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Suppose we are interested in determining the reasons that some countries have long life expectancies while others do not. We might begin by examining the relationship between life expectancy and other variables for various countries. The left panel of Figure 1.1 shows a scatterplot of the average life expectancy for several countries versus the number of newspapers per 1000 persons in each country. The data are in WorldBankData.csv . The fitted linear regression line compared to the data shows the obvious curvature, and linear regression is not appropriate. In the usual fashion, linearity is induced by applying the natural logarithm transformation to the independent variable, as shown in the right panel. The log data are still not completely linear, but are much more linear than the original data.

Figure 1.1 Life expectancy vs. newspapers per 1000 (left) and log(newspapers per 1000) (right) for several countries.