This document describes Project 4 for CMPSC 201, which involves writing a C++ program to perform linear regression on a set of (x,y) coordinate data to find the line of best fit. The program must read in the data from a file, calculate statistics like the mean, standard deviation, and correlation coefficient, then use those values to compute the slope and y-intercept of the regression line. It also provides specifications on the required functions and expected inputs/outputs of the program.

1. CMPSC 201
Programming for Engineers with C++
Project 4
Assigned 7/24/14
Problem:
Suppose we have a set of data consisting of ordered pairs and we suspect
the x and y coordinates are related. It is natural to try to find the best line that
fits the data points. If we can find this line, then we can use it to make all sorts
of other predictions. In this project, we're going to use several functions to find
this line using a technique called least squares regression. The result will be
what we call the least squares regression line (or LSRL for short).
In order to do this, you'll be able to reuse some code you've already written
(improve it if necessary, of course), as the LSRL is more or less based on
statistical calculations we've already automated. You'll need to program one
new statistical computation called the correlation coefficient, denoted by r in
statistical symbols:
Once you have the correlation coefficient, you use it along with the sample
means and sample standard deviations of the x and y-coordinates to compute
the slope and y-intercept of your regression line via these formulas:
(Yes, it correct that b is used for slope here.)
By the way, this is another of those numerical methods that computers do so
well. While it's possible to compute an LSRL by hand, automating all of the

2. tedious calculations makes sense, and leaves us to spend our time interpreting
our results in a practical context.
Specifications:
You may work with one other person in class on this project if you wish. If you wish
to discuss the project with someone else, work with a partner. Otherwise, work
alone. There is to be NO collaboration between individuals/groups who are not
working as partners.
In this project, you must read the x- and y-coordinate pairs in from a data file of
unknown length. Each line in the file must contain both coordinates, separated
by whitespace, as shown in the sample data file on Angel. In addition, you must
use functions in this project, splitting the work up into smaller components and
reinforcing your skills with parameter passing and arrays.
You are required to create the following functions, and you must list them in
this order above the main program (no prototypes, please!):
Number (for
Reference)
Role Method's Objective Input Parameters Output Parameters
Returned
Values
1 Input
To read the input file,
line by line, and store
the x- and y-
coordinates in parallel
arrays
 none
 an array of x-
coordinates
read from the
file
 a parallel array
of y-
coordinates
read from the
file
 logical size of
the arrays
none
2 Process
To compute the sample
mean of a data set.
(Note that this one was
given as an example
and you should, by all
means, use it.)
 an array of
data
 logical size of
the array
 none
the sample
mean of the
data in the
array
3 Process
To compute the sample
standard deviation of a
data set. (Reuse code!
Consult Lab 8 for the
formula.)
 an array of
data
 logical size of
the array
 the sample
mean of the
data
 none
the sample
standard
deviation of
the data in the
array
4 Process
To compute the
correlation coefficient.
 an array of x-
coordinates
 none the correlation
coefficient of

3. read from the
file
 a parallel array
of y-
coordinates
read from the
file
 logical size of
the arrays
the input
arrays
5 Process
To compute the least-
squares regression line.
 an array of x-
coordinates
read from the
file
 a parallel array
of y-
coordinates
read from the
file
 logical size of
the arrays
 the y-intercept
of the line
 the slope of the
line
none
6 Output
To display a the
mathematical
representation of a line
to screen
 the y-intercept
of the line
 the slope of
the line
 none
none
Be sure to comment each function well. You should list the preconditions and
postconditions for each one (essentially what you assume about your inputs and
what your outputs will reflect).
You will also need a main program to drive this program. All computation
should be done in the six methods; the main program should be extremely
short. (I have fewer than a dozen lines of code.)
Testing your program:
This program will again be lengthy, so you should develop it incrementally, testing
each new part as you go. Use cout statements in your debugging when needed to
keep track of program flow and/or the value of variables. Sample test data files and
corresponding correct output will be released shortly for you to test your program
with.
Your program should provide the output that looks something like this:
Regression line: y = 1166.93 + -0.586788x
It will have no user input, so no prompts are needed. Any debug statements should
be commented out or removed before final submission. Your code should also
contain enough comments to an outside observer to follow its logic. In your final

4. submission, your program should open a file named "project_4_data.txt," which can
be assumed is in the same directory as the program.
Submission:
Upload your .cpp file from your project with the following filename (replacing
"abc123" and "def456" with your Penn State user Ids):
abc123_def456_project_4.cpp
Both partners should submit a copy of the program in their Angel account.
In a comment block at the top of your cpp file, please be sure to include the
following information: Name(s), Project number, Date assigned, Date due,
Description of program, Expected inputs, Expected outputs
Due date:
Submit by 11:55 PM on 8/8/14. After this time, the dropbox will no longer be
available. 10 bonus points will be awarded if submitted by 8/5/14.