For the horseshoe crab data with width, color, and spine as predictors, suppose you start a backward elimination process with the most complex model possible. Denoted by C ∗ S ∗ W, it uses main effects for each term as well as the three two-factor interactions and the three-factor interaction. Table 5.9 shows the fit for this model and various simpler models.a. Conduct a likelihood-ratio test comparing this model to the simpler model that removes the three-factor interaction term but has all the two-factor interactions. Does this suggest that the three-factor term can be removed from the model?b. At the next stage, if we were to drop one term, explain why we would select model C ∗ S + C ∗ W.c. For the model at this stage, comparing to the model S + C ∗ W results in an increased deviance of 8.0 on df = 6 (P = 0.24); comparing to the model W + C ∗ S has an increased deviance of 3.9 on df = 3 (P = 0.27). Which term would you take out?a,b, & c please **Table 5.9: Logistic Regression Models for Horseshoe Crab Data**This table presents various logistic regression models applied to horseshoe crab data. Each model is defined by its set of predictors, along with the corresponding deviance, degrees of freedom (\(df\)), and Akaike Information Criterion (AIC) values.| Model | Predictors | Deviance | \(df\) | AIC ||-------|---------------------------|----------|--------|------|| 1 | \(C \ast S \ast W\) | 170.44 | 152 | 212.4|| 2 | \(C \ast S + C \ast W + S \ast W\) | 173.68 | 155 | 209.7|| 3a | \(C \ast S + S \ast W\) | 177.34 | 158 | 207.3|| 3b | \(C \ast W + S \ast W\) | 181.56 | 161 | 205.6|| 3c | \(C \ast S + C \ast W\) | 173.69 | 157 | 205.7|| 4a | \(S + C \ast W\) | 181.64 | 163 | 201.6|| 4b | \(W + C \ast S\) | 177.61 | 160 | 203.6|| 5 | \(C + S + W\) | 186.61 | 166 | 200.6|**Explanation of Columns:**- **Model:** The number assigned to each logistic regression model for identification.- **Predictors:** The interaction terms included in each model. Variables \(C\), \(S\), and \(W\) stand for specific features within the dataset (the exact nature of variables is contextual).- **Deviance:** A measure of the goodness of fit of a model. Lower deviance indicates a better fit.- **\(df\) (Degrees of Freedom):** Reflects the number of values in the final calculation of a statistic that are free to vary.- **AIC (Akaike Information Criterion):** A statistical

The probability measure is performed with the following statistics: 2 * (Loglikelihood (model2) -…

Answered: For the horseshoe crab data with width,…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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For the horseshoe crab data with width, color, and spine as predictors, suppose you start a backward elimination process with the most complex model possible. Denoted by C ∗ S ∗ W, it uses main effects for each term as well as the three two-factor interactions and the three-factor interaction. Table 5.9 shows the fit for this model and various simpler models.

a. Conduct a likelihood-ratio test comparing this model to the simpler model that removes the three-factor interaction term but has all the two-factor interactions. Does this suggest that the three-factor term can be removed from the model?

b. At the next stage, if we were to drop one term, explain why we would select model C ∗ S + C ∗ W.

c. For the model at this stage, comparing to the model S + C ∗ W results in an increased deviance of 8.0 on df = 6 (P = 0.24); comparing to the model W + C ∗ S has an increased deviance of 3.9 on df = 3 (P = 0.27). Which term would you take out?

a,b, & c please