Results of a study of gas chromatography, a technique which is used to detect very small amounts of a substance. Five measurements were taken for each of four specimens containing different amounts of the substance. The amount of the substance in each specimen was determined before the experiment. The response variable is the output reading from the gas chromatograph. The purpose of the study is to calibrate the chromatograph by relating the actual amount of the substance to the chromatograph reading.
Figure 1 shows a plot of response vs. amount with a regression line superimposed. Note the large range of x-values. The regression of amount on response has an R-square of 99.9%. However, despite this, the plot shows that the regression line passes through the data only for the largest amount tested. The responses for other amounts either lie completely above or below the line.
Figure 2 shows this more clearly, and also shows that the variability of the residuals increases as the predicted values increase. These are failures of the regression assumptions of linearity and constant variance. They make the results of the regression suspect. Despite appearances, the data do not seem linear. Perhaps transforming the data would provide a better fit.