hcl={{-13,2571.04`},{-12,2598.04`},{-11,2624.66`},{-10,2651.08`},{-9,2676.72`},{-8,2701.99`},{-7,2726.67`},{-6,2750.97`},{-5,2774.88`},{-4,2798.03`},{-3,2820.59`},{-2,2842.57`},{-1,2863.79`},{1,2905.25`},{2,2924.92`},{3,2943.82`},{4,2962.14`},{5,2979.69`},{6,2996.66`},{7,3012.86`},{8,3028.67`},{9,3043.52`},{10,3057.98`},{11,3071.48`},{12,3084.21`}}

5a - call packet regression

<<LinearRegression`;

5- test regress, and other fit functions

Regress[{{1,2},{3,5},{4,9}},{x},{x}]

hcl={{-13,2571.04`},{-12,2598.04`},{-11,2624.66`},{-10,2651.08`},{-9,2676.72`},{-8,2701.99`},{-7,2726.67`},{-6,2750.97`},{-5,2774.88`},{-4,2798.03`},{-3,2820.59`},{-2,2842.57`},{-1,2863.79`},{1,2905.25`},{2,2924.92`},{3,2943.82`},{4,2962.14`},{5,2979.69`},{6,2996.66`},{7,3012.86`},{8,3028.67`},{9,3043.52`},{10,3057.98`},{11,3071.48`},{12,3084.21`}}

9- this is now the clean file hclmc for the model fit, such as  of equation (10 ) textbook

dplotb=ListPlot[hcl,Ticks->{Automatic,Automatic},PlotRange->All,AxesLabel->{"m","frequency in cm-1"},PlotJoined->False]

10- Clearly function is not linear- line, so try polynomia

func1= Fit[hcl, {1,x, x^2}, x]

Or you may try a longer model, higher order polynom

hcl

func2=Fit[hcl,{1,x,x^2,x^3},x]

regressx=Regress[hcl,{1,x,x^2,x^3},x]
Chop[regressx,10^(-6)]

also, you want predicted values, standard error for values and confidence intervals for predicted values

regress2 = Regress[hcl, {1,x,x^2,x^3,x^4}, x,
RegressionReport ->
 {FitResiduals, SinglePredictionCITable,
 ParameterConfidenceRegion}]