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# Untitled

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1. In[432]:= nPoints = 7;
2. data = Table[{Subscript[x, i], Subscript[y, i]}, {i, nPoints}];
3. errors = Table[{Subscript[dx, i], Subscript[dy, i]}, {i, nPoints}];
4.
5. model[a_, b_, x_] = a x + b;
6.
7. (*The least-squares functional;can be different,i.e.actual distance \
8. to the line*)
9. objFun[a_, b_, data_] :=
10.  Total[(#[[2]] - model[a, b, #[[1]]])^2 & /@ data]
11.
12. (*The usual solution*)
13. solab = First@
14.    Solve[{D[objFun[a, b, data], a] == 0,
15.      D[objFun[a, b, data], b] == 0}, {a, b}];
16.
17. (*The squared deltas relative to the input data*)
18. deltaa = Flatten@{D[a /. solab, #]^2 & /@ data[[All, 1]],
19.     D[a /. solab, #]^2 & /@ data[[All, 2]]};
20. deltab = Flatten@{D[b /. solab, #]^2 & /@ data[[All, 1]],
21.     D[b /. solab, #]^2 & /@ data[[All, 2]]};
22.
23. (*The error is the sum of delta times uncertainty,assuming \
24. independence*)
25. errora = Sqrt[Dot[deltaa, Flatten[errors]^2]];
26. errorb = Sqrt[Dot[deltab, Flatten[errors]^2]];
27.
28. ndata = {{2.04, 1.9975}, {3.06, 3.2160}, {4.08, 4.0939}, {5.10,
29.    4.9878}, {6.12, 6.4685}, {7.14, 7.2003}, {8.16, 8.2944}}
30. nerrors = {{0.02, 0.1696}, {0.03, 0.1793}, {0.04, 0.1821}, {0.05,
31.    0.2568}, {0.06, 0.4197}, {0.07, 0.1342}, {0.08, 0.2304}}
32.
33. nmodel[x_] =
34.  model[a, b,
35.    x] /. (solab /. Thread[Rule[Flatten[data], Flatten[ndata]]])
36. nsolab = solab /. Thread[Rule[Flatten[data], Flatten[ndata]]]
37. nerrorab = {errora, errorb} //.
40.
41. Needs["ErrorBarPlots`"]
42.
43. Show[Plot[{model[(a /. nsolab) - nerrorab[[1]], (b /. nsolab) -
44.      nerrorab[[2]], x],
45.    model[(a /. nsolab) - nerrorab[[1]], (b /. nsolab) + nerrorab[[2]],
46.      x], model[(a /. nsolab) + nerrorab[[1]], (b /. nsolab) -
47.      nerrorab[[2]], x],
48.    model[(a /. nsolab) + nerrorab[[1]], (b /. nsolab) + nerrorab[[2]],
49.      x], nmodel[x]}, {x, -2, 2},
50.   PlotStyle -> {Dashed, Dashed, Dotted, Dotted, Red},
51.   PlotRange -> All],
52.  ErrorListPlot[Transpose[{ndata, ErrorBar @@@ nerrors}]]]
53.
54. During evaluation of In[432]:= LinearModelFit::notdata: The first argument is not a vector, matrix, or a list containing a design matrix and response vector. >>
55.
56. During evaluation of In[432]:= Set::write: Tag LinearModelFit in LinearModelFit[{{{2.04,0.02},{1.9975,0.1696}},{{3.06,0.03},{3.216,0.1793}},{{4.08,0.04},{4.0939,0.1821}}},x,x][a_,b_,x_] is Protected. >>
57.
58. During evaluation of In[432]:= Solve::inex: Solve was unable to solve the system with inexact coefficients or the system obtained by direct rationalization of inexact numbers present in the system. Since many of the methods used by Solve require exact input, providing Solve with an exact version of the system may help. >>
59.
60. During evaluation of In[432]:= ReplaceAll::reps: {-2 (Subscript[{{<<2>>},{<<2>>},{<<2>>},{<<2>>},{<<2>>}}, 1]-LinearModelFit[{<<3>>},x,x][a,b,Subscript[<<2>>]]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,Subscript[x, 1]]-2 (Subscript[{{<<2>>},{<<2>>},{<<2>>},{<<2>>},{<<2>>}}, 2]-LinearModelFit[{<<3>>},x,x][a,b,Subscript[<<2>>]]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,Subscript[x, 2]]-2 (Subscript[{{<<2>>},{<<2>>},{<<2>>},{<<2>>},{<<2>>}}, 3]-LinearModelFit[{<<3>>},x,x][a,b,Subscript[<<2>>]]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,Subscript[x, 3]]-2 (Subscript[{{<<2>>},<<3>>,{<<2>>}}, 4]-<<1>>[a,b,Subscript[<<2>>]]) (LinearModelFit[<<1>>]^(1,0,0))[a,b,Subscript[x, 4]]-2 (Subscript[{{<<2>>},{<<2>>},{<<2>>},{<<2>>},{<<2>>}}, 5]-LinearModelFit[{<<3>>},x,x][a,b,Subscript[<<2>>]]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,Subscript[x, 5]]-2 (Subscript[{{<<2>>},{<<2>>},{<<2>>},{<<2>>},{<<2>>}}, 6]-LinearModelFit[{<<3>>},x,x][a,b,Subscript[<<2>>]]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,Subscript[x, 6]]-2 (Subscript[{{<<2>>},{<<2>>},{<<2>>},{<<2>>},{<<2>>}}, 7]-LinearModelFit[{<<3>>},x,x][a,b,Subscript[<<2>>]]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,Subscript[x, 7]]==0,<<1>>==0} is neither a list of replacement rules nor a valid dispatch table, and so cannot be used for replacing. >>
61.
