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.