STAT 4620/5620 WINTER 2024 Assignment 2

1.  (10 points) Your Research Question (RQ)  1, involved three variables, and was focused on the relationship between one response variable and two ex- planatory variables; at least one of the three variables had to be categorical. Prepare a graph using R that can be used to answer RQ1.

2.  (4 points) Your RQ2 had a descriptive goal. Calculate a confidence interval to answer this question.

3.  (6  points) Your RQ3 had a causative goal,  and involved an explanatory variable and a response variable, where the response variable had to be quantitative. Use a hypothesis test to answer RQ3.

4.  (9 points) Describe the linear model estimators implemented in the lmRob function (in R). Contrast these with what is implemented by the lm function. Explain how to proceed with data analysis when you have good reason to believe that a linear model is reasonable for your data but that there may well be data recording errors. (250 words)

5.  (4 points) Explain how the Akaike information criterion (AIC) is computed for a generalized linear model and how it is commonly utilized for model (or variable) selection purposes. (250 words)

6.  (8 points) Let’s explore the negative binomial distribution.

(a) Write down its density function.

(b) Plot the density curves from a negative binomial distribution for a range of values of it’s two parameters using the dnbinom function in R.

(c) Suppose you elect to use the alternative parametrization (often used in ecology) where the mean is μ and the variance is μ + μ2 /k.  What distribution do you arrive at as the k parameter gets larger and larger? (150 words)

7.  (3 points) Residual checking for GLMs is not always as straightforward as for linear models, and the problems are particularly acute in the case of binary responses. Explain why. (100 words)

8.  (16 points) We are interested in a study concerning lung function in pa- tients with cycstic fibrosis (Altman (1991, p.338)).   Data are in the ISwR package and can be loaded into the workspace with data(cystfibr).

(a) Fit a model relating maximum expiratory pressure (pemax) to the ex- planatory variables contained in the dataset.