STAT 530, Fall 2016
--------------------

Homework 7 (Extra Credit)
-------------------------

THIS HOMEWORK SET IS EXTRA CREDIT FOR *EVERYONE*.  You are not required to do it, but 
you may do it for UP TO 10 bonus homework points (depending on the quality of your 
responses).

Do the following problems:

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


PROBLEM 1:  
---------------

Use the data from Problem 8.2 in the Everitt textbook, but use it for a multivariate regression.  
Treat the "fasting variables" y1, y2, y3 as the response variables and the "sugar"
variables x1, x2, x3 as the predictor variables.  We wish to predict a person's
fasting measurements based on their sugar measurements.

(a)  Fit the multivariate regression model; that is, use R to find the least-squares
estimate of the Beta matrix of regression coefficients.  Based on this matrix, 
assess the nature of the relationship between the fasting measurements and the sugar 
measurements.

(b) For a person with sugar measurements x1 = 100, x2 = 105, x3 = 95, find a point
prediction of her fasting measurements y1, y2, y3, based on your estimated 
regression model.

==============================================================================
- The "Blood Glucose" data from Problem 8.2 are given on the course web page.

The following R code will read in the data:

bloodg <- read.table("http://www.stat.sc.edu/~hitchcock/bloodglucose.txt", header=T)
fast.meas <- bloodg[,1:3]
sugar.meas <- bloodg[,4:6]

PROBLEM 2:  
-------------------------

Do Problem 5.5 in the Everitt textbook.

NOTE:  The "hair/eye" data are given on the course web page.