The data set Walleye from the Minnesota Pollution Control Agency contains data on length (inches) and weight (pound) measurements for a sample of 60 walleye caught in Minnesota lakes during 1990s (Monson (2010)).
(a) Create a scatter plot of weight against length. Does the relationship appear linear?
In fact, biologists have determined that the relationship between length and weight of fish is given by W = aLb, where a and b depend on the species (Ricker (1973, 1975)). We will consider log(W) = log(a) + b log(L) (base 10).
(b) Transform the weight and length variables by log base 10 and then create a scatter plot of log(Weight) against log(Length). Describe the relationship.
(c) Use least-squares to find estimates of a and b based on this sample.
(d) What is the 95% confidence interval for b?