Math 6010, Spring 2004, Project 1 (Due: October 15, 2004)
	
1- INTRODUCTION: 
   For your first project have a look at the file "proj1.dat" in the listed 
   directory. This file contains grades, from a previous term, of a certain 
   section of a large statistics course offered by the Mathematics Department 
   of the University of Utah. In order to be able to analyse this data set 
   properly, you need to know a few things about the aforementioned course:
   It is a rather elementary, first-year course on statistic. Its mathematical 
   content is quite small, and the students are introduced to a number of deep 
   ideas in a setting that is as non-technical as is possible. The students'
   backgrounds vary tremendously; this is a "QB Course." This might explain why 
   about 30% of the students attend the main lectures, and 1-5% of the students 
   invariably miss a midterm exam.

2- ORGANIZATION OF THE COURSE:
   The course in question was based on two weekly lectures delivered by the in-
   structor of the course. Then, the students would meet with a T.A. once a week,
   and solve problems, seek help, etc. The students' grades were based on weekly 
   assignments (totaling nine), three midterms, and a final examination. 

   o The lowest two assignments were dropped. All other homework contributed equally
     to a total of 20% of the final grade.
   o The lowest midterm score was dropped. The other two midterms each contributed
     to 30% of the final grade.
   o The final contributed to 20% of the final grade.

3- ORGANIZATION OF THE FILE "proj1.dat":
   o THE ROWS: Each row corresponds to an individual student in the section that 
     we are studying.  There is one exception to this rule: 
        		THE LAST ROW CONTAINS THE MAXIMUM SCORE FOR EACH COLUMN.
   o THE COLUMNS: The columns respectively denote:
   			H1  H2  H3  M1  H4  H5  H6  M2  H7  H8  M3  H9  F,
     where "Hk" refers to "Homework #k," "Mk" to "Midterm #k," and "F" to "Final."

4- YOUR PROJECT:
   o Load the file "proj1.dat" into the package of your choice. My advice would 
     be "R."
   o Transform the raw data into a data set that has one column for "Homework,"
     one for "Midterm," and one for "Final." 
        - Compute "Homework" by first rescaling all homeworks to make them count 
          the same. Then drop the lowest two homeworks. (HINT: In "R" try "sort".) 
          Add the remaining homework grades and transform them to a percentage out 
          of 20% (max. homework).
        - Perform similar tasks to obtain a column for "Midterm." It should contain 
          percentages out of 60%.
        - Transform the final-exam scores to make them out of 20%. This is "Final."
   o Consider the regression problem,
					Final = a + b Homework + c Midterm + noise.
	- Estimate the parameters a, b, and c by least squares.
	- Assume the normal-error model, and test the hypothesis that "Homework is 
          ineffective toward Final." Do this at 95%.
        - Explore whether or not the normal-errors model is valid.

5- YOUR REPORT:
   o Form teams of 2-3 people. Share the thinking. Divide the technical tasks. But:
        - Write up your own findings independently of your team.
        - Write the report to your boss who runs "your statistical consulting firm." 
          "School term-paper" standards are generally not high enough.
 	- Needless to say, your report MUST be typed. If you are in, or plan to be 
          in, the MSTAT program, then you might as well write your report in 
          LaTeX-2e. If you do not know LaTeX-2e, then learn it; you will soon have 
          to anyway.
        - Your report MUST have a front page. This page contains a title, your name,
          the name(s) of your team-mate(s), and other, relevant, information.
	- Your report must have an introduction. You explain the background here. 
        - Your report must also have at least one technical section. This is where 
          you explain your analysis in detail (and correct prose). 
        - Your findings are reported in a separate section. 
        - You may choose to write a "Conclusions" section, but this is entirely 
          optional. 
        - If you use/cite technical material, then cite carefully a source and add
          the source in your bibilography. This remark applies to your textbook, 
          anything that I have written, others' manuscripts and notes, etc. 

6- BON CHANCE!