Le 03/04/2011 23:02, Daniel Dalton a ?crit :
> On Sun, Apr 03, 2011 at 07:02:36PM +0100, Leo Butler wrote:
>
> ...
>> < Daniel> 3) Suppose I have 5 (x,y) coordinates. On the standard casio devices at
>> < Daniel> school these points can be punched in and the user may trial a linear,
>> < Daniel> quadratic or cubic equation to see which is the best fit for the
>> < Daniel> points. The calculator provides a number of how successful the equation
>>
>> Btw, a cubic always fits at least as good as a quadratic which fits in
>> turn at least as good as a linear model. If your calculator tells you a
>> linear model fits better than a cubic one, this is because it is using
>> some measuring stick other than goodness-of-fit.
>>
> So for examination purposes there is no point trying any other fit than
> a cubic?
>
>
Examination or not, there may be many reasons to try linear or quadratic
fit :
- the computation runs faster
- the solution is more readable, may be more easily interpreted
geometrically, or used for further computations
- you may want to compare how much you improve the fit between linear
and cubic results
- your teacher may want you to show your understanding of different
kinds of approximations
and of course you may try to fit by a polynomial curve of degree 4 or 5
which is usually even better than cubic (but more complicated), or using
other functions than polynomials (trigonometric, exponentials, ...) more
appropriate in some problems. Cubic fit is nothing else than a good
balance in some cases between simplicity, generality and goodness of fit.
Eric