Illuminating Statistical Analysis Using Scenarios and Simulations

42Using Binomials Too

Statistical Scenario—Sex & Weight Regression

What does a simple linear regression model to predict weight using the binomial variable sex look like?

Let's look at the results of a simple regression model with the scaled variable weight as and the binomial variable sex as . First, look at the (strange looking) scatterplot in Figure 42.1. All the male weights are bunched at and all the female weights are bunched at . The regression line will go through the average weight for males and the average weight for females because that is the least-squares fit.¹

Figure 42.1

How can we interpret the slope of this regression line? Rise/run, where the rise is the difference between the sample mean weight for males and the sample mean weight for females, and the run is 1. The slope, then, is simply the difference in the sample means. That is what will be. And the -intercept, ...