Linear Regression
Data Analysis Home

How It Works

Problem 1

Problem 2

Problem 3

Summary

Further Study


On-Line Glossary

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last modified on 1/23/07

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Introduction

In lab you frequently gather data to see how a factor affects a particular response. For example, you might prepare a series of solutions containing different concentrations of Cu2+ (the factor) and measure the absorbance (the response) for each solution at a wavelength of 645 nm. A scatterplot of the data

shows what appears to be a linear relationship between absorbance and [Cu2+]. Fitting a straight-line to this data, a process called linear regression, provides a mathematical model of this relationship

absorbance = 1.207*[Cu2+] + 0.002

that can be used to find the [Cu2+] in any solution by measuring that solution's absorbance. For example, if a solution's absorbance is 0.555, the concentration of Cu2+ is

0.555 = 1.207*[Cu2+] + 0.002

0.555 - 0.002 = 0.553 = 1.207*[Cu2+]

0.553/1.207 = [Cu2+] = 0.458 M

A scatterplot showing the data and the linear regression model

suggests that the model provides an appropriate fit to the data. Unfortunately, it is not always the case that a straight-line provides the best fit to a data set. The purpose of this module is to emphasize the importance of evaluating critically the results of a linear regression analysis.

After you complete this module you should:

Before tackling some problems, use the link on the left to read an explanation of how linear regression works.