nlmSimple =
NonlinearModelFit[data, model, {{a, 20000}, {k1, 300}, {b, 20000}}, t, Weights -> 1/dataErr^2, VarianceEstimatorFunction -> (1 &)];

pearsonTest[obs_, exp_, dof_] /; Length[obs] == Length[exp] :=
Block[{t}, t = Total[(obs - exp)^2/exp] // N;
{t/(Length[exp] - dof),
SurvivalFunction[ChiSquareDistribution[Length[exp] - dof], t]}];