Multiple regression: Difference between revisions

=={{header|Stata}}==

First, build a random dataset:

<lang stata>clear

set seed 17760704

set obs 200

forv i=1/4 {

gen x`i'=rnormal()

}

gen y=1.5+0.8*x1-0.7*x2+1.1*x3-1.7*x4+rnormal()</lang>

Now, use the regress command:

<lang stata>reg y x*</lang>

'''Output'''

The command shows the coefficients along with a bunch of useful information, such as R², F statistic, standard errors of the coefficients...

<pre>

Source | SS df MS Number of obs = 200

-------------+---------------------------------- F(4, 195) = 355.15

Model | 1343.81757 4 335.954392 Prob > F = 0.0000

Residual | 184.458622 195 .945941649 R-squared = 0.8793

-------------+---------------------------------- Adj R-squared = 0.8768

Total | 1528.27619 199 7.67977985 Root MSE = .9726

------------------------------------------------------------------------------

y | Coef. Std. Err. t P>|t| [95% Conf. Interval]

-------------+----------------------------------------------------------------

x1 | .7525247 .0689559 10.91 0.000 .6165295 .8885198

x2 | -.7036303 .0697456 -10.09 0.000 -.8411828 -.5660778

x3 | 1.157477 .072189 16.03 0.000 1.015106 1.299849

x4 | -1.718201 .0621758 -27.63 0.000 -1.840824 -1.595577

_cons | 1.399131 .0697862 20.05 0.000 1.261499 1.536764

------------------------------------------------------------------------------</pre>

The regress command also sets a number of '''ereturn''' values, which can be used by subsequent commands. The coefficients and their standard errors also have a special syntax:

<lang stata>. di _b[x1]

.75252466

. di _b[_cons]

1.3991314

. di _se[x1]

.06895593

. di _se[_cons]

.06978623</lang>

One can compute the covariance matrix of the estimates, the predicted values, residuals... See '''estat''', '''predict''', '''estimates''', '''margins''' and others. Here are a few examples:

<lang stata>. estat ic

Akaike's information criterion and Bayesian information criterion

-----------------------------------------------------------------------------

Model | Obs ll(null) ll(model) df AIC BIC

-------------+---------------------------------------------------------------

. | 200 -487.1455 -275.6985 5 561.397 577.8886

-----------------------------------------------------------------------------

Note: N=Obs used in calculating BIC; see [R] BIC note.

. estat vce

Covariance matrix of coefficients of regress model

e(V) | x1 x2 x3 x4 _cons

-------------+------------------------------------------------------------

x1 | .00475492

x2 | -.00040258 .00486445

x3 | -.00042516 .00017355 .00521125

x4 | -.00011915 -.0002568 .00054646 .00386583

_cons | .00030777 -.00031109 -.00023794 .00058926 .00487012

. predict yhat, xb

. predict r, r</lang>