Introduction

Over the next few minutes, I’ll send you on your way to leveraging linear regression for a bit more than explanation or prediction, rather you’ll utilize them to for the sake of inference.

We will leverage simulation for inference in three ways:

• Understanding model sensitivity
• p-value
• confidence intervals

In this post, we’ll mostly be exploring the first one. It will be foundational to my next posts of using simulation to determine p-value and confidence intervals.

Traditional Regression

If you’re not familiar with how linear regression works in general, jump over to this post.

You can jump over here to find various posts on different variations on linear regression, from creating them, to understanding and explaining them.

Increasing Confidence

Traditionally we use linear regression to make an assessment between a variety of variables. On top of that assessment, what we are going to learn here is how you can adjust the inputs of various regression models to drive deeper understanding of the sensitivity or variability of the relationship between your explanatory & response variables.

So how might we go about determining the variability of the relationship of two variables?

Think about it like this…

What is the key output of a linear regression? If you guessed a line, then you’ve got it right! The regression output is effectively the equation of a line, and the slope of that equation serves as the indication of relationship of X & Y. When seeking to understand the variation of our the relationship between response & explanatory variable… it’s the slope that we’re after. Let’s say you ran your linear regression over different samples… the question we would have, is does our slope vary? Or how much does it vary? Is it positive sometimes and negative others? etc.

The Punchline We’re After

We’ve done a bit of exposition to get to the punch line here, but hopefully this serves to give you a solid foundational footing to really understand and use this is practice.

To sum up our introduction, it comes down to this:

We want to understand the variability and sensitivity to variability of the relationship between two variables when we vary the sample driving the model

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