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 !flforce j lheight, SPECIESgD ?0 C ?1lheight C ?2lb C ?3cp C ?4.lheight x lb/ C ?5.lheight x cp/; where lheight represents log height, lb represents an indicator variable for the second species, and cp represents an indicator variable for the third species. The sample size was 38.
(a) How many degrees of freedom are there in the estimate of a?
(b) What is the p-value for the test of the hypothesis that the slope in the regression of log force on log height is the same for species 2 as it is for species 1?
(c) What is a 95% confidence interval for the amount by which the slope for species 3 exceeds the slope for species 1?