# Question:How to use Maximum Likelyhood Estimator (MLE) in MaplaTA

## Question:How to use Maximum Likelyhood Estimator (MLE) in MaplaTA

Our students use R for solving digital questions about Multivariate Statistics made with MapleTA.

How to use a MLE in MapleTA. Below the code I used in a question?

Remaks about how to program this better or more easy are more than welcome.

://noise. In Dutch ruis means noise;
\$ruislow=range(1,5,1);
\$ruishigh=range(6,9,1);
://data 1;
\$x1=10+rand(\$ruislow,\$ruishigh,1);
\$x2=30+rand(\$ruislow,\$ruishigh,1);
\$x3=50+rand(\$ruislow,\$ruishigh,1);
\$x4=70+rand(\$ruislow,\$ruishigh,1);
\$x5=90+rand(\$ruislow,\$ruishigh,1);
\$x6=125+rand(\$ruislow,\$ruishigh,1);
\$x7=175+rand(\$ruislow,\$ruishigh,1);
\$X=maple("Vector([\$x1,\$x2,\$x3,\$x4,\$x5,\$x6,\$x7])");
\$displayX=maple("printf(MathML:-ExportPresentation(\$X))");
\$TX=maple("LinearAlgebra[Transpose](\$X)");
\$displayTX=maple("printf(MathML:-ExportPresentation(\$TX))");
://data 2;
\$y1=4+rand(\$ruislow,\$ruishigh,1);
\$y2=12+rand(\$ruislow,\$ruishigh,1);
\$y3=32+rand(\$ruislow,\$ruishigh,1);
\$y4=36+rand(\$ruislow,\$ruishigh,1);
\$y5=42+rand(\$ruislow,\$ruishigh,1);
\$y6=36+rand(\$ruislow,\$ruishigh,1);
\$y7=19+rand(\$ruislow,\$ruishigh,1);
\$Y=maple("Vector([\$y1,\$y2,\$y3,\$y4,\$y5,\$y6,\$y7])");
\$displayY=maple("printf(MathML:-ExportPresentation(\$Y))");
\$TY=maple("LinearAlgebra[Transpose](\$Y)");
\$displayTY=maple("printf(MathML:-ExportPresentation(\$TY))");
://data 3;
\$z1=76+rand(\$ruislow,\$ruishigh,1);
\$z2=108+rand(\$ruislow,\$ruishigh,1);
\$z3=128+rand(\$ruislow,\$ruishigh,1);
\$z4=54+rand(\$ruislow,\$ruishigh,1);
\$z5=18+rand(\$ruislow,\$ruishigh,1);
\$z6=4+rand(\$ruislow,\$ruishigh,1);
\$z7=1+rand(\$ruislow,\$ruishigh,1);
\$Z=maple("Vector([\$z1,\$z2,\$z3,\$z4,\$z5,\$z6,\$z7])");
\$displayZ=maple("printf(MathML:-ExportPresentation(\$Z))");
\$TZ=maple("LinearAlgebra[Transpose](\$Z)");
\$displayTZ=maple("printf(MathML:-ExportPresentation(\$TZ))");
://totals;
\$t1=\$y1+\$z1;
\$t2=\$y2+\$z2;
\$t3=\$y3+\$z3;
\$t4=\$y4+\$z4;
\$t5=\$y5+\$z5;
\$t6=\$y6+\$z6;
\$t7=\$y7+\$z7;
\$T=maple("Vector([\$t1,\$t2,\$t3,\$t4,\$t5,\$t6,\$t7])");
\$displayT=maple("printf(MathML:-ExportPresentation(\$T))");
:// percentage Y;
\$py1=\$y1/\$t1;
\$py2=\$y2/\$t2;
\$py3=\$y3/\$t3;
\$py4=\$y4/\$t4;
\$py5=\$y5/\$t5;
\$py6=\$y6/\$t6;
\$py7=\$y7/\$t7;
:// percentage Z;
\$pz1=\$z1/\$t1;
\$pz2=\$z2/\$t2;
\$pz3=\$z3/\$t3;
\$pz4=\$z4/\$t4;
\$pz5=\$z5/\$t5;
\$pz6=\$z6/\$t6;
\$pz7=\$z7/\$t7;
://odds;
\$o1=\$py1/\$pz1;
\$o2=\$py2/\$pz2;
\$o3=\$py3/\$pz3;
\$o4=\$py4/\$pz4;
\$o5=\$py5/\$pz5;
\$o6=\$py6/\$pz6;
\$o7=\$py7/\$pz7;
://logit;
\$ln1=ln(\$o1);
\$ln2=ln(\$o2);
\$ln3=ln(\$o3);
\$ln4=ln(\$o4);
\$ln5=ln(\$o5);
\$ln6=ln(\$o6);
\$ln7=ln(\$o7);
\$L=maple("Vector([\$ln1,\$ln2,\$ln3,\$ln4,\$ln5,\$ln6,\$ln7])");
\$displayL=maple("printf(MathML:-ExportPresentation(\$L))");
://linreg;
://\$fit1=maple("Statistics[LinearFit]([1,t],\$X,\$L,t)");
\$fit=maple("map(rhs, Statistics[Fit](a*x+b, \$X, \$L, x, output=parametervalues))");
\$intercept=maple("\$fit[2]");
\$slope=maple("\$fit[1]");
\$r=maple("evalf(Statistics[Correlation](\$X,\$L))");

Best regards,

Nico

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