Workshop Statistics: Discovery with Data, Fourth Edition

TOPIC 28

Least Squares Regression

Much of statistics involves making predictions. If you find a footprint at the scene of a crime, can its length help you predict the height of the person who left the print? Can you predict the sale price of a house based on its square footage, and how much does each extra square foot add to the predicted price of the house? On average, how much can you expect each additional page of a textbook to add to its price, and what proportion of the variability in textbook prices is explained by knowing the number of pages, as opposed to other factors or random variation? You will investigate all of these questions in this topic.

Overview

In the two previous topics, you studied scatterplots as visual displays of the relationship between two quantitative variables and the correlation coefficient as a numerical measure of the linear association between those variables. With this topic, you will investigate the widely used technique called least squares regression. This technique provides a simple mathematical model (or equation) for describing the relationship between two quantitative variables, enabling you to make predictions about one variable's value from the other's value.

Preliminaries

1. Which would you expect to be a better predictor of the price of a textbook:

   number of pages or year of publication? (Activity 28-4)

2. Guess how much (on average) each additional page of a textbook adds to its price. (Activity 28-4)
3. Would you guess that knowing the number ...