Skip to main content Accessibility help
×
Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-07T20:35:27.790Z Has data issue: false hasContentIssue false

2 - Basic Linear Regression

Published online by Cambridge University Press:  05 June 2012

Edward W. Frees
Affiliation:
University of Wisconsin, Madison
Get access

Summary

Chapter Preview. This chapter considers regression in the case of only one explanatory variable. Despite this seeming simplicity, most of the deep ideas of regression can be developed in this framework. By limiting ourselves to the one variable case, we are able to express many calculations using simple algebra. This will allow us to develop our intuition about regression techniques by reinforcing it with simple demonstrations. Further, we can illustrate the relationships between two variables graphically because we are working in only two dimensions. Graphical tools prove important for developing a link between the data and a model.

Correlations and Least Squares

Regression is about relationships. Specifically, we will study how two variables, an x and a y, are related. We want to be able to answer questions such as, If we change the level of x, what will happen to the level of y? If we compare two subjects that appear similar except for the x measurement, how will their y measurements differ? Understanding relationships among variables is critical for quantitative management, particularly in actuarial science, where uncertainty is so prevalent.

It is helpful to work with a specific example to become familiar with key concepts. Analysis of lottery sales has not been part of traditional actuarial practice, but it is a growth area in which actuaries could contribute.

Example: Wisconsin Lottery Sales. State of Wisconsin lottery administrators are interested in assessing factors that affect lottery sales. Sales consists of online lottery tickets that are sold by selected retail establishments in Wisconsin.

Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • Basic Linear Regression
  • Edward W. Frees, University of Wisconsin, Madison
  • Book: Regression Modeling with Actuarial and Financial Applications
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511814372.003
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • Basic Linear Regression
  • Edward W. Frees, University of Wisconsin, Madison
  • Book: Regression Modeling with Actuarial and Financial Applications
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511814372.003
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Basic Linear Regression
  • Edward W. Frees, University of Wisconsin, Madison
  • Book: Regression Modeling with Actuarial and Financial Applications
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511814372.003
Available formats
×