Workshop Statistics: Discovery with Data, Fourth Edition

TOPIC 29

Inference for Correlation and Regression

By how much do additional pages in a college textbook increase the price? You partially addressed this question in the previous topic, but now you will return to the issue of inference, where your goal is to infer from the sample to the larger population from which the sample was drawn. Does a large sample correlation coefficient necessarily imply a relationship in the population as well? You will investigate this question by considering whether scientists have discovered a biochemical measurement that can predict the level of romantic feelings experienced by someone who claims to be in love.

Overview

In earlier topics of this unit, you studied graphical and numerical techniques for analyzing the relationship between two quantitative variables. In the previous topic, you used least squares regression lines to describe such a relationship. This topic leads you from a descriptive analysis to an inferential analysis, where the goal is to decide how strongly the sample data provide evidence of a relationship in the population from which the sample was selected. You will learn how to conduct significance tests and produce confidence intervals about a population slope coefficient. You will also study a significance test procedure related to a population correlation coefficient. Once again, you will discover the concept of a sampling distribution underlying these inference procedures. You will also see, yet again, that the general structure, ...