## Linear Regression

A way to model the relationship of a one or more explanatory variables to a dependent variable

### Types Of Linear Regression

**Simple Linear Regression** - One explanatory variable
**Multiple Linear Regression** - More than one explanatory variable

### Simple Linear Regression

`y = beta_0 + beta_1 x`

- y - response variable
- x - explanatory variable
- B0 - intercept
- B1 - slope

### Pearson’s Correlation

Correlation is a linear association between two scalar variables

**R** or **Pearson’s R** - Correlation coefficient

- always between -1 and 1
- no unit
- corr(x, y) = corr(y, x)
- magnitude indicates strength
- sign indicates direction of association

### Residuals

A residual is difference between observed and predicted values

`e_i = y_i - hat y_i`