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{3.74565085311819*^9, 3.745650946291975*^9}, {3.745766074455529*^9, 3.745766074588695*^9}, { 3.745817823956843*^9, 3.745817927323584*^9}, {3.745817966665299*^9, 3.745817991707251*^9}, {3.746105428042791*^9, 3.7461054758332853`*^9}, 3.746106486170124*^9, {3.778068810070662*^9, 3.778068816389135*^9}, { 3.778071281902882*^9, 3.778071289940243*^9}},ExpressionUUID->"15cf0c6e-85bb-44a5-b43f-\ e1b5aa142f34"], Cell[CellGroupData[{ Cell[TextData[{ "In case the system is linear, we should have the relation ", Cell[BoxData[ FormBox[ RowBox[{ SubscriptBox["y", "i"], "=", RowBox[{ RowBox[{"a", " ", SubscriptBox["x", "i"]}], "+", "b"}]}], TraditionalForm]], ExpressionUUID->"0694ff1a-1c1e-45ea-853b-3cbb9bfce411"], ", but we sh0uld also take into account the error in the measurement ", Cell[BoxData[ FormBox[ RowBox[{ SubscriptBox["y", "i"], "=", " ", RowBox[{ SubscriptBox["y", RowBox[{"i", ",", " ", "true"}]], "+", " ", SubscriptBox["e", RowBox[{"y", ",", " ", RowBox[{"error", " ", "in", " ", "y"}]}]]}]}], TraditionalForm]], ExpressionUUID->"f2639ec1-7de5-4dbf-a0d8-8339869a5660"], "." }], "Subitem", CellChangeTimes->{{3.744010605902556*^9, 3.744010608647553*^9}, { 3.744010679133648*^9, 3.7440106942012253`*^9}, {3.7440107331291656`*^9, 3.7440107586054688`*^9}, {3.745480510458893*^9, 3.7454805891693487`*^9}, { 3.745480627178793*^9, 3.745480675922556*^9}, {3.74559181529712*^9, 3.745591816492278*^9}, {3.745592319185923*^9, 3.7455923384324083`*^9}, { 3.745594707642692*^9, 3.745594771009461*^9}, {3.7455950115254297`*^9, 3.7455951428367243`*^9}, {3.745595203115478*^9, 3.745595361945335*^9}, { 3.74559539914347*^9, 3.745595444107788*^9}, {3.74559600502468*^9, 3.745596125266101*^9}, {3.745648372256975*^9, 3.745648465723386*^9}, { 3.7456486935273952`*^9, 3.7456486938302717`*^9}, {3.745648968954913*^9, 3.745649132002026*^9}, {3.74564925133853*^9, 3.7456493214027357`*^9}, { 3.7456507479382133`*^9, 3.745650749101879*^9}, {3.74565085311819*^9, 3.745650946291975*^9}, {3.745766074455529*^9, 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" }], "Subitem", CellChangeTimes->CompressedData[" 1:eJwlz2kog3EAx/GnCe8cNaGMbe5iUhpiep7JGUsrhDfLUUJZrpR7KG+ICCNH ORM5XsmVlZbIrGQhtGFjNkkrtFz/37z49nn95RVXS8tYFEXxSHDXsBPJN1oY 1SZbAC9SH4RQLlfHQS5/VgQp2RkN6VXN4+ujhZFUzr3B5c2ydzjU3fIFWQoz HfJkYfb23RnoZTO2wUxdtgK+9tcthRI7smUbUKqVa2GN+koPf9dLnmAUnfQF JSMPVBiRqu10gYKj6Sxo6lwsgkHxPbcM0R4c+wyr9GsuYuLwwJbD+T7/cKj0 aBdB0XlFFhTeR+TCC+dW12TiqHjGofBwhg2v8zO4cGNQkt9EHNFJHdZP/owP EU8KnxchL/N8BeoHUrahk1ZmgKeCEhtszDHZYWnuv3enC8opfN0cj8OuxG9z gNnCfCqbrbAuzeDJJc5zhGxYaVv7gFKd4RM2i93c+US3yzyHqo6xdGh9ic6A PnZjjE+IlekJcE2ABYG3NPSeUDCwvIFzAE1HfmqYFPTN9SVqelk8+AfjVh3n "],ExpressionUUID->"c014a25f-74f2-46ed-a542-8573f5ba456c"], Cell[TextData[{ "In case the system is linear, we should have the relation\n", Cell[BoxData[ FormBox[ RowBox[{" ", RowBox[{ RowBox[{ RowBox[{"a", " ", SubscriptBox["x", "i"]}], "+", "b", "+", SubscriptBox["e", "y"]}], " ", "=", " ", SubscriptBox["y", "i"]}]}], TraditionalForm]],ExpressionUUID-> "a66f07ab-0cc7-4fba-a93c-2e256ee6ab2e"], ", where the measured value of ", Cell[BoxData[ FormBox[ SubscriptBox["y", "i"], TraditionalForm]],ExpressionUUID-> "6d750938-fedd-4edf-bfd5-a61706131a60"], " is assumed to be ", Cell[BoxData[ FormBox[ RowBox[{ SubscriptBox["y", "i"], "=", " ", RowBox[{ SubscriptBox["y", RowBox[{"i", ",", " ", "true"}]], "+", " ", SubscriptBox["e", RowBox[{"y", ",", " ", RowBox[{"error", " ", "in", " ", "y"}]}]]}]}], TraditionalForm]], ExpressionUUID->"eebc5ab9-f024-461f-8142-6a3b5327fdbc"] }], "Subitem", CellChangeTimes->CompressedData[" 1:eJwlz1tIWnEAx/GDkb1VA6N6KM1KC8oxCLcoxzmOdSMlpAvVi82CqMGkG8Fc LW0Qe4iiqCy6QFei6PIU1UbCiNgo3SJp0cJTmdewIVRIl/1/7uHL5/mb8Oad qoZDUZSQBL+wm+lCu4cxrfEk8DDnXAq12u0XUCCckkFKvU9DemnP4XN4GGX9 9F+4sFZzDfs/fbiDHL2LFjk9zNetCAZG+e3tsMCq0ENfT9O8mNihUK9ClUVr gQ3bRzb4uKJxwqf0yzuoHDynUohUo4ELJd8nCuGFYa4SJmV2nTDEQPJzN3xr W+bKiQO960FnuuNToTHyowzKDuoKofQsrQQehraFvSIOySeDSncmefC4LF8A V/uUZe+Jg1ZV0Oaxh5F+4m6Few4mFBwsQlvv6w0YYlGz0CzR+GFr0UUAVpf8 99Q8axzH158fI7Az+97Fd3mYW6POC5ty2ScC4kyclAfr/cs3UGVlb6FOHh4h JIb/Lg1q6hjOg97LZ/kwJmDPiBF5mS5+WBYsTzyhYfSonoG1LXHfoONM/BP+ uvfyY4nFVTdJ0Gj9rIQL7FUx/AdBhSe1 "],ExpressionUUID->"2276c2d4-8b16-4c4b-8bf7-fbeb02feed20"] }, Open ]], Cell["\<\ This is not taking account a line that could be fully vertical (a = \ \[Infinity]), but in this case there would not be any relation between x and \ y, as these would be independent. 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", Cell[BoxData[ FormBox[ RowBox[{"a", ",", RowBox[{"b", " ", "\[Tilde]", RowBox[{"Uniform", "[", " ", "]"}]}]}], TraditionalForm]],ExpressionUUID-> "b82a505b-7205-4e3d-9ce8-34c25775fcff"], ". 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In this case we want to know what is the probable value of y, \ based on all the data \[ScriptCapitalD], given some value x. 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"\[RightPointer]", " "}], FontSize -> 25, GrayLevel[0.7]], ButtonData -> "ScrollPageNext", Appearance -> None], DynamicBox[ FEPrivate`FrontEndResource[ "SlideshowToolbarText", "TooltipNextSlide"]]], "\[InvisibleSpace]", TooltipBox[ ButtonBox[ StyleBox[ RowBox[{" ", "\[LastPage]", " "}], FontSize -> 25, GrayLevel[0.7]], ButtonData -> "ScrollPageLast", Appearance -> None], DynamicBox[ FEPrivate`FrontEndResource[ "SlideshowToolbarText", "TooltipLastSlide"]]]}], ButtonBoxOptions -> {Alignment -> {Automatic, FEPrivate`If[ FEPrivate`SameQ[ FEPrivate`$OperatingSystem, "Unix"], -0.4, -0.5]}, Appearance -> "Palette", ButtonFunction :> (FEPrivate`FrontEndExecute[ FrontEnd`FrontEndToken[ FrontEnd`ButtonNotebook[], #]]& ), Evaluator -> None, FrameMargins -> 0, ImageMargins -> 0, ImageSize -> Medium}], DynamicModuleBox[{$CellContext`cells$$ = {}, \ $CellContext`tagFind$$ = False}, TagBox[ DynamicBox[ PopupMenuBox[ Dynamic[ 0, With[{$CellContext`nb$ = ButtonNotebook[]}, 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