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Page 312 shows the analysis of covariance. With the xi3 command, you indicate a continuous variable by not providing a coding scheme for it. Hence, there is no c. or u. in front of the variable x. We use the test command to obtain the F value shown in the text. You can download the xi3 command by typing findit xi3 (see How can I use the findit command to search for programs and get additional help? for more information about using findit).
use http://www.ats.ucla.edu/stat/stata/examples/da/chap14, clear
xi3: regress y c.a x
c.a _Ia_1-3 (naturally coded; _Ia_1 omitted)
Source | SS df MS Number of obs = 24
-------------+------------------------------ F( 3, 20) = 5.50
Model | 275.828162 3 91.9427208 Prob > F = 0.0064
Residual | 334.171838 20 16.7085919 R-squared = 0.4522
-------------+------------------------------ Adj R-squared = 0.3700
Total | 610 23 26.5217391 Root MSE = 4.0876
------------------------------------------------------------------------------
y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_Ia_2 | 3.843675 2.044417 1.88 0.075 -.4209034 8.108254
_Ia_3 | 6.563246 2.103897 3.12 0.005 2.174594 10.9519
x | 1.250597 .3993861 3.13 0.005 .4174919 2.083701
_cons | .6205251 3.109435 0.20 0.844 -5.865643 7.106693
------------------------------------------------------------------------------
test _Ia_2 _Ia_3
( 1) _Ia_2 = 0.0
( 2) _Ia_3 = 0.0
F( 2, 20) = 4.96
Prob > F = 0.0178
Below we show how to compute the adjusted means shown on page 314. The adjust command adjusts the means for x and lists them separately for each level of a.
adjust x, by(a)
--------------------------------------------------
Dependent variable: y Command: regress
Variables left as is: _Ia_2, _Ia_3
Covariate set to mean: x = 7.5
--------------------------------------------------
----------------------
a | xb
----------+-----------
1 | 6.53103
2 | 10.3747
3 | 13.0943
----------------------
Key: xb = Linear Prediction
On pages 314-316 Keppel shows how to compare group 1 with 2 and 3. We create Acomp1 using the char command that shows the comparison of interest, and add a second comparison that is orthogonal to the first.
char a[user] (1 -.5 -.5\0 -1 1)
We now use the user-defined contrasts and the test command to obtain the results shown in the test. These results are slightly different from Keppel's on page 316, but do match results from other packages. We think the differences may be simply due to rounding error.
xi3: regress y u.a x
u.a _Ia_1-3 (naturally coded; _Ia_3 omitted)
Source | SS df MS Number of obs = 24
-------------+------------------------------ F( 3, 20) = 5.50
Model | 275.828162 3 91.9427208 Prob > F = 0.0064
Residual | 334.171838 20 16.7085919 R-squared = 0.4522
-------------+------------------------------ Adj R-squared = 0.3700
Total | 610.00 23 26.5217391 Root MSE = 4.0876
------------------------------------------------------------------------------
y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_Ia_1 | -5.20346 1.784189 -2.92 0.009 -8.925214 -1.481707
_Ia_2 | 2.71957 2.116299 1.29 0.213 -1.694951 7.134092
x | 1.250597 .3993861 3.13 0.005 .4174919 2.083701
_cons | .6205251 3.109435 0.20 0.844 -5.865643 7.106693
------------------------------------------------------------------------------
test _Ia_1
( 1) _Ia_1 = 0.0
F( 1, 20) = 8.51
Prob > F = 0.0085
At the bottom of page 320 Keppel shows how to test for homogeneity of regression across groups. This is equivalent to testing the interaction of a*x, where an interaction would indicate that the regression coefficient for x is significantly different across the levels of a. We see that the test of a*x corresponds to that shown at the bottom of page 320.
xi3: regress y c.a*x
c.a _Ia_1-3 (naturally coded; _Ia_1 omitted)
Source | SS df MS Number of obs = 24
-------------+------------------------------ F( 5, 18) = 3.64
Model | 306.630482 5 61.3260965 Prob > F = 0.0189
Residual | 303.369518 18 16.8538621 R-squared = 0.5027
-------------+------------------------------ Adj R-squared = 0.3645
Total | 610 23 26.5217391 Root MSE = 4.1053
------------------------------------------------------------------------------
y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_Ia_2 | 12.59373 7.515511 1.68 0.111 -3.195776 28.38323
_Ia_3 | 14.24079 7.872543 1.81 0.087 -2.298813 30.78039
x | 1.089651 .4314027 2.53 0.021 .1833076 1.995995
_Ia2Xx | -1.102471 .9093853 -1.21 0.241 -3.013019 .8080762
_Ia3Xx | -1.053637 1.085943 -0.97 0.345 -3.335119 1.227845
_cons | 1.704052 3.262729 0.52 0.608 -5.150687 8.55879
------------------------------------------------------------------------------
test _Ia2Xx _Ia3Xx
( 1) _Ia2Xx = 0
( 2) _Ia3Xx = 0
F( 2, 18) = 0.91
Prob > F = 0.4188
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