Question

Caterpillar nitrogen assimilation and body mass. we explored the relationship between nitrogen assimilation and body mass (both on log scales) for data on a sample of caterpillars in Caterpillars. The Instar variable in the data codes different stages (1 to 5) of caterpillar development.

a. Fit a model to predict log nitrogen assimilation (LogNassim) using log body mass (LogMass). Report the value of for this model.
b. Fit a model to predict LogNassim using appropriate indicators for the categories of Instar. Report the value of for this model and compare it to the model based on LogMass.
c. Give an interpretation (in context) for the first two coefficients of the fitted model in (b).
d. Fit a model to predict LogNassim using LogMass and appropriate indicators for Instar. Report the value of and compare it to the earlier models.
e. Is the LogMass variable really needed in the model of part (d). Does the linear trend appear to be better when the caterpillars are in a free growth period? (Again, we are not ready to fit more complicated models, but we are looking at the plot for linear trend in the two groups.)

Answer 1

The question requires statistical analysis of biological data, fitting various regression models to predict log nitrogen assimilation in caterpillars using log body mass and developmental stages. It involves comparing model fits and interpreting the significance and contribution of different predictors.

Step-by-step explanation:

The question presented involves the analysis of a biological data set and requires statistical modeling and interpretation within the context of Biology and Applied Statistics. The question is divided into several parts, where each requires fitting different statistical models to predict log nitrogen assimilation (LogNassim) using other variables such as log body mass (LogMass) and caterpillar development stages (Instar).

To address part (a), one would fit a simple linear regression model with LogNassim as the response variable and LogMass as the predictor. After fitting this model, the β coefficient (slope) and statistical significance will be reported. Part (b) asks for a model involving categorical variables for the Instar stages, which would likely involve dummy coding the categorical variable and fitting a multiple regression model. Comparison of the R-squared values would indicate how much of the variation in LogNassim is explained by each model.

For part (c), the interpretation of the coefficients involves explaining the expected change in LogNassim associated with each unit increase in the predictors. In part (d), a combined model with both LogMass and Instar indicators would be fitted, and the R-squared would be compared to the previous models to see if there's an improvement in predictive power. Part (e) would involve assessing the necessity of LogMass in the combined model, possibly via model comparison techniques such as ANOVA or by reviewing the coefficients' p-values.

Answer 2

A. Produce a scatterplot for predicting nitrogen assimilation (Nassim) based on Mass. Comment on any patterns.

b B.Produce a similar plot using the log (base 10) transformed variables, LogNassim versus Log Mass. Again, comment on any patterns.

C. Would you prefer the plot in part (a) or part (b) to predict the nitrogen assimilation of caterpillars with a linear model? Fit a linear regression model for the plot you chose and write down the prediction equation.