Dear reader,

My questions about Multivariate Statistics are all programmed the hard way. When using R in the classroom, which has all the commands available this looks a little awkward. Thing is that every command should give a specific answer which can be related to a question box.

A little help would be nice. I am more than happy to share questions

$e=maple("Vector([1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1])");

$n=maple("evalf(Statistics[Count]($e))");

$k=2;

:// data input;

:// dependent variable Y;

$Y=maple("[11.259,11.238,11.492,11.479,11.016,11.241,10.949,10.690,10.964,10.733,10.493,10.684,10.459,10.595,10.953,10.838,10.545,10.806,10.455,10.299,10.608,10.605,10.536,10.492]");

$vY=maple("Vector([$Y])");

$nY=maple("evalf(Statistics[Count]($Y))");

$muY=maple("evalf(Statistics[Mean]($Y))");

$sumY=maple("add($Y)");

:// independent variable X1;

$X1=maple("[7.5,7.5,6.5,7,8,7.5,7.5,8,8.5,8,8,8.5,8,8,8,8,8,8,8.5,8.5,8.5,8,8,8]");

$vX1=maple("Vector([$X1])");

$nX1=maple("evalf(Statistics[Count]($X1))");

$muX1=maple("evalf(Statistics[Mean]($X1))");

$sumX1=maple("add($X1)");

:// independent variable X2;

$X2=maple("[22,22,20,22.5,21.5,22,21.5,21,21.5,21,20.35,21,20.35,20.75,21.5,21.35,20.75,21.1,20.35,20,20.75,20.75,20.75,20.35]");

$vX2=maple("Vector([$X2])");

$nX2=maple("evalf(Statistics[Count]($X2))");

$muX2=maple("evalf(Statistics[Mean]($X2))");

$stdvX2=maple("evalf(Statistics[StandardDeviation]($X2))");

$sumX2=maple("add($X2)");

:// independent variable X3;

$X3=maple("[8.01,9.1,8.39,8.37,8.73,9.11,7.52,7.17,7.54,7.24,6.79,7.09,3.6,6.95,7.52,7.34,5.82,7.29,5.68,5.45,6.97,8.03,5.8,4.69]");

$vX3=maple("Vector([$X3])");

$nX3=maple("evalf(Statistics[Count]($X3))");

$muX3=maple("evalf(Statistics[Mean]($X3))");

$stdvX3=maple("evalf(Statistics[StandardDeviation]($X3))");

$sumX3=maple("add($X3)");

$X3s=maple("$vX3.$vX3");

:// small variables based on deviation around average value;

$y=maple("$vY-$muY*$e");

$x1=maple("$vX1-$muX1*$e");

$x2=maple("$vX2-$muX2*$e");

$x3=maple("$vX2-$muX2*$e");

:// summation of deviation values;

$sumysq=maple("$y.$y");

$sumx1sq=maple("$x1.$x1");

$sumx2sq=maple("$x2.$x2");

$sumx3sq=maple("$x3.$x3");

$sumyx1=maple("$y.$x1");

$sumyx2=maple("$y.$x2");

$sumyx3=maple("$y.$x3");

$sumx1x2=maple("$x1.$x2");

$sumx1x3=maple("$x1.$x3");

$sumx2x3=maple("$x2.$x3");

:// calculation of the coefficients;

:// coefficient betha1;

$b1=maple("(($sumyx1)*($sumx2sq)-($sumyx2)*($sumx1x2))/(($sumx1sq)*($sumx2sq)-($sumx1x2)^2)");

$b2=maple("(($sumyx2)*($sumx1sq)-($sumyx1)*($sumx1x2))/(($sumx1sq)*($sumx2sq)-($sumx1x2)^2)");

$a=maple("($muY)-($b1)*($muX1)-($b2)*($muX2)");

:// calculate estimate based on given values;

$valuex1=range(8,8,1/10);

$valuex2=range(21,21,1/10);

$yhatvalue=$a+($b1)*$valuex1+($b2)*$valuex2;

:// standard deviations;

$stdvy=maple("evalf(Statistics[StandardDeviation]($y))");

$stdvx1=maple("evalf(Statistics[StandardDeviation]($x1))");

$stdvx2=maple("evalf(Statistics[StandardDeviation]($x2))");

$stdvx3=maple("evalf(Statistics[StandardDeviation]($x3))");

:// correlation coefficients;

$ryx1=maple("($sumyx1)/($n*$stdvy*$stdvx1)");

$ryx2=maple("($sumyx2)/($n*$stdvy*$stdvx2)");

$ryx3=maple("($sumyx3)/($n*$stdvy*$stdvx3)");

$rx1x2=maple("($sumx1x2)/($n*$stdvx1*$stdvx2)");

$rx1x3=maple("($sumx1x3)/($n*$stdvx1*$stdvx3)");

$rx2x3=maple("($sumx2x3)/($n*$stdvx2*$stdvx3)");

:// estimated values;

$Yhat=maple("($a)*$e+($b1)*$vX1+($b2)*$vX2");

$error=maple("$vY-$Yhat");

$sumerror=maple("$error.$e");

$sumerrorsq=maple("$error.$error");

:// $errortr=maple("LinearAlgebra[Transpose]($error)");

:// $sumerrorsq=maple("LinearAlgebra[MatrixMatrixMultiply]($errortr,$error)");

$errorstdv=maple("sqrt($sumerrorsq/($n-2-1))");

:// standard error of the coefficients;

$errorb1=maple("$errorstdv/sqrt((($sumx1sq*$sumx2sq)-(($sumx1x2)^2))/($sumx2sq))");

$errorb2=maple("$errorstdv/sqrt((($sumx1sq*$sumx2sq)-(($sumx1x2)^2))/($sumx1sq))");

:// R-squared;

$Rsq=maple("1-$sumerrorsq/$sumysq");

:// adjusted R-squared;

$Rasq=maple("1-($sumerrorsq/($n-$k-1))/($sumysq/($n-1))");

:// hypothesis: does variable X[i] influence Y? H[0]: it does not so b=0;

$tb1=maple("$b1/$errorb1");

$tb2=maple("$b2/$errorb2");

$Tdf=$n-$k-1;

$alpha=range(0.05,0.05,1/100);

$T=maple("Statistics[Quantile](StudentT($Tdf),(1-$alpha/2))");

$ptb1=maple("Statistics[CDF](StudentT($Tdf),$tb1)");

$ptb2=maple("1-Statistics[CDF](StudentT($Tdf),$tb2)");