STAT 530, Fall 2014
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Homework 6
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Do the following problems:

IMPORTANT NOTE: For EACH of these problems, also write several sentences 
explaining in words what substantive conclusions about the data
that you can draw from the plots and/or analyses.


PROBLEM 1:  
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Do Problem 7.3(ii) in the textbook.  Use your discriminant function to classify a baby with 
HR = 100, BW = 3000, Factor68 = 0.3, Gesage = 40.

Also answer 7.3(iii) in terms of how this would be addressed with the lda function in R.


PROBLEM 2:  
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Use Hotelling's T^2 test and the data in the test score data set (scores on math and reading tests
given to a sample of girls and a sample of boys) to test for a difference in the mean score vector 
of the boys and the mean vector of the girls.

The following R code will read in the data:

testdata <- read.table("http://www.stat.sc.edu/~hitchcock/testscoredata.txt", header=T)
attach(testdata)
testdata.noIDs <- testdata[,-1]  #to remove the ID numbers


PROBLEM 3:  
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Suppose we have gathered the following data on female athletes 
in three sports.  The measurements we have made are the athletes' heights and 
vertical jumps, both in inches.  The data are listed as (height, jump) as follows:

Basketball Players:  (66, 27), (65, 29), (68, 26), (64, 29), (67, 29)
Track Athletes:  (63, 23), (61, 26), (62, 23), (60, 26)
Softball Players:  (62, 23), (65, 21), (63, 21), (62, 23), (63.5, 22), (66, 21.5)

#The following R code should read in the data as 3 vectors:

sport <- c('B','B','B','B','B','T','T','T','T','S','S','S','S','S','S')
height <- c(66,65,68,64,67,63,61,62,60,62,65,63,62,63.5,66)
jump<-c(27,29,26,29,29,23,26,23,26,23,21,21,23,22,21.5)

###############################################

(a) Conduct the MANOVA F-test using Wilks' Lambda to test for a difference in 
(height, jump) mean vectors across the three sports.

(b) Check to see whether the assumptions of your test are met.  Do you believe 
your inference is valid?

(c) Examine the sample mean vectors for each group.  Informally comment on the 
differences among the groups in terms of the specific variables.