62. During evaluation of In[432]:= ReplaceAll::reps: {-2 (Subscript[{{<<2>>},{<<2>>},{<<2>>},{<<2>>},{<<2>>}}, 1]-LinearModelFit[{<<3>>},x,x][a,b,Subscript[<<2>>]]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,Subscript[x, 1]]-2 (Subscript[{{<<2>>},{<<2>>},{<<2>>},{<<2>>},{<<2>>}}, 2]-LinearModelFit[{<<3>>},x,x][a,b,Subscript[<<2>>]]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,Subscript[x, 2]]-2 (Subscript[{{<<2>>},{<<2>>},{<<2>>},{<<2>>},{<<2>>}}, 3]-LinearModelFit[{<<3>>},x,x][a,b,Subscript[<<2>>]]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,Subscript[x, 3]]-2 (Subscript[{{<<2>>},<<3>>,{<<2>>}}, 4]-<<1>>[a,b,Subscript[<<2>>]]) (LinearModelFit[<<1>>]^(1,0,0))[a,b,Subscript[x, 4]]-2 (Subscript[{{<<2>>},{<<2>>},{<<2>>},{<<2>>},{<<2>>}}, 5]-LinearModelFit[{<<3>>},x,x][a,b,Subscript[<<2>>]]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,Subscript[x, 5]]-2 (Subscript[{{<<2>>},{<<2>>},{<<2>>},{<<2>>},{<<2>>}}, 6]-LinearModelFit[{<<3>>},x,x][a,b,Subscript[<<2>>]]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,Subscript[x, 6]]-2 (Subscript[{{<<2>>},{<<2>>},{<<2>>},{<<2>>},{<<2>>}}, 7]-LinearModelFit[{<<3>>},x,x][a,b,Subscript[<<2>>]]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,Subscript[x, 7]]==0,<<1>>==0} is neither a list of replacement rules nor a valid dispatch table, and so cannot be used for replacing. >>
63.
64. During evaluation of In[432]:= ReplaceAll::reps: {-2 (Subscript[{{<<2>>},{<<2>>},{<<2>>},{<<2>>},{<<2>>}}, 1]-LinearModelFit[{<<3>>},x,x][a,b,Subscript[<<2>>]]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,Subscript[x, 1]]-2 (Subscript[{{<<2>>},{<<2>>},{<<2>>},{<<2>>},{<<2>>}}, 2]-LinearModelFit[{<<3>>},x,x][a,b,Subscript[<<2>>]]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,Subscript[x, 2]]-2 (Subscript[{{<<2>>},{<<2>>},{<<2>>},{<<2>>},{<<2>>}}, 3]-LinearModelFit[{<<3>>},x,x][a,b,Subscript[<<2>>]]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,Subscript[x, 3]]-2 (Subscript[{{<<2>>},<<3>>,{<<2>>}}, 4]-<<1>>[a,b,Subscript[<<2>>]]) (LinearModelFit[<<1>>]^(1,0,0))[a,b,Subscript[x, 4]]-2 (Subscript[{{<<2>>},{<<2>>},{<<2>>},{<<2>>},{<<2>>}}, 5]-LinearModelFit[{<<3>>},x,x][a,b,Subscript[<<2>>]]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,Subscript[x, 5]]-2 (Subscript[{{<<2>>},{<<2>>},{<<2>>},{<<2>>},{<<2>>}}, 6]-LinearModelFit[{<<3>>},x,x][a,b,Subscript[<<2>>]]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,Subscript[x, 6]]-2 (Subscript[{{<<2>>},{<<2>>},{<<2>>},{<<2>>},{<<2>>}}, 7]-LinearModelFit[{<<3>>},x,x][a,b,Subscript[<<2>>]]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,Subscript[x, 7]]==0,<<1>>==0} is neither a list of replacement rules nor a valid dispatch table, and so cannot be used for replacing. >>
65.
66. During evaluation of In[432]:= General::stop: Further output of ReplaceAll::reps will be suppressed during this calculation. >>
67.
