Finding original equation from rounded values So I have an interesting problem, suppose you have a formula:$$y=2.41\times x+3.85$$
and you use this formula to compute a table of values for $y$, with x ranging from $0$ to $20$, you then round the y values to the nearest $0.5$. 
My question is, if you are only given the rounded values for y, and the corresponding values for x, is it possible to recover the original formula used to generate the values?
I figured if you plot the data and calculate a linear regression you'd still end up with the original formula, however this is not the case, when I tried this example problem in excel, the regression was $$y=2.3989x+3.8368$$Which is close but not perfect. So I'm not sure if there is a mathematical approach to this, or even using MATLAB or similar. Or if it's simply not possible.

Without a proof, I am going to guess that no, it is not possible.
Since you are rounding, there are an entire family of lines from which the rounded data could be derived from.  For instance if your points are (5,1) then the original point could be (4.9,0.9) or (4.89,1.98) etc, etc.  
The problem is thus underdetermined.
