Illuminating Statistical Analysis Using Scenarios and Simulations

44Loose End I (Collinearity)

Statistical Scenario—Loose End #1

In Chapter 41 our simple regression model to predict weight using only height has of 0.81, and in Chapter 42 our simple regression model to predict weight using only sex has of 0.64.

In Chapter 43, our multiple regression using both height and sex has of 0.82.

Why such a small improvement from 0.81 to 0.82 when we added sex to our height model?

Before we pursue this specific question, let's look at an extreme hypothetical example.

Consider Table 44.1. It tells us the number of bedrooms and bathrooms of new houses being built in the community along with the list price for each. There are many houses, but they are all one of the three types and they are all priced very close to their respective list prices.

Table 44.1 House features and prices.

(Number of bedrooms)	(Number of bathrooms)	(House list price)