68. During evaluation of In[432]:= ReplaceAll::reps: {-2 (Subscript[{{<<2>>},{<<2>>},{<<2>>},{<<2>>},{<<2>>}}, 1]-LinearModelFit[{<<3>>},x,x][a,b,Subscript[<<2>>]]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,Subscript[x, 1]]-2 (Subscript[{{<<2>>},{<<2>>},{<<2>>},{<<2>>},{<<2>>}}, 2]-LinearModelFit[{<<3>>},x,x][a,b,Subscript[<<2>>]]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,Subscript[x, 2]]-2 (Subscript[{{<<2>>},{<<2>>},{<<2>>},{<<2>>},{<<2>>}}, 3]-LinearModelFit[{<<3>>},x,x][a,b,Subscript[<<2>>]]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,Subscript[x, 3]]-2 (Subscript[{{<<2>>},<<3>>,{<<2>>}}, 4]-<<1>>[a,b,Subscript[<<2>>]]) (LinearModelFit[<<1>>]^(1,0,0))[a,b,Subscript[x, 4]]-2 (Subscript[{{<<2>>},{<<2>>},{<<2>>},{<<2>>},{<<2>>}}, 5]-LinearModelFit[{<<3>>},x,x][a,b,Subscript[<<2>>]]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,Subscript[x, 5]]-2 (Subscript[{{<<2>>},{<<2>>},{<<2>>},{<<2>>},{<<2>>}}, 6]-LinearModelFit[{<<3>>},x,x][a,b,Subscript[<<2>>]]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,Subscript[x, 6]]-2 (Subscript[{{<<2>>},{<<2>>},{<<2>>},{<<2>>},{<<2>>}}, 7]-LinearModelFit[{<<3>>},x,x][a,b,Subscript[<<2>>]]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,Subscript[x, 7]]==0,<<1>>==0} is neither a list of replacement rules nor a valid dispatch table, and so cannot be used for replacing. >>
69.
70. During evaluation of In[432]:= ReplaceAll::reps: {-2 (Subscript[{{<<2>>},{<<2>>},{<<2>>},{<<2>>},{<<2>>}}, 1]-LinearModelFit[{<<3>>},x,x][a,b,Subscript[<<2>>]]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,Subscript[x, 1]]-2 (Subscript[{{<<2>>},{<<2>>},{<<2>>},{<<2>>},{<<2>>}}, 2]-LinearModelFit[{<<3>>},x,x][a,b,Subscript[<<2>>]]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,Subscript[x, 2]]-2 (Subscript[{{<<2>>},{<<2>>},{<<2>>},{<<2>>},{<<2>>}}, 3]-LinearModelFit[{<<3>>},x,x][a,b,Subscript[<<2>>]]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,Subscript[x, 3]]-2 (Subscript[{{<<2>>},<<3>>,{<<2>>}}, 4]-<<1>>[a,b,Subscript[<<2>>]]) (LinearModelFit[<<1>>]^(1,0,0))[a,b,Subscript[x, 4]]-2 (Subscript[{{<<2>>},{<<2>>},{<<2>>},{<<2>>},{<<2>>}}, 5]-LinearModelFit[{<<3>>},x,x][a,b,Subscript[<<2>>]]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,Subscript[x, 5]]-2 (Subscript[{{<<2>>},{<<2>>},{<<2>>},{<<2>>},{<<2>>}}, 6]-LinearModelFit[{<<3>>},x,x][a,b,Subscript[<<2>>]]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,Subscript[x, 6]]-2 (Subscript[{{<<2>>},{<<2>>},{<<2>>},{<<2>>},{<<2>>}}, 7]-LinearModelFit[{<<3>>},x,x][a,b,Subscript[<<2>>]]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,Subscript[x, 7]]==0,<<1>>==0} is neither a list of replacement rules nor a valid dispatch table, and so cannot be used for replacing. >>
71.
72. During evaluation of In[432]:= ReplaceAll::reps: {-2 (Subscript[{{<<2>>},{<<2>>},{<<2>>},{<<2>>},{<<2>>}}, 1]-LinearModelFit[{<<3>>},x,x][a,b,Subscript[<<2>>]]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,Subscript[x, 1]]-2 (Subscript[{{<<2>>},{<<2>>},{<<2>>},{<<2>>},{<<2>>}}, 2]-LinearModelFit[{<<3>>},x,x][a,b,Subscript[<<2>>]]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,Subscript[x, 2]]-2 (Subscript[{{<<2>>},{<<2>>},{<<2>>},{<<2>>},{<<2>>}}, 3]-LinearModelFit[{<<3>>},x,x][a,b,Subscript[<<2>>]]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,Subscript[x, 3]]-2 (Subscript[{{<<2>>},<<3>>,{<<2>>}}, 4]-<<1>>[a,b,Subscript[<<2>>]]) (LinearModelFit[<<1>>]^(1,0,0))[a,b,Subscript[x, 4]]-2 (Subscript[{{<<2>>},{<<2>>},{<<2>>},{<<2>>},{<<2>>}}, 5]-LinearModelFit[{<<3>>},x,x][a,b,Subscript[<<2>>]]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,Subscript[x, 5]]-2 (Subscript[{{<<2>>},{<<2>>},{<<2>>},{<<2>>},{<<2>>}}, 6]-LinearModelFit[{<<3>>},x,x][a,b,Subscript[<<2>>]]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,Subscript[x, 6]]-2 (Subscript[{{<<2>>},{<<2>>},{<<2>>},{<<2>>},{<<2>>}}, 7]-LinearModelFit[{<<3>>},x,x][a,b,Subscript[<<2>>]]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,Subscript[x, 7]]==0,<<1>>==0} is neither a list of replacement rules nor a valid dispatch table, and so cannot be used for replacing. >>
73.
