Math 331, Fall 2002: Problems 7-10
NOTE: Each exercise is worth 10 points and can be
turned in at any time before its ``expiration date''.
At the end of the semester, I will expect you to have
turned in at least 2/5 of the exercises assigned. If you do more, I
will pick your best grades. If you do less, the missing grades will be
counted as zeros. Altogether, these will count the same as one project.
- 7.
- (expires 9/30)
Fit the points
by means of a quadratic function
, using the least square method. First, do this
step by step, as we did in class; then, use the built-in Maple command,
described in the notes. Check that the two solutions agree.
- 8.
- (expires 9/30)
Fit the set of points
with
a line, using the least square method we used in class. You will see
that this is not a good fit. Think of a better way to do the fit and
use Maple to do it. Explain in your solution why you think your better
way is better.
- 9.
- (expires 10/7)
[In this problem use Maple only as a word
processor. If you're more confortable with paper, you can turn in a
paper instead of a Maple worksheet.] Let points of the form
,
, be given. What is the quadratic
function
that best fits them? Prove your
answer. Does it depend on the optimization method (least square or
others)?
- 10.
- (expires 10/7)
Once we have calculated the
line (or any other curve, for that matter) that best fits a sets of
points, we can get an idea how good the fit is by plotting the line
together with the points. It is much more scientific, however, to have
a measure for this. Come up with a function of the data and parameters
of a given best-fit problem that is small when the fit is good and
large when the fit is bad, no matter how many points are used.
Justify your answer.
MAT 331
2002-09-25