* A very simple program, "ols1" estimates linear regression coefficients using ordinary least squares.

program ols1
	version 8.0

* The syntax allows only for a variable list with one or more numeric variables.
	
	syntax varlist(min=1 numeric)

* "tempname..." assigns names to temporary matrices to be usined in this program.  When ols1 has finished, they drop.

	tempname crossYX crossX crossY b

* "matrix accum..." forms a cross-product matrix.  The K variables in varlist, and the N observations with nonmissing
* values on all K variables, comprise an N row, K column data matrix we might call yX.  The cross product matrix YX equals
* the transpose of yX times yX.  Written algebraically, crossYX=(yX)'yX

	quietly matrix accum `crossYX' = `varlist'

* Matrix crossX extracts rows 2 through K, and column 2 through K from crossYX:
*	crossX = X'X

	matrix `crossX' = `crossYX'[2...,2...]

* Column vector crossY extracts rows 2 through K, and column 1 from crossYX:
*	crossY = X'y

	matrix `crossY' = `crossYX'[2...,1]

* The column vector b contains OLS regression coefficients, obtained by the classic estimating equation b = inverse(X'X)X'y

	matrix `b' = syminv(`crossX') * `crossY'

* Finally, we list the coefficient estimates, which are the contents of b. 

	matrix list `b'
end