74. During evaluation of In[432]:= General::stop: Further output of ReplaceAll::reps will be suppressed during this calculation. >>
75.
76. Out[442]= {{2.04, 1.9975}, {3.06, 3.216}, {4.08, 4.0939}, {5.1,
77.   4.9878}, {6.12, 6.4685}, {7.14, 7.2003}, {8.16, 8.2944}}
78.
79. Out[443]= {{0.02, 0.1696}, {0.03, 0.1793}, {0.04, 0.1821}, {0.05,
80.   0.2568}, {0.06, 0.4197}, {0.07, 0.1342}, {0.08, 0.2304}}
81.
82. During evaluation of In[432]:= ReplaceAll::reps: {-2 (1.9975 -LinearModelFit[{<<3>>},x,x][a,b,2.04]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,2.04]-2 (3.216 -LinearModelFit[{<<3>>},x,x][a,b,3.06]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,3.06]-2 (4.0939 -LinearModelFit[{<<3>>},x,x][a,b,4.08]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,4.08]-2 (4.9878 -LinearModelFit[{<<3>>},x,x][a,b,5.1]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,5.1]-2 (6.4685 -LinearModelFit[{<<3>>},x,x][a,b,6.12]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,6.12]-2 (7.2003 -LinearModelFit[{<<3>>},x,x][a,b,7.14]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,7.14]-2 (8.2944 -LinearModelFit[{<<3>>},x,x][a,b,8.16]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,8.16]==0,<<1>>==0}
83.  is neither a list of replacement rules nor a valid dispatch table, and so cannot be used for replacing. >>
84.
85. Out[444]=
86. LinearModelFit[{{{2.04, 0.02}, {1.9975, 0.1696}}, {{3.06,
87.       0.03}, {3.216, 0.1793}}, {{4.08, 0.04}, {4.0939, 0.1821}}}, x,
88.    x][a, b,
89.   x] /. {-2 (1.9975 -
90.        LinearModelFit[{{{2.04, 0.02}, {1.9975, 0.1696}}, {{3.06,
91.             0.03}, {3.216, 0.1793}}, {{4.08, 0.04}, {4.0939,
92.             0.1821}}}, x, x][a, b, 2.04])
93. \!\(\*SuperscriptBox[\(LinearModelFit[{{{2.04`, 0.02`}, {1.9975`,
94.            0.1696`}}, {{3.06`, 0.03`}, {3.216`, 0.1793`}}, {{4.08`,
95.            0.04`}, {4.0939`, 0.1821`}}}, x, x]\), \*
96. TagBox[
97. RowBox[{"(",
98. RowBox[{"1", ",", "0", ",", "0"}], ")"}],
99. Derivative],
100. MultilineFunction->None]\)[a, b, 2.04] -
101.     2 (3.216 -
102.        LinearModelFit[{{{2.04, 0.02}, {1.9975, 0.1696}}, {{3.06,
103.             0.03}, {3.216, 0.1793}}, {{4.08, 0.04}, {4.0939,
104.             0.1821}}}, x, x][a, b, 3.06])
105. \!\(\*SuperscriptBox[\(LinearModelFit[{{{2.04`, 0.02`}, {1.9975`,
106.            0.1696`}}, {{3.06`, 0.03`}, {3.216`, 0.1793`}}, {{4.08`,
107.            0.04`}, {4.0939`, 0.1821`}}}, x, x]\), \*
108. TagBox[
109. RowBox[{"(",
110. RowBox[{"1", ",", "0", ",", "0"}], ")"}],
111. Derivative],
112. MultilineFunction->None]\)[a, b, 3.06] -
113.     2 (4.0939 -
114.        LinearModelFit[{{{2.04, 0.02}, {1.9975, 0.1696}}, {{3.06,
115.             0.03}, {3.216, 0.1793}}, {{4.08, 0.04}, {4.0939,
116.             0.1821}}}, x, x][a, b, 4.08])
117. \!\(\*SuperscriptBox[\(LinearModelFit[{{{2.04`, 0.02`}, {1.9975`,
118.            0.1696`}}, {{3.06`, 0.03`}, {3.216`, 0.1793`}}, {{4.08`,
119.            0.04`}, {4.0939`, 0.1821`}}}, x, x]\), \*
120. TagBox[
121. RowBox[{"(",
122. RowBox[{"1", ",", "0", ",", "0"}], ")"}],
123. Derivative],
124. MultilineFunction->None]\)[a, b, 4.08] -
125.     2 (4.9878 -
126.        LinearModelFit[{{{2.04, 0.02}, {1.9975, 0.1696}}, {{3.06,
127.             0.03}, {3.216, 0.1793}}, {{4.08, 0.04}, {4.0939,
