<< Statistics`NonlinearFit`
<< Graphics`MultipleListPlot`
SetDirectory["C:/cowan/teach/ph215"]

data  =  
        ReadList["errinput.txt",  {Number, Number,  
            Number}];
xvec  =  Transpose[data][[1]];
yvec  =  Transpose[data][[2]];
dyvec  =  Transpose[
            data][[3]];
dxvec  =  Table[0,  {Length[data]}];
xy  =  Transpose[{xvec,  yvec}];
ebars  =  
        Apply[ErrorBar, 
          Transpose[{dxvec,  dyvec}],  {1}];
plotdata  =  Transpose[{xy,  ebars}];

dp  =  
        MultipleListPlot[plotdata,  
          PlotStyle -> {PointSize[0.02]}];
f  =  theta1  +  x^theta2;
NonlinearRegress[xy,  f,  
      x,  {theta1,  theta2}, 
Weights -> 
        dyvec]

g[x_]  =  
        NonlinearFit[xy,  f,  
          x,  {theta1,  theta2}, 
Weights -> 
            dyvec];

fp  =  
        Plot[g[x],  {x,  0,  6},  
          PlotRange -> {0, 20}];

Show[fp,  dp,  AxesLabel -> {"x",  "y"}]