confidInterval = Thread[{c1, c2} -> Around@*Interval /@ nlm["ParameterConfidenceIntervals"] nlm["ParameterConfidenceIntervals"]] (* {c1 -> Around[9.297969154154664, 1.0182007406816869`], c2 -> Around[22.62894607083057, 3.89519370692895]} *) Plot[nlm[log10q], {log10q, Min[data[[All, 1]]], Max[data[[All, 1]]]}, Epilog -> {Red, AbsolutePointSize[4], Point[data]}, Frame -> True, Axes -> False, GridLines -> Automatic, GridLinesStyle -> Lighter[Gray, .8], FrameLabel -> (Style[#, 14, Bold] & /@ {HoldForm@Log10["q (K/s)"], Row[{Subscript[T, f'], " (", Degree, " C)"}]})] nlm = NonlinearModelFit[data, {model2, c1 > 5, c2 > 5}, {c1, c2}, log10q]; param = nlm["BestFitParameters"] (* {c1 -> 9.29797, c2 -> 22.629} *) nlm["ParameterTable"] // Quiet 
Plot[nlm[log10q], {log10q, Min[data[[All, 1]]], Max[data[[All, 1]]]}, Epilog -> {Red, AbsolutePointSize[4], Point[data]}, Frame -> True, Axes -> False, GridLines -> Automatic, GridLinesStyle -> Lighter[Gray, .8], FrameLabel -> (Style[#, 14, Bold] & /@ {HoldForm@Log10["q (K/s)"], Row[{Subscript[T, f'], " (", Degree, " C)"}]})] nlm = NonlinearModelFit[data, {model2, c1 > 5, c2 > 5}, {c1, c2}, log10q]; param = nlm["BestFitParameters"] (* {c1 -> 9.29797, c2 -> 22.629} *) Plot[nlm[log10q], {log10q, Min[data[[All, 1]]], Max[data[[All, 1]]]}, Epilog -> {Red, AbsolutePointSize[4], Point[data]}, Frame -> True, Axes -> False, GridLines -> Automatic, GridLinesStyle -> Lighter[Gray, .8], FrameLabel -> (Style[#, 14, Bold] & /@ {HoldForm@Log10["q (K/s)"], Row[{Subscript[T, f'], " (", Degree, " C)"}]})] nlm = NonlinearModelFit[data, {model2, c1 > 5, c2 > 5}, {c1, c2}, log10q]; param = nlm["BestFitParameters"] (* {c1 -> 9.29797, c2 -> 22.629} *) nlm["ParameterTable"] // Quiet
Plot[nlm[log10q], {log10q, Min[data[[All, 1]]], Max[data[[All, 1]]]}, Epilog -> {Red, AbsolutePointSize[4], Point[data]}, Frame -> True, Axes -> False, GridLines -> Automatic, GridLinesStyle -> Lighter[Gray, .8], FrameLabel -> (Style[#, 14, Bold] & /@ {HoldForm@Log10["q (K/s)"], Row[{Subscript[T, f'], " (", Degree, " C)"}]})]