128.             0.1821}}}, x, x][a, b, 5.1])
129. \!\(\*SuperscriptBox[\(LinearModelFit[{{{2.04`, 0.02`}, {1.9975`,
130.            0.1696`}}, {{3.06`, 0.03`}, {3.216`, 0.1793`}}, {{4.08`,
131.            0.04`}, {4.0939`, 0.1821`}}}, x, x]\), \*
132. TagBox[
133. RowBox[{"(",
134. RowBox[{"1", ",", "0", ",", "0"}], ")"}],
135. Derivative],
136. MultilineFunction->None]\)[a, b, 5.1] -
137.     2 (6.4685 -
138.        LinearModelFit[{{{2.04, 0.02}, {1.9975, 0.1696}}, {{3.06,
139.             0.03}, {3.216, 0.1793}}, {{4.08, 0.04}, {4.0939,
140.             0.1821}}}, x, x][a, b, 6.12])
141. \!\(\*SuperscriptBox[\(LinearModelFit[{{{2.04`, 0.02`}, {1.9975`,
142.            0.1696`}}, {{3.06`, 0.03`}, {3.216`, 0.1793`}}, {{4.08`,
143.            0.04`}, {4.0939`, 0.1821`}}}, x, x]\), \*
144. TagBox[
145. RowBox[{"(",
146. RowBox[{"1", ",", "0", ",", "0"}], ")"}],
147. Derivative],
148. MultilineFunction->None]\)[a, b, 6.12] -
149.     2 (7.2003 -
150.        LinearModelFit[{{{2.04, 0.02}, {1.9975, 0.1696}}, {{3.06,
151.             0.03}, {3.216, 0.1793}}, {{4.08, 0.04}, {4.0939,
152.             0.1821}}}, x, x][a, b, 7.14])
153. \!\(\*SuperscriptBox[\(LinearModelFit[{{{2.04`, 0.02`}, {1.9975`,
154.            0.1696`}}, {{3.06`, 0.03`}, {3.216`, 0.1793`}}, {{4.08`,
155.            0.04`}, {4.0939`, 0.1821`}}}, x, x]\), \*
156. TagBox[
157. RowBox[{"(",
158. RowBox[{"1", ",", "0", ",", "0"}], ")"}],
159. Derivative],
160. MultilineFunction->None]\)[a, b, 7.14] -
161.     2 (8.2944 -
162.        LinearModelFit[{{{2.04, 0.02}, {1.9975, 0.1696}}, {{3.06,
163.             0.03}, {3.216, 0.1793}}, {{4.08, 0.04}, {4.0939,
164.             0.1821}}}, x, x][a, b, 8.16])
165. \!\(\*SuperscriptBox[\(LinearModelFit[{{{2.04`, 0.02`}, {1.9975`,
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177. \!\(\*SuperscriptBox[\(LinearModelFit[{{{2.04`, 0.02`}, {1.9975`,
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189. \!\(\*SuperscriptBox[\(LinearModelFit[{{{2.04`, 0.02`}, {1.9975`,
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192. TagBox[
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201. \!\(\*SuperscriptBox[\(LinearModelFit[{{{2.04`, 0.02`}, {1.9975`,
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204. TagBox[
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209.     2 (4.9878 -
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213. \!\(\*SuperscriptBox[\(LinearModelFit[{{{2.04`, 0.02`}, {1.9975`,
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225. \!\(\*SuperscriptBox[\(LinearModelFit[{{{2.04`, 0.02`}, {1.9975`,
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228. TagBox[
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233.     2 (7.2003 -
234.        LinearModelFit[{{{2.04, 0.02}, {1.9975, 0.1696}}, {{3.06,
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237. \!\(\*SuperscriptBox[\(LinearModelFit[{{{2.04`, 0.02`}, {1.9975`,
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245.     2 (8.2944 -
246.        LinearModelFit[{{{2.04, 0.02}, {1.9975, 0.1696}}, {{3.06,
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249. \!\(\*SuperscriptBox[\(LinearModelFit[{{{2.04`, 0.02`}, {1.9975`,
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257.
