Читать книгу Statistics - David W. Scott - Страница 13

In the left frame of Figure 1.4, we plot the brain and body weights of 62 land mammals from the MASS library. The relationship, if any, is hard to discern since 59 of the measurements are overplotted near the origin. We might choose to exclude the two elephant measurements and even the human data point as outliers, and then replot.

However, Tukey introduced a power transformation ladder to re‐express a variable :

see Problem 3 for an explanation of why is used in place of when .

In the right frame of Figure 1.4, we use the log function to dramatic effect. There clearly is a strong relationship that allows highly accurate prediction of the log(brain weight) of a land mammal knowing its log(body weight). (The body weight is easily measured for a living specimen, but not its brain weight.) Moreover, the relationship appears to be linear. In this re‐expressed scatter diagram, the two or three outliers identified in the first plot are no longer outliers.