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True and predicted data obtained from : https://community.wolfram.com/groups/-/m/t/3569104
In[]:=
DATA={{0.1049,0.1049},{0.11281,0.1047},{0.12713,0.1249},{0.11231,0.1129},{0.20345,0.2132},{0.09509,0.1032},{0.08027,0.0825},{0.09639,0.0958},{0.01995,0.0102},{0.08948,0.0828},{0.10695,0.097},{0.06766,0.0924},{0.11862,0.1253},{0.12037,0.1215},{0.01848,0.0129},{0.10515,0.1151},{0.08943,0.0883},{0.02101,0.0116},{0.23344,0.2087},{0.15512,0.1607},{0.18859,0.198}};
In[]:=
TableForm@DATA
Out[]//TableForm=
0.1049
0.1049
0.11281
0.1047
0.12713
0.1249
0.11231
0.1129
0.20345
0.2132
0.09509
0.1032
0.08027
0.0825
0.09639
0.0958
0.01995
0.0102
0.08948
0.0828
0.10695
0.097
0.06766
0.0924
0.11862
0.1253
0.12037
0.1215
0.01848
0.0129
0.10515
0.1151
0.08943
0.0883
0.02101
0.0116
0.23344
0.2087
0.15512
0.1607
0.18859
0.198
In[]:=
ytrue=(Transpose@DATA)[[2]]
Out[]=
{0.1049,0.1047,0.1249,0.1129,0.2132,0.1032,0.0825,0.0958,0.0102,0.0828,0.097,0.0924,0.1253,0.1215,0.0129,0.1151,0.0883,0.0116,0.2087,0.1607,0.198}
In[]:=
ypred=(Transpose@DATA)[[1]]
Out[]=
{0.1049,0.11281,0.12713,0.11231,0.20345,0.09509,0.08027,0.09639,0.01995,0.08948,0.10695,0.06766,0.11862,0.12037,0.01848,0.10515,0.08943,0.02101,0.23344,0.15512,0.18859}
Computing all eight metrics
n=Length[ytrue];
p=14;(*numberofpredictors;adjustasneeded*)
residuals=ytrue-ypred;
Compute metrics
mse=Mean[residuals^2];
rmse=Sqrt[mse];
stdRes=StandardDeviation[residuals];
percentAARD=100*Mean[Abs[residuals/(ytrue+10^-8)]];
r2=1-Total[residuals^2]/Total[(ytrue-Mean[ytrue])^2];
Simple estimate
r2Predicted=1-(1-r2)*(n-1)/(n-2);
r2Adjusted=1-(1-r2)*(n-1)/(n-p-1);
mae=Mean[Abs[residuals]];
Create table
metricsTable={{"Metric","Value"},{"MSE",mse},{"RMSE",rmse},{"STD Residuals",stdRes},{"%AARD",percentAARD},{"R²",r2},{"R² Predicted",r2Predicted},{"R² Adjusted",r2Adjusted},{"MAE",mae}};
Display table nicely
Text@Style[Grid[metricsTable,Frame->All,Background->{None,{Lighter[Blend[{Blue,Red}],.8],{Lighter[Blend[{Yellow,Darker@Green}],.2],Lighter[Green,.5]}}},ItemSize->{2.5{4.2,4.2,4.2,4.2,4.2},1.},Frame->Darker[Gray,.6],ItemStyle->14,Spacings->{8,1.5}]]
Out[]=
Conclusion : the model is moderately accurate, with predictions roughly within ± 15 % of actual values .

CITE THIS NOTEBOOK

Commonly used metrics for model evaluation​
by Housam Binous and Ahmed Bellagi
Wolfram Community, STAFF PICKS, January 18, 2026
​https://community.wolfram.com/groups/-/m/t/3609130