Represent polynomial time complexity as linearythmic To determine the experimental time complexity of radix sort, I wrote a program that counted the number of steps the algorithm took to sort N points. I ran that program for multiple N length arrays, and I plotted the steps taken in Excel. Then, using the trend line tool, I calculated the polynomial that best fit the function. 

It gave me something along the line :
$$Steps = 16n^{1.0932}$$

This seems to be $O(n)$, but my prof is telling us to represent this as $O(n \log n)$ . How would I go about to demonstrate this. 

Thanks. 

PS: If anyone is interested, here are my results.
You cannot "demonstrate" that a running time is $\Theta(n\log n)$ experimentally. All you can do is give evidence. Such evidence would be a constant $C$ such that for large $n$, $Cn\log n$ is a good approximation to the empirical running time.

You found the best polynomial approximation to your input. Since $Cn\log n$ is not a polynomial, this kind of approach cannot possibly give you the answer $Cn\log n$. If you want $Cn\log n$ to be a possible answer, you need to include such functions in the family of functions you are optimizing over.

Finally, to demonstrate that $Cn\log n$ is a better approximation that your polynomial approximation or a linear approximation, all you have to do is to compare the error in the approximation $Cn\log n$ to the errors in the other two options. Smallest error wins.