258. Out[445]= {-2 (1.9975 -
259.       LinearModelFit[{{{2.04, 0.02}, {1.9975, 0.1696}}, {{3.06,
260.            0.03}, {3.216, 0.1793}}, {{4.08, 0.04}, {4.0939, 0.1821}}},
261.          x, x][a, b, 2.04])
262. \!\(\*SuperscriptBox[\(LinearModelFit[{{{2.04`, 0.02`}, {1.9975`,
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265. TagBox[
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267. RowBox[{"1", ",", "0", ",", "0"}], ")"}],
268. Derivative],
269. MultilineFunction->None]\)[a, b, 2.04] -
270.    2 (3.216 -
271.       LinearModelFit[{{{2.04, 0.02}, {1.9975, 0.1696}}, {{3.06,
272.            0.03}, {3.216, 0.1793}}, {{4.08, 0.04}, {4.0939, 0.1821}}},
273.          x, x][a, b, 3.06])
274. \!\(\*SuperscriptBox[\(LinearModelFit[{{{2.04`, 0.02`}, {1.9975`,
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282.    2 (4.0939 -
283.       LinearModelFit[{{{2.04, 0.02}, {1.9975, 0.1696}}, {{3.06,
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285.          x, x][a, b, 4.08])
286. \!\(\*SuperscriptBox[\(LinearModelFit[{{{2.04`, 0.02`}, {1.9975`,
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289. TagBox[
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294.    2 (4.9878 -
295.       LinearModelFit[{{{2.04, 0.02}, {1.9975, 0.1696}}, {{3.06,
296.            0.03}, {3.216, 0.1793}}, {{4.08, 0.04}, {4.0939, 0.1821}}},
297.          x, x][a, b, 5.1])
298. \!\(\*SuperscriptBox[\(LinearModelFit[{{{2.04`, 0.02`}, {1.9975`,
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306.    2 (6.4685 -
307.       LinearModelFit[{{{2.04, 0.02}, {1.9975, 0.1696}}, {{3.06,
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309.          x, x][a, b, 6.12])
310. \!\(\*SuperscriptBox[\(LinearModelFit[{{{2.04`, 0.02`}, {1.9975`,
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313. TagBox[
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318.    2 (7.2003 -
319.       LinearModelFit[{{{2.04, 0.02}, {1.9975, 0.1696}}, {{3.06,
320.            0.03}, {3.216, 0.1793}}, {{4.08, 0.04}, {4.0939, 0.1821}}},
321.          x, x][a, b, 7.14])
322. \!\(\*SuperscriptBox[\(LinearModelFit[{{{2.04`, 0.02`}, {1.9975`,
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330.    2 (8.2944 -
331.       LinearModelFit[{{{2.04, 0.02}, {1.9975, 0.1696}}, {{3.06,
332.            0.03}, {3.216, 0.1793}}, {{4.08, 0.04}, {4.0939, 0.1821}}},
333.          x, x][a, b, 8.16])
334. \!\(\*SuperscriptBox[\(LinearModelFit[{{{2.04`, 0.02`}, {1.9975`,
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337. TagBox[
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342.   0, -2 (1.9975 -
343.       LinearModelFit[{{{2.04, 0.02}, {1.9975, 0.1696}}, {{3.06,
344.            0.03}, {3.216, 0.1793}}, {{4.08, 0.04}, {4.0939, 0.1821}}},
345.          x, x][a, b, 2.04])
346. \!\(\*SuperscriptBox[\(LinearModelFit[{{{2.04`, 0.02`}, {1.9975`,
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349. TagBox[
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353. MultilineFunction->None]\)[a, b, 2.04] -
354.    2 (3.216 -
355.       LinearModelFit[{{{2.04, 0.02}, {1.9975, 0.1696}}, {{3.06,
356.            0.03}, {3.216, 0.1793}}, {{4.08, 0.04}, {4.0939, 0.1821}}},
357.          x, x][a, b, 3.06])
358. \!\(\*SuperscriptBox[\(LinearModelFit[{{{2.04`, 0.02`}, {1.9975`,
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366.    2 (4.0939 -
367.       LinearModelFit[{{{2.04, 0.02}, {1.9975, 0.1696}}, {{3.06,
368.            0.03}, {3.216, 0.1793}}, {{4.08, 0.04}, {4.0939, 0.1821}}},
369.          x, x][a, b, 4.08])
370. \!\(\*SuperscriptBox[\(LinearModelFit[{{{2.04`, 0.02`}, {1.9975`,
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378.    2 (4.9878 -
379.       LinearModelFit[{{{2.04, 0.02}, {1.9975, 0.1696}}, {{3.06,
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381.          x, x][a, b, 5.1])
382. \!\(\*SuperscriptBox[\(LinearModelFit[{{{2.04`, 0.02`}, {1.9975`,
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385. TagBox[
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390.    2 (6.4685 -
391.       LinearModelFit[{{{2.04, 0.02}, {1.9975, 0.1696}}, {{3.06,
392.            0.03}, {3.216, 0.1793}}, {{4.08, 0.04}, {4.0939, 0.1821}}},
393.          x, x][a, b, 6.12])
394. \!\(\*SuperscriptBox[\(LinearModelFit[{{{2.04`, 0.02`}, {1.9975`,
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402.    2 (7.2003 -
403.       LinearModelFit[{{{2.04, 0.02}, {1.9975, 0.1696}}, {{3.06,
404.            0.03}, {3.216, 0.1793}}, {{4.08, 0.04}, {4.0939, 0.1821}}},
405.          x, x][a, b, 7.14])
406. \!\(\*SuperscriptBox[\(LinearModelFit[{{{2.04`, 0.02`}, {1.9975`,
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414.    2 (8.2944 -
415.       LinearModelFit[{{{2.04, 0.02}, {1.9975, 0.1696}}, {{3.06,
416.            0.03}, {3.216, 0.1793}}, {{4.08, 0.04}, {4.0939, 0.1821}}},
417.          x, x][a, b, 8.16])
418. \!\(\*SuperscriptBox[\(LinearModelFit[{{{2.04`, 0.02`}, {1.9975`,
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426.
