solution

 

. Because distributions of variables such as PCB and the PCB congeners tend to be skewed, researchers frequently

analyze the logarithms of the measured variables. Create a data set that has the logs of each of the variables in the PCB data set. Note that zero is a possible value for PCB126; most software packages will eliminate these cases when you request a log transformation.

(a) If you do not do anything about the 16 zero values of PCB126, what does your software do with these cases? Is there an error

message of some kind?

(b) If you attempt to run a regression to predict the log of PCB using the log of PCB126 and the log of PCB52, are the cases

with the zero values of PCB126 eliminated? Do you think that is a good way to handle this situation?

(c) The smallest nonzero value of PCB126 is 0.0052. One common practice when taking logarithms of measured values is to

replace the zeros by one-half of the smallest observed value. Create a logarithm data set using this procedure; that is, replace

the 16 zero values of PCB126 by 0.0026 before taking logarithms. Use numerical and graphical summaries to describe the

distributions of the log variables. Exercises 11.104 to 11.110 use theCROPdata file which contains the U.S. yield (bushels/acre) of corn and soybeans from 1957 to 2007.27