Clear[XY,f];
XY={{1, 3.7}, {2, 4.1}, {2.5, 4.3}, {3, 5}};
f[x_]=Fit[XY, {1,x}, x]

Clear[dots, least];
dots = ListPlot[XY,PlotStyle->{PointSize[0.02]},
                DisplayFunction->Identity];
least= Plot[f[x],{x,1,3.2},
                DisplayFunction->Identity];
Show[least, dots, DisplayFunction->$DisplayFunction,
PlotLabel->txt,AxesLabel->{"x","y    "}]

Clear[XY,f];
XY={{0.24, 0.23}, {0.65, -0.26}, {0.95, -1.10},
{1.24, -0.45}, {1.73,0.27}, {2.01, 0.10}, {2.23, -0.19},
 {2.52, 0.24}, {2.77,0.56}, {2.99, 1.00}};

f[x_]=Fit[XY, {1,x,x^2}, x]

Clear[dots, least];
dots = ListPlot[XY,PlotStyle->{PointSize[0.02]},
                DisplayFunction->Identity];
least= Plot[f[x],{x,0,3.2},
                DisplayFunction->Identity];
Show[least, dots, DisplayFunction->$DisplayFunction,
PlotLabel->txt,AxesLabel->{"x","y    "}]

Clear[f];
f[x_]=Fit[XY, {1,x,x^2, x^3, x^4, x^5,x^6}, x]

Clear[dots, least];
dots = ListPlot[XY,PlotStyle->{PointSize[0.02]},
                DisplayFunction->Identity];
least= Plot[f[x],{x,0.2,3.05},
                DisplayFunction->Identity];
Show[least, dots, DisplayFunction->$DisplayFunction,
PlotLabel->txt,AxesLabel->{"x","y    "}]

Clear[XY, n]; 
f[x_]:=1 + Sin[10 x]; 
pt[x_]:= 10+ (x-1)/14;  
n=15;
XY=N[Table[{pt[i], f[pt[i]]},  {i, 1,n}],10];

Clear[f];
f[x_]=Fit[XY, {1,x,x^2, x^3, x^4, x^5,x^6}, x]

Clear[dots, least];
dots = ListPlot[XY,PlotStyle->{PointSize[0.02]}, 
                DisplayFunction->Identity];
least= Plot[f[x],{x,10,11},
                DisplayFunction->Identity];
Show[least, dots, DisplayFunction->$DisplayFunction,
PlotLabel->txt,AxesLabel->{"x","y    "}]