

Linear Regression

Sometimes we want to map $x$ to $y$ and we need the 'how'. One way is a linear-fit. Our job will then be to find those constants. Common examples include:

• simple linear regression: $y = c_1 x + c_0$
• multivariable or multiple linear regression $y = \sum_i c_i x_i$
• multivariate or general linear regression $y_j = \sum_i c_{ji} x_i = \mathbf{C}_j \cdot x$
• polynomial linear regression: $y = \sum x_i^ic_i$

linear here means that the coefficients independent and of power 1.

santifoo

Simple Linear Regression

Say that we have data regarding two variables:

y	x
2	1
5	2
10	3