Hallo Raghunathan,

as Paul is not responding to your question, I try to give an answer.
But first: Topic is very complicated, when you go into mathematical detail! Now you will probably say, that we should avoid too much mathematics. Ok, but then don't wonder about the results...
There are many traps in this topic, sometimes leading to very strange performance. E.g. If you have a set of n data points which from theory must be represented by 2-order polynomial but you try to fit by a n-order polynomial after NEWTON (a curve, which hits every point), a desaster can happen!! Especially, if data set is not equally spaced on x-achsis and if data is some noisy, means, if data set does not look like a pure 2-order polynomial. You will suddenly get spikes and artefacts, which never can represent your data. Performance of such n-order polynomial can be totally ridiculous, especially if two or more data points are very close to each other sitting on x-achsis and are very noisy.

But how to fit a data set of n points by a 2-order polynomial, especially with noisy and not equally spaced data points? Well, today with our fast PC this is very easy. We do not make the according math, which forces us to do sophisticated matrix and determinants calculations, we make a simulation with PC.
Simulation is quite easy, you simply need a PC with Q-BASIC and can write the program by yourself. Of course, you can take any other suited programming language. The methode is called 'least-square fit'. Means we take THIS 2-order polynomial, which minimizes the following term:



[Oops, is that big! Sorry, I don't want to shout...{grin}]
Xi/Yi represents your data set of n points. Xi is MM data, Yi is °C data. Sum symbol means, that you sum up over all data points. Now, you still need to change a, b and c e.g. by FOR-NEXT loops and search for miminum value of the sum.

If you are interested in a very good book: 'Data reduction and error analysis for the physical sciences' by Philip R.Bevington, McGraw-Hill book company. It's from 1969, but so brillant, that my professor recommended it to me 'very urgently', when I a studied physics. But believe me, it's not complicate, at all. Very easy to understand, with many examples and computer programs.

By writing this, I want to focuse, that I do not recommend polynomial fits for usual cases. It's my experience, that a good linear fit, having enough 'milestones' (data points), with straight lines from point to point, can also result in a 'curved' line with enough precision. A polynomial fit can be much more unprecise, when curve shows spikes and artefacts. It depends, of course...

Hope it helps,
Kai