Question

8. (Fitting Percentage of Body Fat to Simple Body Measurements) Per- centage of body fat, age, weight, height, and ten body circumference measurements (e.g., abdomen) are recorded for 252 men. The following two links provide a description to the dataset and the list of the data values,

     http://jse.amstat.org/datasets/fat.txt
     http://jse.amstat.org/datasets/fat.dat.txt
   

   The R function read.table() can then be used to read the data values
   into R from the given link,
   fat < − read.table(”http://jse.amstat.org/datasets/fat.dat.txt”,header=FALSE) You can then use the function colnames() to name the variables (columns), colnames(fact) < − c(”ID”,’pctfat.brozek’, ... , ’age’, ’weight’, ’height’,
   ...)
   (a) Use the function plot(x,y) in R to obtain four scatterplots: ”Per-
   cent body fat using Brozek’s equation” versus ”Neck circumference”,
   ”Percent body fat using Brozek’s equation” versus ”Chest circumfer-
   ence” , ”Percent body fat using Brozek’s equation” versus ”Weight”,
   and ”Percent body fat using Brozek’s equation” versus ”Height”. Use par(mfrow=c(2,2)) in R to combine the four plots into one overall
   graph. Then compute, using R function cor(x,y), the four correlation coefficients. Which variable, among Neck circumference, Chest circum-
   ference, Weight, and Height has the strongest linear association with
   Percent body fat using Brozek’s equation?
   (b) Use Fisher’s transformation to test the hypothesis that theoreti-
   cally ”height” and ”pctfat.brozek” have zero correlation; i.e., rho = 0.
   Read the section on Fisher’s transformation of correlation in the lecture
   notes of 03/19 and then follow the examples.

Answer 1

Two ways to increase the statistical power of an experiment overlap in the two sampling distributions for null hypothesis and alternative hypothesis Larger the sample size, the higher the power 2. Decrease random error - Reduce the variance: smaller variance yields higher power. Power is higher when the standard deviation is smaller than when it applied consistently.