EXAMPLE 2.5 Smooth Relationship for Education Spending

Figure 2.3 is a scatterplot of the population versus education spending for the 50 states in the United States with a smooth curve generated by software. The smooth curve follows the data very closely and is somewhat bumpy. We can adjust the extent to which the relationship is smoothed by changing the smoothing parameter. Figure 2.4 is the result. Here we see that the smooth curve is very close to our plot with the line in Figure 2.2. In this way, we have confirmed our view that we can summarize this relationship with a line.