427. During evaluation of In[432]:= ReplaceAll::reps: {-2 (1.9975 -LinearModelFit[{<<3>>},x,x][a,b,2.04]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,2.04]-2 (3.216 -LinearModelFit[{<<3>>},x,x][a,b,3.06]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,3.06]-2 (4.0939 -LinearModelFit[{<<3>>},x,x][a,b,4.08]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,4.08]-2 (4.9878 -LinearModelFit[{<<3>>},x,x][a,b,5.1]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,5.1]-2 (6.4685 -LinearModelFit[{<<3>>},x,x][a,b,6.12]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,6.12]-2 (7.2003 -LinearModelFit[{<<3>>},x,x][a,b,7.14]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,7.14]-2 (8.2944 -LinearModelFit[{<<3>>},x,x][a,b,8.16]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,8.16]==0,<<1>>==0}
428.  is neither a list of replacement rules nor a valid dispatch table, and so cannot be used for replacing. >>
429.
430. During evaluation of In[432]:= General::ivar: 2.04` is not a valid variable. >>
431.
432. During evaluation of In[432]:= ReplaceAll::reps: {-2 (1.9975 -LinearModelFit[{<<3>>},x,x][a,b,2.04]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,2.04]-2 (3.216 -LinearModelFit[{<<3>>},x,x][a,b,3.06]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,3.06]-2 (4.0939 -LinearModelFit[{<<3>>},x,x][a,b,4.08]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,4.08]-2 (4.9878 -LinearModelFit[{<<3>>},x,x][a,b,5.1]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,5.1]-2 (6.4685 -LinearModelFit[{<<3>>},x,x][a,b,6.12]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,6.12]-2 (7.2003 -LinearModelFit[{<<3>>},x,x][a,b,7.14]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,7.14]-2 (8.2944 -LinearModelFit[{<<3>>},x,x][a,b,8.16]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,8.16]==0,<<1>>==0}
433.  is neither a list of replacement rules nor a valid dispatch table, and so cannot be used for replacing. >>
434.
435. During evaluation of In[432]:= General::ivar: 4.08` is not a valid variable. >>
436.
437. During evaluation of In[432]:= ReplaceAll::reps: {-2 (1.9975 -LinearModelFit[{<<3>>},x,x][a,b,2.04]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,2.04]-2 (3.216 -LinearModelFit[{<<3>>},x,x][a,b,3.06]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,3.06]-2 (4.0939 -LinearModelFit[{<<3>>},x,x][a,b,4.08]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,4.08]-2 (4.9878 -LinearModelFit[{<<3>>},x,x][a,b,5.1]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,5.1]-2 (6.4685 -LinearModelFit[{<<3>>},x,x][a,b,6.12]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,6.12]-2 (7.2003 -LinearModelFit[{<<3>>},x,x][a,b,7.14]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,7.14]-2 (8.2944 -LinearModelFit[{<<3>>},x,x][a,b,8.16]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},x,x]^(1,0,0))[a,b,8.16]==0,<<1>>==0}
438.  is neither a list of replacement rules nor a valid dispatch table, and so cannot be used for replacing. >>
439.
440. During evaluation of In[432]:= General::stop: Further output of ReplaceAll::reps will be suppressed during this calculation. >>
441.
442. During evaluation of In[432]:= General::ivar: 6.12` is not a valid variable. >>
443.
444. During evaluation of In[432]:= General::stop: Further output of General::ivar will be suppressed during this calculation. >>
445.
446. Out[446]= Out[446]
447.
