Skip to main content Accessibility help
×
Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-09T17:10:23.655Z Has data issue: false hasContentIssue false

3 - More on least squares

Published online by Cambridge University Press:  05 June 2012

Robert de Levie
Affiliation:
Bowdoin College, Maine
Get access

Summary

In this chapter we will describe some of the more sophisticated uses of least squares, especially those for fitting experimental data to specific mathematical functions. First we will describe fitting data to a function of two or more independent parameters, or to a higher-order polynomial such as a quadratic. In section 3.3 we will see how to simplify least-squares analysis when the data are equidistant in the dependent variable (e.g., with data taken at fixed time intervals, or at equal wavelength increments), and how to exploit this for smoothing or differentiation of noisy data sets. In sections 3.4 and 3.5 we will use simple transformations to extend the reach of least-squares analysis to many functions other than polynomials. Finally, in section 3.6, we will encounter so-called non-linear least-squares methods, which can fit data to any computable function.

Multi-parameter fitting

We can expand least-squares fitting to encompass more than one dependent variable. Here we will fit data to an equation of the form y = a0 + a1 x1 + a2 x2. Please note that the method to be used is not restricted to merely two dependent variables, but can in principle be applied to any number of xi-values. In practice, the Regression routine of Excel can handle up to 16 different dependent variables.

Type
Chapter
Information
How to Use Excel® in Analytical Chemistry
And in General Scientific Data Analysis
, pp. 90 - 120
Publisher: Cambridge University Press
Print publication year: 2001

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.

  • More on least squares
  • Robert de Levie, Bowdoin College, Maine
  • Book: How to Use Excel® in Analytical Chemistry
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511808265.004
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.

  • More on least squares
  • Robert de Levie, Bowdoin College, Maine
  • Book: How to Use Excel® in Analytical Chemistry
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511808265.004
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.

  • More on least squares
  • Robert de Levie, Bowdoin College, Maine
  • Book: How to Use Excel® in Analytical Chemistry
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511808265.004
Available formats
×