STAT 705 Spring 2009
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Homework 6
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28.13(a), 28.14, 28.15(a,b,c), 28.16(b)
18.25, 18.27, 22.1, 22.6, 22.9(b,c), 22.10(a,b,c,d,f), 22.23, 
26.2, 26.4, 26.5(c,d,e,f), and the extra 
problems given below:

Extra problem 1:

Four varieties of soybean were planted in each of three 
separate regions of a field.  The resulting yields were:

               Variety
           A       B      C      D
Region
1          45      48     43     41
2          49      45     42     39
3          38      39     35     36

Use Friedman's test (with a 0.05 significance level) to test 
whether the four varieties have the same effect on yield.
Give the test statistic value and P-value of your test.

Extra Problem 2:  In the "Muscle Mass" data set, the 
first column (Y) is a measure of muscle mass for a sample 
of women and the second column (X) is age in years.  It is 
conjectured that the regression of muscle mass on age follows 
a two-piece linear relation, with the slope changing at 
age 60 years without discontinuity.

(a) State the regression model that applies if the conjecture 
is correct.  What are the respective mean response functions 
when age is 60 or less and when age is over 60?

(b) Fit the regression model specified in part (a) and state 
the estimated regression function.

(c) Plot the data with the estimated piecewise regression 
function overlain on top of it.

(d) Test whether the piecewise linear regression function is 
needed; use alpha=0.05.  State the alternatives, decision rule,
and conclusion.  What is the P-value of the test?

(e) Specify the regression model for the case when the slope 
changes at age 40 and again at age 60, with no discontinuities.


NOTE: Problems 28.14, 28.15, 18.25, 22.9, 22.10, 26.4, 26.5(c,d,e,f)
and the extra problems require analysis using a computer 
package such as SAS or R.


NOTE: For 28.14, do the residual plot (vs. fitted values), 
the normal Q-Q plot, and the Shapiro-Wilk test.

NOTE:  For 18.25, where it says "nonparametric rank F test", do the
Kruskal-Wallis test (they are equivalent).

NOTE: For 22.9(b), do the residual plot (vs. fitted values), 
the normal Q-Q plot, and the Shapiro-Wilk test (and state your
conclusions).

NOTE: For 22.10(c), you don't have to fit the full and reduced 
models separately if you let SAS or R do the appropriate F-test.

HINT:  For 22.10(f), to decide which is "more efficient", compare 
(22.18) to the square root of (22.17) on page 930.

HINT:  For 22.23, note that you are deriving the LS estimator 
for ANY PARTICULAR delta_i.  So if you want, you could derive 
it for delta_1, and then just generalize your result.  In any 
case, note that in #22.23 you will be solving two equations 
with two unknowns.

NOTE: For 26.4(b), show the residuals plotted for each machine
level, and state your conclusions.

The "Hardware Sales", , "Telephone Communications", "Questionnaire Color #22.9", 
"Bottling Plant Production", and "Muscle Mass" data sets are given on the 
course web page.

Please write your answers neatly and clearly!