Each female crab in a study of nesting horseshoe crabs had a male crab attached

Question

Each female crab in a study of nesting horseshoe crabs had a male crab attached to her in her nest. The study investigated factors that affect whether the female crab had any other males, called satellites, residing near her. Explanatory variables that are thought to affect this included the female crab's color (color), spine condition (spine), weight (weight), and carapace width (width). The response outcome for each female crab is her number of satellites (Sa). Data are available for 173 female crabs crabs read.table( /Desktop/2014-Qual/crabs2/crab.txt", col name ("ID "color spine "width' "weight". "Sa") summary (crabs) ID color spine width weight 1 Min 1.000 Min :1.000 Min :21.0 Min 1.200 Min 0.000 Min. 1st Qu 44 1st Qu :2.000 1st Qu. :2.000 1st Qu. 24.9 1st Qu. :2.000 1st Qu 0.000 Median 87 Median :2.000 Median 3.000 Median :26.1 Median 2.350 Median 2.000 Mean 87 Mean 2.439 Mean 2.486 Mean 26.3 Mean 2.437 Mean 2.919 3rd Qu. 130 3rd Qu. :3.000 3rd Qu. 3.000 3rd Qu. 27.7 3rd Qu. 2.850 3rd Qu 5.000 3.000 Max 33.5 Max. 5.200 Max. 15.000 Max 173 Max 4.000 Max. attach crabs) width shifted C- vidth mean (width) fit1 glm( Sa width shifted factor (color) factor (spine) veight family poisson link "log")) summary (fit1) Only part of the summary included here Coefficients Estimate Std. Error z value Pr(>Izl) (Intercept) 0.07705 0.43557 0.177 0.85960 width shifted 0.01651 0.04894 0.337 0.73582 factor(color)2 -0.26491 0.16811 1.576 0.11507 factor (color) 3 -0.51374 0.19536 2.630 0.00855 factor (color) -0.53126 0.22692 2,341 0.01922 factor (spine)2 -0.15044 0.21358 -0.704 0.48119 factor (spine)3 0.08742 0.11993 0.729 0.46604 weight 0.49712 0.16628 2.990 0.00279 Signif. codes 0 0.001 0.01 0.05 0.1 1 (Dispersion parameter for poisson family taken to be 1) Null deviance: 632.79 on 172 degrees of freedon Residual deviance 549.56 on 165 degrees of freedon AIC: 920.86 Number of Fisher Scoring iterations: 6

Explanation / Answer

Solution:

a) Sa = 0.077 + 0.0165(weight.shifted) - 0.264(factor(color)2) - 0.513(factor(color)3) - 0.532(factor(color)4) - 0.150(factor(spine)2 +0.087(factor(spine)3) + 0.497(weight)

the above model is the full model with intercept

but if we include only the statistically significant variable then our model would be,

Sa=0.077 - 0.514(factor(color)3) - 0.531(factor(color)4 + 0.497(weight) would be our logistic equation

b)

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