Is this Time analysis strategy right?

Question

I'm working in the time analysis for an algorithm with two optional optimizations variant applied and followed next approach:

1. Create inputs of different lengths for the algorithm
2. Using these inputs to execute the two algorithm variants and count the asymptopic number of operations (steps)
3. Graph the operations count

4. Graph typical time complexity curves and compare with result:

   • Polynomial graph graphed by using $N^6$
   • Quasy-Polynomial graphed by using $2^{LOG(N)^6}$ ($K=6$)
   • $N$ = input length

I'm a newbie on this kind of analysis and some advise on how to proceed to complete the analysis will be welcome as I feel I'm doing something wrong.

So the questions is, how is the right way/process to do a Time Analysis for an algorithm.

Just in case this helps I provide the raw data for both algorithm Optimizations

Optimization 1 (# of steps)
==========
18   168.444   
19   334.625   
20   671.042   
21   1.869.381   
22   2.664.066   
23   5.318.839   
24   10.656.909   
25   21.008.570   
26   42.226.829   
27   84.365.073   
28   143.803.905   
29   343.807.896   
30   676.068.035   
31   1.372.590.031   
32   2.742.788.213   


Optimization 2 (# of steps)
==============

18   109.533   
19   65.720   
20   250.565   
21   1.324.926   
22   866.908   
23   2.638.451   
24   4.328.395   
25   12.265.480   
26   15.808.379   
27   43.385.582   
28   75.952.700   
29   206.996.787   
30   267.098.278   
31   730.593.681   
32   1.278.315.507