b. Informally assess the fit of a function by plotting and analyzing residuals.

Once we have the data and the a function to fit it, we can try and determine how well our function fits the data.

If students want to find out how well their function fits the data points, they can plot the differences between the actual y values and those provided by the function. These differences are called residuals, and are represented by the symbol e. They're always the predicted value (ŷ) minus the actual value (y). These residuals can then be plotted.

So if our weight-height relationship is expressed by the linear formula w = 5.29h – 219, where h is the height and w is the weight, we can calculate the residuals from the data points and come up with a scatter plot.

Students should know that these residual plots are diagnostic tools (not hammers or screwdrivers, but mathematical tools). They should also be able to use these plots to determine if a function is a good fit for the data. If the scatter plot of the residuals has data points that are randomly scattered about the zero line and about the same spread throughout the plot, it's a sign that our function is a good fit.