Assignment 7

Due Date

Friday, March 2, 2012

Data Source

The data for this assignment are from Michael Crawlely's web site. The files are fertilizer.txt and farms.txt.

Part 1

Overview

The data set fertilizer.txt records the root length (root) of twelve plants (plant) measured at two-week intervals (week) for a total of ten weeks. One half the plants had fertilizer added, the other half, the controls, did not (fertilizer). Thus we have multiple measurements made on the same plant as well as measurements made on different plants.

Questions

1. Fit a model in which root size is allowed to vary as a function of time. Be sure in fitting your model that you properly account for the manner in which the data were obtained.
2. Determine the effect of fertilizer on root growth.
3. For your final model from Question 2 determine if there is any lingering temporal correlation that should be accounted for.
4. Graph your final model superimposed on the raw data. Clearly show the population average model as well as the various subject-specific models.

Part 2

Overview

The data set farms.txt records plant size (size) and soil nitrogen levels (N) at 120 locations. A random sample of 24 farms (farm) was initially obtained and then measurements were taken at five locations on each farm.

Questions

1. Fit a variance components model and partition the variability in plant size as variability between plants on the same farm and variability between plants from different farms. Where does most of the variability occur?
2. Estimate the correlation of the response variable for observations coming from the same farm.
3. Fit a regression model that estimates the overall linear relationship between plant size and soil nitrogen levels while properly accounting for the structure of the data set.

Cited reference

Crawley, M. J. 2007. The R Book. John Wiley, New York

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