Statistics: Principles and Methods, 7th Edition

11

Regression Analysis I Simple Linear Regression

1 Regression with a Single Predictor

2 A Straight Line Regression Model

3 The Method of Least Squares

4 The Sampling Variability of the Least Squares Estimators—Tools for Inference

5 Important Inference Problems

6 The Strength of a Linear Relation

7 Remarks about the Straight Line Model Assumptions

The Highest Roller Coasters Are Fastest

Some roller coasters are designed to twist riders and turn them upside down. Others are designed to provide fast rides over large drops. Among the 12 tallest roller coasters in the world, the maximum height (feet) is related to top speed (miles per hour). Each data point, consisting of the pair of values (height, speed), represents one roller coaster. The fitted line predicts an increase in top speed of .19 miles per hour for each foot of height, or 19 miles per hour for each 100 feet in height.

This linear relation can be used to predict the top speed of future roller coasters. For instance, that of the next 410 foot roller coaster.

Except for the brief treatment in Sections 4 and 5 of Chapter 3, we have only discussed statistical inferences based on the sample measurements of a single variable. In many investigations, two or more variables are observed for each experimental unit in order ...