We were discussing  Bootstrap method, confidence intervals and accuracy of model parameters. A model may have parameters that correspond to m dimensions. Since each of these dimensions can allow variations, the probability distribution is a function defined on M-dimensional space. With this probability distribution, we choose a region that has a high percentage of the total distribution relative to the selected model parameters  This region is called the confidence interval. Depending on the degree of distribution chosen, confidence intervals may be mentioned in levels as percentages. The region shape of the distribution may also be mentioned such as ellipsoids. 
As we work with model parameters, some rules of thumb come into view. For example, if we define a progressive rate constant, it cannot turn out to be negative. These facts should not be violated.
It should be noted that confidence interval is tied to the model. If the model were transformed from non-linear to linear, the confidence interval varies. It is often cited as oversimplification because it violates assumptions. This leads to more error in the model parameter values.


We were saying that a model based on linearization is easy but it is not accurate especially when transforming non-linear models.
Usually non-linear models are solved with an objective function such as the chi-square error function. The gradients of the chi-square function with respect to the parameters must approach zero at the minimum of the objective function. In the steepest descent method, the minimization proceeds iteratively until it stops decreasing.

#codingexercise 
Find the square root of a number 
Double sqrt(double n)
{
Double x = n;
Double y = 1;
Double threshold = 1E-5;
while (x – y > threshold)
{
x = (x+y)/2;
y= n/x;
}
return x;
}