If I want to calculate the slope (velocity) of the absorbance curve at the linear region, how small/large should this region be for the most exact results? Should I go for the region where the substrate converted is less than 5%? Or the longest stretch from zero which gives me R2 = 0.99?
What kind of consistency should I have between results (e.g. if one linear region is shorter than the other, should I get the longest for each, or the most linear for each)?
Are there any agreed-upon standards that published kinetics studies follow?
I'm not aware of a standard definition of how long the linear region is of the reaction progress curve. I don't trust a hard cutoff like 5% or 10% of substrate consumed because it doesn't take into account that sometimes the product can be strongly inhibitory. I generally judge it by eye using a straight edge, with one end at time zero: the linear range ends to the time when the curve starts to drop below the straight edge. If you have a lot of time points spaced close together, you can plot the slope versus time: the linear range extends until the slope begins to decrease.
I think it should be the longest region with R2=0.99 because you essentially want to find where the inflexion point is after which your log region starts.
If you wish to publish your data then you probably need to at least determine Vmax, because velocity depends on substrate concentration.
The basic Henri-Michaelis-Menten equation, v/Vmax = [S]/(Ks + [S], is one way, where by plotting the slopes from various determinations, each of which uses a different but fixed substrate concentration, gives you an idea of Vmax (usually by plotting 1/v versus 1/[S] gives you 1/Vmax at the y-intercept).
The problem with using R2 is that it is not exactly a measurement of goodness-of-fit of the data to a straight line - it is a measure of the amount of scatter in the data assuming it is a straight line. The noise in the data could give you an R2 well below 0.99 while still in the linear range.
The recommendation is to fit the most linear from each. I suggest to take a look to the book of Cornish-Bowden: Fundamentals of Enzyme Kinetics, fourth edition 2012. In the page 86, the section "Estimating the linear rate", there is a good review about this problem.
As someone else already pointed out, the coefficient of determination (a.k.a. "R-square" or R2) is not a suitable measure of linearity or non-linearity, as many people mistakenly believe. This is one of the most pervasive misconceptions circulated in the enzyme kinetics literature.
Please take a look at Figure 1 in the attached preprint and please read section entitled Nonlinearity of the no-inhibitor control curve in the Results, p. 3. What you see is an enzyme progress curve, duration 25 minutes, that is characterized by R2 = 0.99 but is very clearly nonlinear.
What is even more instructive is to look at the first 10 minutes (inset to Figure 1). There you see a "linear portion" (upon visual examination) but, at the same time, Figure 2 shows you that within those first 10 minutes the reaction rate already decreased by about 20%.
Certainly if the entire curve is an exponential (as this one is: it must be because [S]0
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