Regresja

Grzegorz Siudem

Regresja

X=RandomVariate[NormalDistribution[],{1000}];
Y=Sin[X]+RandomVariate[NormalDistribution[0,0.1],{1000}];
ListPlot[Transpose[{X,Y}],PlotTheme->"Scientific",GridLines->Automatic]

Histogram[Extract[Y,Position[X,x_ /; -.15<x<.15]]]

ListPlot[Transpose[{X,Y}],PlotTheme->"Scientific"]

Show[ListPlot[Mean/@GatherBy[Transpose[{X,Y}],Quotient[#[[1]],0.5]&]],ListPlot[Transpose[{X,Y}],PlotTheme->"Scientific"],Plot[Evaluate[a Sin[ b x]/.FindFit[Transpose[{X,Y}],a Sin[ b x],{a,b},x]],{x,-4,4}]]

Plot[Evaluate[a Sin[ b x]/.FindFit[Transpose[{X,Y}],a Sin[ b x],{a,b},x]],{x,-4,4}]

Anscombe

anscombe=Transpose[Partition[#,2]&/@{{10.0,8.04,10.0,9.14,10.0,7.46,8.0,6.58},{8.0,6.95,8.0,8.14,8.0,6.77,8.0,5.76},{13.0,7.58,13.0,8.74,13.0,12.74,8.0,7.71},{9.0,8.81,9.0,8.77,9.0,7.11,8.0,8.84},{11.0,8.33,11.0,9.26,11.0,7.81,8.0,8.47},{14.0,9.96,14.0,8.10,14.0,8.84,8.0,7.04},{6.0,7.24,6.0,6.13,6.0,6.08,8.0,5.25},{4.0,4.26,4.0,3.10,4.0,5.39,19.0,12.50},{12.0,10.84,12.0,9.13,12.0,8.15,8.0,5.56},{7.0,4.82,7.0,7.26,7.0,6.42,8.0,7.91},{5.0,5.68,5.0,4.74,5.0,5.73,8.0,6.89}}];

GraphicsColumn[ListPlot[#,PlotTheme->"Scientific",GridLines->Automatic]&/@anscombe]

FindFit[#,a x+b,{a,b},x]&/@anscombe

Mean/@anscombe