Dungeness Crab MoltingThe data for this project were collected as part of a study of the adultfemale Dungeness crab. Two sets of data are provided. The first consistsof premolt and postmolt widths of the carapaces (shells) of 472 female Dun-geness crabs. These data are a mixture of some laboratory data and somecapture–recapture data. They were obtained by scientists and commercialfisheries over three fishing seasons. The first two seasons were in 1981 and1982. The third season was in 1992.Variable DescriptionPremolt Size of the carapace before molting.Postmolt Size of the carapace after molting.Increment postmolt–premolt.Year Collection year (not provided for recaptured crabs).Source 1=molted in laboratory; 0=capture–recapture.• Predict the premolt size of a crab given only its postmolt size using lin-ear regression. Examine a subset of the data collected, say those crabswith postmolt carapace width between 147.5 and 152.5 mm. Comparethe prediction estimates of premolt size for this subset with the actualpremolt size distribution of the subset.• Use your procedure to describe the premolt size distribution of themolted crabs collected immediately following the 1983 molting season.• One simple biological model for growth that is derived from the notionof cell duplication is the multiplicative growth model. It says that therelative growth of a crab should be constant, A crab’s molt incrementis an approximation to its growth rate, and relative growth can beapproximated by normalizing the molt increment by the premolt size:(post − pre)pre,For our case, constant relative growth can be expressed asmolt increment/premolt = c.Plot the molt increment against the premolt size to see if this is anappropriate model.1• Another model is constant growth increment is simply expressed asmolt increment = c.Use a plot to determine if this is appropriate model for the data.• A third model is the allometric relationship between crab weight andwidth giveslog(molt increment/premolt) = a − c × log(premolt),where c is the exponent in the allometric relationship. Fit the data tothis model; what value of c does it give? Does it make sense? Does themodel fit well?• Use cross-validation to compare the predictive ability of these
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