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Student Support Forum: 'Re: goodness of fit' topicStudent Support Forum > General > Archives > "Re: goodness of fit"

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David Belisle
04/21/97 11:48pm

Reply to message #307 from Sean Dempsey: > When I fit a function to
a data set I can't seem to get a value for how much uncertainty is
in the function. For example I need to use the slope of a fitted function
as one piece of data in a larger analysis and then do an error propogation;
I need to know that I can trust my slope +/- some level of uncertainty,
how do I determine this? The standard errors (SE) may actually be
better than the ci's. Here is an example (sorry about the junk, but
if you paste it into a notebook it should format properly): In[1]:=
<<Statistics`LinearRegression` In[2]:= data=Table[{i,i^1.12},{i,30}];
ListPlot[data] Out[2]= \[SkeletonIndicator]Graphics\[SkeletonIndicator]
In[7]:= Regress[data,{1,x},x, RegressionReport->{ParameterTable,RSquared,EstimatedVariance,AnovaTable,
MeanPredictionCITable}] Out[7]= \!\(\* RowBox[{''{'', RowBox[{ RowBox[{''ParameterTable'',
''\[Rule]'', TagBox[GridBox[{ {\(''''\), \(''Estimate''\), \(''SE''\),
\(''TStat''\), \(''PValue''\)}, {''1'', \(-1.7742931978831768`\),
''0.186314618135504659`'', \(-9.52310245776180686`\), ''2.79888778820236439`*^-10''},
{''x'', ''1.53626833905827631`'', ''0.0104948634306131061`'', ''146.382880464841669`'',
''0.`''} }, RowSpacings->1, ColumnSpacings->3, RowAlignments->Baseline,
ColumnAlignments->{Left}], (TableForm[ #, TableHeadings -> {{1, x},
{''Estimate'', ''SE'', ''TStat'', ''PValue''}}]&)]}], '','', \(RSquared
\[Rule] 0.998695000547149192`\), '','', \(EstimatedVariance \[Rule]
0.247544501065177691`\), '','', ''AnovaTable'', '','', RowBox[{''MeanPredictionCITable'',
''\[Rule]'', TagBox[GridBox[{ {\(''Observed''\), \(''Predicted''\),
\(''SE''\), \(''CI''\)}, {''1.`'', \(-0.238024858824900542`\), ''0.177225483997540012`'',
\({\(-0.601054805953580295`\), 0.125005088303779254`}\)}, {''2.17346972505211644`'',
''1.29824348023337577`'', ''0.168300005175876759`'', \({0.953496547666933302`,
1.64299041279981832`}\)}, {''3.42275493484426007`'', ''2.8345118192916523`'',
''0.15956564675108618`'', \({2.50765640890155028`, 3.16136722968175432`}\)},
{''4.72397064571812208`'', ''4.37078015834992861`'', ''0.151055565342158537`'',
\({4.0613568594951328`, 4.68020345720472441`}\)}, {''6.06521785586315331`'',
''5.90704849740820492`'', ''0.142809860778029911`'', \({5.61451575867170404`,
6.19958123614470579`}\)}, {''7.43925422715672812`'', ''7.44331683646648123`'',
''0.134877029797129921`'', \({7.16703376536591019`, 7.71959990756705227`}\)},
{''8.84117129177548832`'', ''8.97958517552475754`'', ''0.127315569806704775`'',
\({8.7187910530709729`, 9.24037929797854218`}\)}, {''10.2674071805032363`'',
''10.5158535145830334`'', ''0.120195589687685266`'', \({10.2696440102544883`,
10.7620630189115784`}\)}, {''11.7152513440007344`'', ''12.052121853641311`'',
''0.113600130116075592`'', \({11.8194225358026706`, 12.2848211714799493`}\)},
{''13.1825673855640745`'', ''13.5883901926995864`'', ''0.107625664510202523`'',
\({13.3679290128764294`, 13.8088513725227436`}\)}, {''14.6676253154941216`'',
''15.1246585317578619`'', ''0.102380965403684598`'', \({14.9149406310410626`,
15.3343764324746629`}\)}, {''16.1689938396911303`'', ''16.6609268708161373`'',
''0.0979832884198764908`'', \({16.4602172030402797`, 16.8616365385919948`}\)},
{''17.6854679106051504`'', ''18.1971952098744154`'', ''0.0945508956013076762`'',
\({18.0035164800615596`, 18.3908739396872711`}\)}, {''19.2160181366739379`'',
''19.7334635489326899`'', ''0.0921916657041215437`'', \({19.5446174824903664`,
19.9223096153750134`}\)}, {''20.75975434706113`'', ''21.269731887990968`'',
''0.0909891142304729783`'', \({21.0833491365756442`, 21.4561146394062918`}\)},
{''22.3158986616064947`'', ''22.8060002270492434`'', ''0.0909891142304729783`'',
\({22.6196174756339196`, 22.9923829784645672`}\)}, {''23.8837651416195617`'',
''24.3422685661075188`'', ''0.0921916657041215437`'', \({24.153422499665198`,
24.5311146325498441`}\)}, {''25.462744117561713`'', ''25.8785369051657943`'',
''0.0945508956013076939`'', \({25.6848581753529403`, 26.0722156349786526`}\)},
{''27.0522899165855434`'', ''27.4148052442240741`'', ''0.0979832884198765086`'',
\({27.2140955764482139`, 27.6155149119999299`}\)}, {''28.6519111109829438`'',
''28.9510735832823495`'', ''0.10238096540368462`'', \({28.7413556825655458`,
29.1607914839991479`}\)}, {''30.2611626687279544`'', ''30.487341922340625`'',
''0.107625664510202567`'', \({30.2668807425174701`, 30.7078031021637842`}\)},
{''31.8796395616344696`'', ''32.0236102613989004`'', ''0.113600130116075637`'',
\({31.7909109435602621`, 32.2563095792375387`}\)}, {''33.5069715061233441`'',
''33.5598786004571758`'', ''0.120195589687685311`'', \({33.3136690961286285`,
33.8060881047857231`}\)}, {''35.14281859512284`'', ''35.0961469395154557`'',
''0.127315569806704798`'', \({34.8353528170616666`, 35.3569410619692447`}\)},
{''36.7868676390812243`'', ''36.6324152785737311`'', ''0.13487702979713001`'',
\({36.3561322074731574`, 36.9086983496743048`}\)}, {''38.4388290770810048`'',
''38.1686836176320056`'', ''0.142809860778029946`'', \({37.8761508788955003`,
38.4612163563685083`}\)}, {''40.0984343506193585`'', ''39.7049519566902819`'',
''0.151055565342158608`'', \({39.3955286578354844`, 40.014375255545076`}\)},
{''41.7654336561131778`'', ''41.2412202957485618`'', ''0.159565646751086216`'',
\({40.9143648853584629`, 41.5680757061386607`}\)}, {''43.4395940098836064`'',
''42.7774886348068328`'', ''0.168300005175876821`'', \({42.4327417022403885`,
43.1222355673732771`}\)}, {''45.1206975728564252`'', ''44.3137569738651126`'',
''0.177225483997540038`'', \({43.9507270267364269`, 44.6767869209937895`}\)}
}, RowSpacings->1, ColumnSpacings->3, RowAlignments->Baseline, ColumnAlignments->{Left}],
(TableForm[ #, TableDepth -> 2, TableHeadings -> {None, {''Observed'',
''Predicted'', ''SE'', ''CI''}}]&)]}]}], ''}''}]\) In[6]:= Options[RegressionReport]
Out[6]= {}


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