Statistics for Data Science by James D. Miller

Author:James D. Miller
Language: eng
Format: epub, pdf
Tags: COM077000 - COMPUTERS / Mathematical and Statistical Software, COM018000 - COMPUTERS / Data Processing, COM037000 - COMPUTERS / Machine Theory
Publisher: Packt Publishing
Published: 2017-11-16T08:57:46+00:00

Introducing statistical regression

As promised, let's get going in this chapter with a section that provides a clear explanation of what statistical regression is.

For starters, statistical regression is also routinely referred to as regression analysis and is a process for estimating the relationships among variables. This process encompasses numerous techniques for modeling and analyzing variables, focusing on the relationship between a dependent variable and one (or more) independent variables (or predictors).

So specifically, regression analysis is the work done to identify and understand how the (best representative) value of a dependent variable (a variable that depends on other factors) changes when any one of the independent variables (a variable that stands alone and isn't changed by the other variables) is changed while the other independent variables stay the same.

A simple example might be how the total dollars spent on marketing (an independent variable example) impacts the total sales dollars (a dependent variable example) over a period of time (is it really as simple as more marketing equates to higher sales?), or perhaps there is a correlation between the total marketing dollars spent (independent variable), discounting a products price (another independent variable), and the amount of sales (a dependent variable)?

Keep in mind this key point that regression analysis is used to understand which among the independent variables are related to the dependent variable(s), not just the relationship of these variables. Also, the inference of causal relationships (between the independent and dependent variables) is an important objective. However, this can lead to illusions or false relationships, so caution is recommended!

Overall, regression analysis can be thought of as estimating the conditional expectations of the value of the dependent variable, given the independent variables being observed, that is, endeavoring to predict the average value of the dependent variable when the independent variables are set to certain values. I call this the lever affect—meaning when one increases or decreases a value of one component, it directly affects the value at least one other (variable).

An alternate objective of the process of regression analysis is the establishment of location parameters or the quantile of a distribution. In other words, this idea is to determine values that may be a cutoff, dividing a range of a probability distribution values.

You'll find that regression analysis can be a great tool for prediction and forecasting (not just complex machine learning applications). We'll explore some real-world examples later, but for now, let's us look at some techniques for the process.

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