Another horseshoe crab dataset9 (Crabs2.dat at www.stat.ufl.edu/~

aa/glm/data) comes from a study of factors that affect sperm traits of male crabs. A response variable, SpermTotal, is measured as the log of the total number of sperm in an ejaculate. It has mean 19.3 and standard deviation 2.0. Two explanatory variables are the crab’s carapace width (in centimeters, with mean 18.6 and standard deviation 3.0) and color (1 = dark, 2 = medium,

3 = light). Explain how to interpret the estimates in the following table. Is the model fitted equivalent to a GLM with the log link for the expected number of sperm? Why or why not?
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> summary(lm(SpermTotal ~ CW + factor(Color))
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 11.366 0.638 17.822 < 2e-16 CW 0.391 0.034 11.651 < 2e-16 factor(Color)2 0.809 0.246 3.292 0.00114 factor(Color)3 1.149 0.271 4.239 3.14e-05

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