Crab Claws Reconsider the data on claw closing force
Crab Claws. Reconsider the data on claw closing force and claw size for three species of crabs, shown in Exercise 7.22. Display 10.18 shows output from the least squares fit to the separate lines model for the regression of log force on log height. The regression model for log force was
Exercise
Crab Claw Size and Force. As part of a study of the effects of predatory intertidal crab species on snail populations, researchers measured the mean closing forces and the propodus heights of the claws on several crabs of three species. Their data (read from their Figure 3) appear in Display 7.15. (Data from S. B. Yamada and E. G. Boulding, “Claw Morphology, Prey Size Selection and Foraging Efficiency in Generalist and Specialist Shell-Breaking Crabs,” Journal of Experimental Marine Biology and Ecology, 220 (1998): 191–211.)
(a) Estimate the slope in the simple linear regression of log force on log height, separately for each crab species. Obtain the standard errors of the estimated slopes.
(b) Use a t-test to compare the slopes for C. products and L. bellus. Then compare the slopes for C. productus and H. nudus. The standard error for the difference in two slope estimates from independent samples is the following:
where 
represents the estimate of slope from sample j . Use t-tests with the sum of the degrees of freedom associated with the two standard errors. What do you conclude?
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