R Tutorial : Three ways to describe a model

Want to learn more? Take the full course at https://learn.datacamp.com/courses/multiple-and-logistic-regression at your own pace. More than a video, you'll learn hands-on coding & quickly apply skills to your daily work. --- Regression models are abstract things, and as such we human beings have developed various ways of characterizing them. Models can be described by mathematical equations. In many cases, they can be visualized as geometric objects in two- or three-dimensions. And of course, they can be communicated to R via a suggestive syntax. Going forward, we will emphasize the connections between these three characterizations of models, and illustrate how an understanding of one can lead to a deeper understanding of another. A multiple regression model can be expressed as an equation for the response variable y in terms of some explanatory variables x 1 and x 2. The coefficients of the model---beta 0, beta 1 , and beta 2---allow us to translate our knowledge about x into information about y. A statistical model will always include an error term like epsilon that captures our uncertainty. These errors---which are manifest as residuals---are critical to the process of statistical inference---but that is a subject for a later course. In this course, we will focus on the variables and the coefficients. Math isn't everyone's cup of tea, and while this doesn't make it any less important, we will develop geometric intuition about regression models in this course. Our data live in a "space," and we will refer to this as the "data space." In this scatterplot, we view the highway gas mileage of several popular cars along with the corresponding size of their engines---as measured by displacement. Each point on the scatterplot represents an observation. A simple linear regression model can be visualized as a line through this data space. Finally, R doesn't really understand math or geometry. But of course, R is really good at performing the computations that we will