Assignment 2

Due Date

Friday, January 27, 2012

Data Source

The data for this assignment is the RIKZ data set, the same data set that was used in Assignment 1

Questions

1. Fit a regression model in which the Simpson diversity index is the response and NAP, week, and the interaction of NAP and week are predictors. (This is the same model you fit in Assignment 1). This model fits a separate linear relationship between the diversity index and NAP in each week. Obtain separate 95% confidence intervals for the slopes and intercepts of the four lines that this model yields and display the results in two side by side error bar graphs.
2. To the error bar graphs obtained in Question 1, add additional error bars to the display that allow you to make pairwise comparisons of the slopes across different weeks and the intercepts across different weeks. Report the confidence levels that you used to obtain the new error bars. Based on the graph which pairs of slopes appear to be significantly different from each other?
3. Carry out a series of calculations or produce one or more graphs that clearly demonstrate that this model can yield nonsensical predictions of Simpson diversity. Explain why there are two different types of nonsense predictions here. (See the hint.)

Hints

• To answer Question 2 you will need the material and R code covered in lecture 6, January 23.
• Review the definition of Simpson's diversity. Based on the definition argue in Question 3 that there are two boundary values that need to be considered and demonstrate that the model will routinely generate observations that exceed one or the other boundary.

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