448. During evaluation of In[432]:= LinearModelFit::notdata: The first argument is not a vector, matrix, or a list containing a design matrix and response vector. >>
449.
450. During evaluation of In[432]:= LinearModelFit::notdata: The first argument is not a vector, matrix, or a list containing a design matrix and response vector. >>
451.
452. During evaluation of In[432]:= LinearModelFit::notdata: The first argument is not a vector, matrix, or a list containing a design matrix and response vector. >>
453.
454. During evaluation of In[432]:= General::stop: Further output of LinearModelFit::notdata will be suppressed during this calculation. >>
455.
456. During evaluation of In[432]:= ReplaceAll::reps: {-2 (1.9975 -LinearModelFit[{<<3>>},-1.99992,-1.99992][a,b,2.04]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},-1.99992,-1.99992]^(1,0,0))[a,b,2.04]-2 (3.216 -LinearModelFit[{<<3>>},-1.99992,-1.99992][a,b,3.06]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},-1.99992,-1.99992]^(1,0,0))[a,b,3.06]-2 (4.0939 -<<1>>) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},-1.99992,-1.99992]^(1,0,0))[a,b,4.08]-2 (<<1>>) <<1>>-2 (6.4685 -<<1>>) (LinearModelFit[<<1>>]^(1,0,0))[a,b,6.12]-2 (7.2003 -LinearModelFit[{<<3>>},-1.99992,-1.99992][a,b,7.14]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},-1.99992,-1.99992]^(1,0,0))[a,b,7.14]-2 (8.2944 -LinearModelFit[{<<3>>},-1.99992,-1.99992][a,b,8.16]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},-1.99992,-1.99992]^(1,0,0))[a,b,8.16]==0,<<1>>}
457.  is neither a list of replacement rules nor a valid dispatch table, and so cannot be used for replacing. >>
458.
459. During evaluation of In[432]:= ReplaceAll::reps: {-2 (1.9975 -LinearModelFit[{<<3>>},-1.99992,-1.99992][a,b,2.04]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},-1.99992,-1.99992]^(1,0,0))[a,b,2.04]-2 (3.216 -LinearModelFit[{<<3>>},-1.99992,-1.99992][a,b,3.06]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},-1.99992,-1.99992]^(1,0,0))[a,b,3.06]-2 (4.0939 -<<1>>) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},-1.99992,-1.99992]^(1,0,0))[a,b,4.08]-2 (<<1>>) <<1>>-2 (6.4685 -<<1>>) (LinearModelFit[<<1>>]^(1,0,0))[a,b,6.12]-2 (7.2003 -LinearModelFit[{<<3>>},-1.99992,-1.99992][a,b,7.14]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},-1.99992,-1.99992]^(1,0,0))[a,b,7.14]-2 (8.2944 -LinearModelFit[{<<3>>},-1.99992,-1.99992][a,b,8.16]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},-1.99992,-1.99992]^(1,0,0))[a,b,8.16]==0,<<1>>}
460.  is neither a list of replacement rules nor a valid dispatch table, and so cannot be used for replacing. >>
461.
462. During evaluation of In[432]:= General::ivar: 1.9975` is not a valid variable. >>
463.
464. During evaluation of In[432]:= ReplaceAll::reps: {-2 (1.9975 -LinearModelFit[{<<3>>},-1.99992,-1.99992][a,b,2.04]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},-1.99992,-1.99992]^(1,0,0))[a,b,2.04]-2 (3.216 -LinearModelFit[{<<3>>},-1.99992,-1.99992][a,b,3.06]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},-1.99992,-1.99992]^(1,0,0))[a,b,3.06]-2 (4.0939 -<<1>>) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},-1.99992,-1.99992]^(1,0,0))[a,b,4.08]-2 (<<1>>) <<1>>-2 (6.4685 -<<1>>) (LinearModelFit[<<1>>]^(1,0,0))[a,b,6.12]-2 (7.2003 -LinearModelFit[{<<3>>},-1.99992,-1.99992][a,b,7.14]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},-1.99992,-1.99992]^(1,0,0))[a,b,7.14]-2 (8.2944 -LinearModelFit[{<<3>>},-1.99992,-1.99992][a,b,8.16]) (LinearModelFit[{{<<2>>},{<<2>>},{<<2>>}},-1.99992,-1.99992]^(1,0,0))[a,b,8.16]==0,<<1>>}
465.  is neither a list of replacement rules nor a valid dispatch table, and so cannot be used for replacing. >>
466.
467. During evaluation of In[432]:= General::stop: Further output of ReplaceAll::reps will be suppressed during this calculation. >>
468.
469. During evaluation of In[432]:= General::ivar: 2.04` is not a valid variable. >>
470.
471. During evaluation of In[432]:= General::ivar: 3.06` is not a valid variable. >>
472.
473. During evaluation of In[432]:= General::stop: Further output of General::ivar will be suppressed during this calculation. >>
474.
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