Least-squares regression theory can also provide estimates of the slope and intercept and their respective variance estimates. The computed slope and intercept terms are assumed to be unbiased and have a normal distribution for deviations from the true underlying value.
The regression model for the ordinary least-square case is:
Y = mX + b
with a design Matrix X:
| x1 1 |
| x2 2 |
| xn n |
where each point x is appropriately transformed depending on the presumed rate order.
The Variance-Covariance Matrix, which is central to assessing the precision of the rate order estimate, is created by taking the matrix inverse of [ matrix product of [transpose of Matrix X] times [Matrix X]]]. It is further scaled by an estimate of the variance of the regression model fit (computed from the differences between fitted and reported for each point which is further squared, summed for all points, and divided by (n-2). See Wikipedia discussion of statistical theory at https://en.wikipedia.org/wiki/Ordinary_least_squares.
Then, one could apply a hypothesis testing procedure (like the t-test) as to whether the slope is o or 1 or 2. However, this is not precisely correct, and one should examine other data or theory (like looking at the expected slow rate-determining step coefficients), and then proceed to selected just one value from (0, 1, 2) for testing.
However, in the case of getting a fractional value (as a regression model of the above data actually indicates), try a direct test for linearity (see, for example, a proposed idea of modifying the regression at http://essedunet.nsd.uib.no/cms/topics/regression/4/3.html ). This consists of introducing a quadratic term in time, and if the latter fails a t-test of being different from zero, the model is deemed to have passed a linearity test.