Linear Regression
Let's revisit the multiple linear regression from Chapter 3, Introduction to Supervised Learning. The following equation is the mathematical representation of a linear equation, or linear predictor function, with p explanatory variables and n observations:
Where each 
is a vector of column values (explanatory variable) and 
is the unknown parameters or coefficients. 
, makes this equation suitable for simple linear regression. There are many algorithms to fit this function onto the data. The most popular one is Ordinary Least Square (OLS).
Before understanding the details of OLS, first let's interpret the equation we got while trying to fit the Beijing PM2.5 data from the model building section of simple and multiple linear regression from Chapter 3, Introduction to Supervised Learning.
If we substitute the values of regression coefficients, 
and 
from the output of the lm() function, we get:
The preceding equation attempts to answer the question "Are the factors DEWP, TEMP...
