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Inference in Regression

We end the course with a look at the regression model you studied in Data 8. This is a set of probabilistic assumptions about two variables that appear to be linearly related. If the assumptions are valid for your data, then the calculations of this chapter will help you make predictions about one of the variables based on the other.

Our focus will be simple regression, in which the goal is to use one variable to predict another. We will also look briefly at multiple regression, in which the goal is to use several variables to predict another.

A good starting point is the visual representation of the model in the Data 8 textbook. According to the model, we believe that the two variables are linearly related, except that we can't see the line. What we see are points that look as though they were generated by starting with points that on a straight line and then bumping each point above or below the line by a random amount.

This creates a cloud of points instead of a line of points. The goal of regression is to figure out where the hidden line is.