To choose the optimal value of the scale you will require some physical knowledge of the system that is under analysis.  What does the signal that you wish to analyze correspond to and in the scaleogram what do you want to detect ( slowly varying processes,  point discontinuities or anomalous readings). Only then you can come up with a deterministic or heuristic criteria for the scale selection 

See the image file for more details on question

Source: http://www.sid.ir/en/vewssid/j_pdf/1005220101410.pdf

What I understand from the given information is that the authors are trying to fit a line to some data points.  They are trying to estimate parameters for the equation of sort y=mx+b.  The authors say that coif let give big values for the slope m. I donot have in depth understanding of the chemistry so I may not be of further help

Exactly 

what you got is perfect.

I dont have any issue with the fit and that was later part.

before that they select a best optimal scale from "scalogram" after wavelet transformation.

My issue are same what information scalogram give to me and how to get best optimal scale from scalogram.

I dont have any idea interpret or understand scalogram actually.

I even search the many book and net but fail to find that answer.

As you know  that the wavelet transform is based on calculating correlation of the signal with wavelets of different time scaling. In discrete wavelet transform the scales (time scaling)  is multiple of powers of two.  In the scaleogram the results of  the wavelet transform are represented as a function of time and scale. Coefficients at different scale and time shifts are represented. 

According to my understanding of the matter you require a scale which will give you the appropriate zero crossings in the frequency spectrum