# NUMERICAL METHODS PROBLEM SET 9

**PS9-1 Statistics**

Given the data

determine (a) the mean, (b) the standard deviation, (c)
the variance, (d) the coefficient of

variation .

**PS9-2 Least- Square Regression **

Suppose you want to fit a quadratic curve ( parabola ) to the following data
points using least

square regression .

(1) What is the function S_{r} to be minimized to find the
least square regression curve?

(2) What are the three conditions to find the coefficients of the quadratic
curve of the least

square regression? Write the matrix equation of the three conditions.

**PS9-3
Two Dimensional Quadratic Regression
**

Read and understand section 17.3 of the textbook. The mathematical background of this

programming assignment is very similar to the one in section 17.3.

The goal of two dimensional quadratic regression is to find the “best” values of the coefficients

of a quadratic function y of x

_{1}and x

_{2}

The coefficients , and
can be
determined such that they define a function y

that minimizes the sum of the squares of the errors, or residuals,

Differentiation of S _{r} with respect to each of the unknown
coefficients, , and

, gives six linear algebraic equations , or a 6 x 6 matrix equation,
[M]{a}={b}, similar to

equation (17.22) on p.461 of the textbook.

(1) Derive the matrix equation [M]{a}={b} for two-dimensional quadrilateral
regression. Show

all the derivation process.

(2) Given the following data points write a program for finding coefficients

, and of the quadratic regression function.

To show that your program is properly implemented, your
program has to generate: (1) a text

file, output.txt, that contains the 6 x 6 matrix [M], and values of coefficients

, and ; and (2) a VRML file, output.wrl, that
illustrates the data

points and the quadratic regression surface.

Your VRML file should look something like Figure 1. To minimize your work to
generate

the VRML output the following subroutines and a sample code are provided.

In your hand-in directory on AFS, make a new directory
called ps9 (in lower case ) and hand

in the following in the directory. Don’t copy object files (*.obj, *.o).

• Source code files and header file

• Executable file

• Text file name output.txt

• Output VRML file named output.wrl.

Also hand in a printout of the following:

• Source code files and header files

• Text file, ourput.txt

• Two images of the VRML files that look like Figure 1.

PS9-1 (20 pts) |
PS9-2 (20 pts) |
PS9-3a (30 pts) For handing in all the files and printouts (code and wrl files) |
PS9-3b (30 pts) For the correct method and the results |
Total (100 pts) |

Prev | Next |