Assignment # 2, Stat 8053, Fall 2010

Reading

The reading for this week is Chapters 11 & 12 of Faraway.

Problems

The following problems are due on Wednesday, September 29, 2010, in class.

1. Page 229, Problem 2. What does the suggested plot of the square root of the absolute residuals tell you? If you only had the averages and SDs of Wage for each value of Educ, what information would have been lost? Hint: You can create a data.frame with a variable year and the means, SD and count each level of educ as follows:

       data(uswages}
       grouped.data <- with(uswages, data.frame(
          educ = tapply(educ,educ,mean),
          meanWage = tapply(wage,educ,mean),
          sdWage = tapply(wage,educ,sd),
          count = tapply(wage,educ,length)))
   

2. Page 230, Problem 5. Use the data in this example to examine the question of whether or not temperature is increasing over time. Beyond the suggestions in the problem, you should also consider (i) fitting parametric models, perhaps linear, quadratic and cubic fits; (ii) test interesting hypotheses (Hint: you may want to design a bootstrap to do this); (iii) whether or not the pre-1881 data should be used.

3. The data in the file

   http://www.stat.umn.edu/~sandy/courses/8053/Data/BGSgirlsLong.csv

   has longitudinal data on 10 girls born in Berkeley California in 1928 or 1929. We will be interested in modeling height (the variable Ht_cm) as a function of Age. The variable Subject is the subject number.
   1. Using regression splines and mixed models, obtain a summary of the average growth curve for girls like these. You should use cross validation to select the df or the number of knots for the b-spline basis.
   2. People interested in growth curves are particular interested in the derivative of the regression function fit in the first part. Humans are thought to undergo a ``growth spurt'' when the rate of increase accelerates for a time and then abates. Explore the derivative of the growth curve you have fit, and if you can derive and perform a test for a growth spurt. (Hint: my program for computing the derivative of a b-spline basis is available at

      http://www.stat.umn.edu/~sandy/courses/8053/Data/mybs.R

      If you look at the code you should be able to figure out what it does and how to use it.)