Course Outline

segmentGetting Started (Don't Skip This Part)

segmentStatistics and Data Science: A Modeling Approach

segmentPART I: EXPLORING VARIATION

segmentChapter 1  Welcome to Statistics: A Modeling Approach

segmentChapter 2  Understanding Data

segmentChapter 3  Examining Distributions

segmentChapter 4  Explaining Variation

4.1 Welcome to Explaining Variation


segmentPART II: MODELING VARIATION

segmentChapter 5  A Simple Model

segmentChapter 6  Quantifying Error

segmentChapter 7  Adding an Explanatory Variable to the Model

segmentChapter 8  Models with a Quantitative Explanatory Variable

segmentPART III: EVALUATING MODELS

segmentChapter 9  The Logic of Inference

segmentChapter 10  Model Comparison with F

segmentChapter 11  Parameter Estimation and Confidence Intervals

segmentPART IV: MULTIVARIATE MODELS

segmentChapter 12  Introduction to Multivariate Models

segmentChapter 13  Multivariate Model Comparisons

segmentFinishing Up (Don't Skip This Part!)

segmentResources
list College / Advanced Statistics and Data Science (ABCD)
Chapter 4  Explaining Variation
4.1 Introduction to Explaining Variation
Examining distributions of single variables is always an important starting place. But as data analysts, our interests usually go beyond exploring patterns of variation in a single variable. We want to explain the variation. In this section we begin thinking about what it means to explain variation.
We can start with an intuitive definition of “explain”: if knowing someone’s score on one variable helps you make a slightly better guess about that person’s score on another variable, then we can say that the first variable explains some variation in the second variable.
For example, if we knew someone’s sex, could that help us make a better prediction of their height? You probably already have a sense that males are taller, on average, than females. If we knew that someone was male, even without meeting them, we would predict that they would be taller than if we knew they were female.
This is what we mean when we say sex explains some of the variation in height. It doesn’t explain all the variation because some females are taller than some males. But it does explain some of the variation.
Explaining variation could help us in three ways: it helps us understand what causes the variation in a variable; it helps us predict future observations; or, it helps us change the system we are studying to produce different outcomes.
In this chapter we develop some informal methods for representing and exploring relationships among variables. We start by graphing relationships between two variables, looking for evidence that one variable explains variation in another, and representing these relationships with word equations. (In the next chapters we will introduce more quantitative methods for explaining variation using the concept of statistical model.)