Foortran Toolkit

Fortran toolkit

Borja Petit

olsreg

subroutine olsreg(coeffs,yvar,xvar1,xvar2,...,xvar8,w,mask,table)
  implicit none
  real(kind=8) , intent(out)           :: coeffs(:)
  real(kind=8) , intent(in)            :: yvar(:)
  real(kind=8) , intent(in)            :: xvar1(:)
  real(kind=8) , intent(in) , optional :: xvar2(:),xvar3(:),...,xvar8(:)
  real(kind=8) , intent(in) , optional :: w(:)     
  logical      , intent(in) , optional :: mask(:)
  integer      , intent(in) , optional :: table

This subroutine returns the OLS coefficients from a linear regression model:

\[\texttt{yvar} = \beta_0 + \beta_1 \cdot \texttt{xvar1} + \beta_2 \cdot\texttt{xvar2} + ... + \beta_8 \cdot\texttt{xvar8} + u\]

The subroutine allows up to 8 explanatory variables. The subroutine automatically includes a constant terms if size(coeffs) equals n+1, where n is the number of explanatory variables. The user can supply a vector of weights, w of the same size as yvar. If not supplied, the program assums uniform weigthing.

The user can also supply a mask to compute the impose a condition. The input mask is a logical array of the same size of yvar. For example:

call olsreg(coeffs,yvar,xvar1,xvar2,mask = xvar1.gt.0.0d0 .and. xvar2.lt.5.0d0)

This code computes the OLS coefficients from a linear regression of yvar on xvar1 and xvar2 conditional on xvar1 being positive and xvar2 being smaller than 5. If coeffs is of size 3, the model includes a contant term so that $\texttt{coeffs} = (\beta_0,\beta_1,\beta_2)$. If the size of coefs is 2, then the returned vector is $\texttt{coeffs} = (\beta_1,\beta_2)$.

Finally, the variable table controls the output of the subroutine. If table is 0 (or missing), the subroutine returns the coefficients in the vector coeffs. If table is 1, the subroutine prints a regression table with the coefficients and some additional statistics (t-stats, R-squared, etc).

Dependencies: error, varmean, varvar

(back to index)

Example

Imagine we have four vectors (x0, x1, x2, x3) each with 100 normal random numbers (all with mean zero). And we define a vector y such that

\[\texttt{y} = 0.10 + \texttt{x0} + 0.7\cdot\texttt{x1} - 0.5\cdot \texttt{x2} + 0.2\cdot\texttt{x3}\]

We want to estimate the following regression model

\[\texttt{y} = \beta_0 + \beta_1 \cdot \texttt{x1} + \beta_2 \cdot\texttt{x2} + \beta_3 \cdot\texttt{x3} + u\]

To do so we first define a vector coeffs of dimension 4 and the run:

call olsreg(coeffs,y,x1,x2,x3)

! coeffs = (/ 0.1000 , 0.7265 , -0.4519 , 0.2535 /)

If we specify table = 1, the command prints the following:

call olsreg(coeffs,y,x1,x2,x3,table=1)

! Output:
!
!                               Number of variables =       4
!                            Number of observations =     100
!                      Number of valid observations =     100
!                                         R-squared =  0.6240
!                                Adjusted R-squared =  0.6122
!   
! -----------------------------------------------------------
!                beta     sd(b)      minb      maxb    t-stat
! -----------------------------------------------------------
! Constant     0.1000    0.0311    0.0390    0.1610    3.2141
! Var 1        0.8205    0.0839    0.6560    0.9850    9.7767
! Var 2       -0.4489    0.0664   -0.5791   -0.3187    6.7593
! Var 3        0.1603    0.0526    0.0571    0.2635    3.0456
! -----------------------------------------------------------

If we want to run the same regression model without a constant, we just define the vector coeffs to have dimension 3.

call olsreg(coeffs,y,x1,x2,x3)

! coeffs = (/ 0.7265 , -0.4519 , 0.2535 /)

call olsreg(coeffs,y,x1,x2,x3,table=1)

! Output:
!   
!                               Number of variables =       3
!                             Number of observatios =     100
!                       Number of valid observatios =     100
!                                         R-squared =  0.5997
!                                Adjusted R-squared =  0.5915
!   
! -----------------------------------------------------------
!                beta     sd(b)      minb      maxb    t-stat
! -----------------------------------------------------------
! Var 1        0.8205    0.0879    0.6483    0.9927    9.3379
! Var 2       -0.4489    0.0695   -0.5852   -0.3126    6.4560
! Var 3        0.1603    0.0551    0.0523    0.2683    2.9089
! -----------------------------------------------------------

Note: the R-squared in a regression without a constant term is not well defined. This subroutine deals with this issue as Stata does. See the following thread for a discussion on this.