public function regresionMultiple(MatrixBase $x, MatrixBase $y, $tipo = 'lineal')
{
$precision = $this->precision;
$newX = new MatrixBase($x->getNumRows() + 1, $x->getNumCols(), $precision);
for ($m = 1; $m <= $newX->getNumRows(); $m++) {
for ($n = 1; $n <= $newX->getNumCols(); $n++) {
$newX->setPoint($m, $n, $m == 1 ? 1 : $x->getPoint($m - 1, $n, $precision), $precision);
}
}
$xx = $newX->multiplicationMatrix($newX->transposed());
$xy = $y->multiplicationMatrix($newX->transposed());
$b = $xy->multiplicationMatrix($xx->inversa());
$result = array();
$result['tipo'] = $tipo;
for ($m = 1; $m <= $b->getNumCols(); $m++) {
$result['B' . ($m - 1)] = $b->getPoint(1, $m, $precision);
}
$predicted = array();
$residual = array();
$SE = 0;
$ST = 0;
for ($n = 1; $n <= $x->getNumCols(); $n++) {
$Y = $b->getPoint(1, 1, $precision);
for ($m = 1; $m <= $x->getNumRows(); $m++) {
$Y = bcadd($Y, bcmul($b->getPoint(1, $m + 1), $x->getPoint($m, $n, $precision), $precision), $precision);
}
$predicted[$n] = $Y;
$residual[$n] = bcsub($y->getPoint(1, $n, $precision), $predicted[$n], $precision);
$SE = bcadd($SE, $residual[$n], $precision);
$ST = bcadd($ST, $y->getPoint(1, $n, $precision), $precision);
}
$MSE = bcdiv($SE, $x->getNumCols(), $precision);
$MST = bcdiv($ST, $x->getNumCols(), $precision);
$SSE = bcadd(0, 0, $precision);
$SST = bcadd(0, 0, $precision);
for ($n = 1; $n <= $x->getNumCols(); $n++) {
$SSE = bcadd($SSE, bcmul(bcsub($residual[$n], $MSE, $precision), bcsub($residual[$n], $MSE, $precision), $precision), $precision);
$SST = bcadd($SST, bcmul(bcsub($y->getPoint(1, $n, $precision), $MST, $precision), bcsub($y->getPoint(1, $n, $precision), $MST, $precision), $precision), $precision);
}
$FR = bcdiv(bcmul(bcsub(bcsub($x->getNumCols(), $x->getNumRows(), $precision), 1, $precision), bcsub($SST, $SSE, $precision), $precision), bcmul($x->getNumRows(), $SSE, $precision), $precision);
$RRSQ = bcsub(1, bcdiv($SSE, $SST, $precision), $precision);
$result['correlacion'] = bcsqrt($RRSQ, $precision);
$result['r2'] = $RRSQ;
$result['estadisticoF'] = $FR;
return $result;
}
