Simple Linear Regression

A linear comparison of only two quantitative variables.

Correlation Coefficient r

The strenght and direction of a linear relationship.

It's always between -1 and 1.

r is a very field dependant measure. The bounderies are different in social sciences because humans are unpredictable, than environmental sciences.

But in general:

Linear regression line

b0 is used for the statistic (sample) and Beta0 for the parameter - the population.

y-hat defines the point of the line while the y defines the point of the real measure.

Least-Squares algorithm

The main algorithm used to find the best fit line is called the least-squares algorithm, which finds the line that minimizes

There are other functions like below, but this one is built into python by default, it tends to work well for most data sets, and has calculus properties that make it good to use.