[2021] STAT2401: Analysis of Experiments - Q2 Crab-Version
2
As part of a study of the effects of predatory intertidal crab species (Species) on snail populations, researchers measured the mean closing forces (Force) in newton (N) and the propodus heights (Height) in millimetre (mm) of the claws on several crabs of three species. The data for this question comes from Yamada and Boulding (1998) “Claw Morphology, Prey Size Selection and Foraging Effciency in Generalist and Specialist Shell-Breaking Crabs,” in Journal of Experimental Marine Biology and Ecology, 220, pp 191–211.
This dataset Crab-Version-0.csv is available in LMS unit STAT2401 online. Please download the data, save it in “your working directory”, and read in the data by
setwd("your working directory")
Crab = read.csv(file="Crab-Version-0.csv",header=T)
(a) Fit the following models in order to explain the response variable log force (log(Force)) based on log height (log(Height)) and species (Species):
- M1, a simple linear regression for all observations (i.e. intercept and slope not dependent on di↵erent species.)
- M2, parallel regressions for observations from each species (i.e. re- gressions have the same slope but the intercept varies from species to species.)
- M3, separate regression for observations from each species (i.e. regres- sions have intercept and slope that varies from species to species.) Report the R code (NOT the R-output) that you used to fit these models. [3 marks]
(b) Use F tests to select the most appropriate model from M1, M2, and M3, working at a 5% significance level. Explain your reasoning clearly, and include the p-values that you obtain for your tests, also report your R code (NOT the R-output). [6 marks]
(c) For your preferred model, report the fitted models for each of the three species. [marks]
(d) Consider the Model M3 in part (a).
(i) What is the p-value for the test of the hypothesis that the slope in the re- gression of log(Force) on log(Height) is the same for species “Cancer productus” as it is for species “Hemigrapsus nudus”? [3 marks]
(ii) What is a 95% confidence interval for the amount by which the slope for species “Cancer productus” exceeds the slope for species “Hemigrapsus nudus”? (Report also your R-code.) [3 marks]
(iii) Report the estimated mean Force for species “Hemigrapsus nudus” and Height 9mm and its confidence interval (Report also your R-code). [4 marks]
(iv) ReportthepredictedForceforspecies“Hemigrapsusnudus”andHeight 9mm and its prediction interval (Report also your R-code). [4 marks]
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