204.1.2 Regression in Python

Link to the previous post : https://statinfer.com/204-1-1-correlation-in-python/

In the last post we went through the concept of Correlation and implemented it using python on a dataset.

In this post we will walk from correlation to Regression.

Correlation is just a measure of association
It can’t be used for prediction.
Given the predictor variable, we can’t estimate the dependent variable.
In the air passengers example, given the promotion budget, we can’t get an estimated value of passengers
We need a model, an equation, a fit for the data.
That is known as regression line

A regression line is a mathematical formula that quantifies the general relation between a predictor/independent (or known variable x) and the target/dependent (or the unknown variable y)
Below is the regression line. If we have the data of x and y then we can build a model to generalize their relation

y = β 0 + β 1 x

- What is the best fit for our data?
- The one which goes through the core of the data
- The one which minimizes the error

The best line will have the minimum error.
Some errors are positive and some errors are negative. Taking their sum is not a good idea.
We can either minimize the squared sum of errors Or we can minimize the absolute sum of errors.
Squared sum of errors is mathematically convenient to minimize.
The method of minimizing squared sum of errors is called least squared method of regression.

\sum e 2 = \sum (y - y^) 2

\sum e 2 = \sum (y - (β 0 + β 1 x)) 2

The next post is a practice session on regression line fitting.

Link to the next post : https://statinfer.com/204-1-3-practice-regression-line-fitting/

21st June 2017