Biometry Assignment #11 – (Due 12/12/05)
Problem 1 –Weight of Paddlefish
These data on paddlefish were collected by the Iowa Department of Natural Resources. Provided by Ann Runstrom of the Wisconsin DNR (Paddlefish.JMP)
Your goal is to develop a regression model for the weight (kg) of paddlefish using age (yrs) and fork length (cm) as predictors. You will need to consider transformations of some/all of these variables to construct adequate models. Summarize your final models for a general audience.
a) Develop a model for predicting the weight (kg) using only age (yrs.). Make sure that you include appropriate plots showing the adequacy of your model. (5 pts.)
b) Use your model from part (a) to estimate the “typical” weight (kg) of 8 year old paddlefish, also give a 95% confidence interval for the typical weight of all 8 year old paddlefish. (3 pts.)
c) Develop a model for predicting the weight (kg) using fork length (cm). Make sure that you include appropriate plots showing the adequacy of your model. (5 pts.)
d) Use your model to estimate the “typical” weight (kg) of all paddlefish that are 119.38 cm in length, also give a confidence interval for the typical weight of all paddlefish that are this length. (3 pts.)
f) Compare the R-squares of your final models. Which model provides better predictions of weight? Explain reasoning. (2 pts.)
Problem 2 - Effects of Environment on the Claw Development in Lobsters
Data File: Lobster-claws.JMP
The two claws of the lobster (Homarus americanus) are identical in the juvenile stages. By adulthood, however, the two claws normally have differentiated into a stout claw called a "crusher" and slender claw called a "cutter". In a study of the differentiation process, 26 juvenile animals were reared in smooth plastic trays and 18 were reared in trays containing oyster chips (which they could use to exercise their claws.) Another 23 animals were reared in trays containing only one oyster chip. The claw configurations of all animals as adults are summarized in these data.
The variables in this data file are:
Claw - claw configuration as an adult
Treatment - environment reared in
Freq - frequency of lobsters in each treatment/claw configuration combination
a) Contruct a mosaic plot for the relationship between treatment and claw configuration. Also calculate the conditional probabilities of the form P(claw configuation | treatment) and discuss the results. (2 pts.)
b) Perform a test to determine whether the proportions of each claw configuration are homogenous across treatment groups. Discuss. Also explain why this is a test of homogeneity versus a test of independence. (4 pts.)
Problem 3 – Leaf Type and Serpentine Soil
A plant ecologist samples n = 100 trees of a rare species from a 400-square-mile area. She records for each tree whether or not it is rooted in serpentine soils and whether its leaves are pubescent or smooth. The table below contains the results of her study.
Leaf TypeSoil / Pubescent / Smooth / Row Totals
Serpentine / 12 / 22 / 34
Not Serpentine / 16 / 50 / 66
Column Totals / 28 / 72 / 100
Is there a significant relationship between leaf type and soil type? Use the test you feel is most appropriate for analyzing these data and answering the question of interest (justify your test choice). (5 pts.)
Problem 4 –
Comparison of Tooth Wear between Big Cats, Hyaenas, and Wolves/Wild Dogs
Excerpt from the paper “Incidence of Tooth Breakage Amongst Large, Predatory Animals” by Valkenburgh in the The American Naturalist is given below:
The sample is described as…
In this analysis you will be comparing wear stage across species, where wear stage is categorized as follows:
Question and Tasks for Problem 4 (Data File: Skull Tooth Wear)
a) Is there evidence to suggest that the species differ in terms of tooth wear? Use an appropriate test to answer this research question. Obtain the results using both the broad species and individual species categorization and then summarize your findings. (6 pts.)
b) Use correspondence analysis to construct a display showing the difference in tooth wear across individual species. Discuss what this plot, along with the mosaic plot, show regarding differences in wear between the species examined. (3 pts.)
5 - Oxygen Consumption in Males with Sedentary Occupations
Data File: Oxygen Consumption
The variables in this data file are:
Response
Oxycon (Y)= oxygen consumption
Predictors
SBP = systolic blood pressure (mmHg)
Total HDL= total cholesterol (mg/DL)
HDL chol= HDL cholesterol (mg/DL)
Trigly = Triglycerides (mg/DL)
a) Examine scatter plots of Oxygen Consumption (Y) vs. each of the predictors using a scatter plot matrix and find all the pair-wise correlations between Y and each of the predictors. Which predictor has the strongest relationship with oxygen consumption?
(4 pts.)
b) Fit the multiple regression model using all of the available predictors. (5 pts.)
Discuss/interpret each of the following:
- R-square (R2)/coefficient of determination
- “slope” parameters for each of the predictors
c) Which predictor has the strongest adjusted relationship with response? Explain how you determined this. (2 pts.)
d) Find a 95% CI for the Coefficient of SBP in the regression model. Interpret this
interval. (3 pts.)
e) Predict the oxygen consumption for individuals with the
following predictor values (2 pts.)
SBP = 130, Total Cholesterol = 199, HDL Cholesterol = 55, Triglyceride = 205
SBP = 147, Total Cholesterol = 251, HDL Cholesterol = 37, Triglyceride = 165
f) Check and discuss model assumptions. (3 pts.)