olsqr2¶
Purpose¶
Computes OLS coefficients, residuals, and predicted values using the QR decomposition.
Format¶

{ b, r, p } =
olsqr2
(depvar, indepvars)¶ Parameters:  depvar (Nx1 vector) – dependent variable
 indepvars (NxP matrix) – independent variables
Returns:  b (Px1 vector) – least squares estimates of regression of y on x. If x does not have full rank, then the coefficients that cannot be estimated will be zero.
 r (Px1 vector) – OLS residuals. (\(r = y  x*b\))
 p (Px1 vector) – predicted values. (\(p = x*b\))
Examples¶
rndseed 129727134;
// Assign random matrices
x = rndn(150, 4);
y = rndn(150, 1);
// Solve OLS coefficient using QR decomposition
{ b, r, p } = olsqr2(y, x);
Remarks¶
This provides an alternative to \(y/x\) for computing least squares coefficients.
This procedure is slower than the /
operator. However, for near singular
matrices, it may produce better results.
The olsqr2()
procedure handles matrices that do not have full rank by returning zeros
for the coefficients that cannot be estimated.