In daviddalpiaz/appliedstats: Applied Statistics with R

Explanation

Suppose you are employed by a car manufacturer. You are an engineer tasked with designing the brake system of a car, and you have a dataset similar to the one we've used in this chapter that includes stopping distance and speed. From your perspective, you would like to create a model which can explain the relationship between stopping distance and speed. If speed increases, what happens to stopping distance? If speed decreases, what happens to stopping distance?

In this chapter, we used simple linear regression for this task. So we modeled this relationship using a straight line, which then explains the relationship between the two variables, but only up to a point, as there is some left over error. If we think of the model as "Response = Explainable + Unexplainable," what is the source of this unexplainable variation? There are usually two possible sources: missing predictor variables (that are unmeasured) and measurement error.

In the future, we will look at incorporating more than one predictor variable into a model. In this example, suppose we also had additional information about the cars such as: weight, engine displacement, year, model, drivetrain, etc. We could attempt to use these to explain some of the unexplained. We will also learn to determine which predictor variables among a large group of variables are actually useful for explaining the response.

Prediction

Now, instead of working on making cars, suppose you own a car. How long does it take you to stop when you're driving a certain speed? Your goal here is to simply predict your stopping distance based on your current speed. We have seen above how a model can be used to accomplish this task.

If we were using a larger model which took into account additional information such as weight, model, and year, you would not care about their relationship with stopping distance. You are only interested in the stopping distance at a certain speed for a car with the attributes of your car, not how those attributes relate to the response, in general.