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