We continue our discussion on determining a model to represent the system. A model articulates how a system behaves quantitatively. 
An inverse model is a mathematical model that fits experimental data. It aims to provide a best fit to the data. 
There are two ways by which we can select the appropriate model. The first is by observing trend lines which correspond to some well known mathematical formula. The second is on the observation of underlying physical processes which contribute towards the system. These physical interpretations contribute to model parameters.
 In order to fit the data points, a model may use least squares of errors. the errors called residuals may be both positive or negative which result in inaccurate measure. Instead the squares of the errors can be minimized to give a better fit.
#codingexercise
Find next greater number using the same digits as the given number. If no other number is possible return the original
This is an alternative to the technique discussed earlier.
Int GetNextHigher(int n)
{
Var digits = Integer.ToDigits(n);
For (int I = n+1; I < INT_MAX; I++)
{
   Var newdigits = Integer.ToDigits(I);
   If (digits.ToHashTable().Equals(newdigits.ToHashTable()))
       Return I;
}
Return –1;
}
There are two things to observe here
1) we don't need to compare the hash table for each increment. if we have a slot array for digits 0 to 9, we only consider numbers, we quickly discard numbers that increment digits not in the original number
2) the range from the number to its next higher is very small.