[Stata Program]
note: ATI example -- Pedhazur data p. 464
use http://www.gseis.ucla.edu/courses/data/ati
generate x4 = x1*x3
summarize y x3
regress y x3, beta
regress y x3 x1, beta
regress y x3 x1 x4, beta
plot y x3
plot y x3 if x1==1
plot y x3 if x1==0
[Stata Output]
generate x4 = x1*x3
summarize y x3
Variable | Obs Mean Std. Dev. Min Max
---------+-----------------------------------------------------
y | 40 4.2 1.897367 1 7
x3 | 40 31.25 17.52178 5 63
regress y x3, beta
Source | SS df MS Number of obs = 40
---------+------------------------------ F( 1, 38) = 0.13
Model | .469787447 1 .469787447 Prob > F = 0.7229
Residual | 139.930213 38 3.68237401 R-squared = 0.0033
---------+------------------------------ Adj R-squared = -0.0229
Total | 140.40 39 3.60 Root MSE = 1.919
------------------------------------------------------------------------------
y | Coef. Std. Err. t P>|t| Beta
---------+--------------------------------------------------------------------
x3 | -.0062638 .0175369 -0.357 0.723 -.0578452
_cons | 4.395745 .6264144 7.017 0.000 .
------------------------------------------------------------------------------
regress y x3 x1, beta
Source | SS df MS Number of obs = 40
---------+------------------------------ F( 2, 37) = 0.30
Model | 2.21859402 2 1.10929701 Prob > F = 0.7448
Residual | 138.181406 37 3.73463259 R-squared = 0.0158
---------+------------------------------ Adj R-squared = -0.0374
Total | 140.40 39 3.60 Root MSE = 1.9325
------------------------------------------------------------------------------
y | Coef. Std. Err. t P>|t| Beta
---------+--------------------------------------------------------------------
x3 | -.0072097 .0177149 -0.407 0.686 -.0665803
x1 | .4194662 .6129853 0.684 0.498 .1119473
_cons | 4.215571 .6835853 6.167 0.000 .
------------------------------------------------------------------------------
regress y x3 x1 x4, beta
Source | SS df MS Number of obs = 40
---------+------------------------------ F( 3, 36) = 116.93
Model | 127.332425 3 42.4441416 Prob > F = 0.0000
Residual | 13.0675753 36 .362988203 R-squared = 0.9069
---------+------------------------------ Adj R-squared = 0.8992
Total | 140.40 39 3.60 Root MSE = .60249
------------------------------------------------------------------------------
y | Coef. Std. Err. t P>|t| Beta
---------+--------------------------------------------------------------------
x3 | -.1067964 .007699 -13.871 0.000 -.9862426
x1 | -5.999715 .3950574 -15.187 0.000 -1.601206
x4 | .2051554 .0110504 18.565 0.000 2.217581
_cons | 7.193213 .2667243 26.969 0.000 .
------------------------------------------------------------------------------
plot y x3
7 +
| * * * * *
|
t |
e |
a | * * * * * * *
c |
h |
e | * * ** * * * *
r |
|
r | * **
a |
t |
i | * * * * * *
n |
g |
s | * * * * * * *
|
|
1 + * * *
+----------------------------------------------------------------+
5 tolerance of ambiguity 63
plot y x3 if x1==1
7 +
| * *
|
t |
e |
a | * * * * *
c |
h |
e | * * * *
r |
|
r | * *
a |
t |
i | * * *
n |
g |
s | * * *
|
|
1 + *
+----------------------------------------------------------------+
5 tolerance of ambiguity 62
plot y x3 if x1==0
7 +
| * * *
|
t |
e |
a | * *
c |
h |
e | * * **
r |
|
r | **
a |
t |
i | * * *
n |
g |
s | * * * *
|
|
1 + * *
+----------------------------------------------------------------+
5 tolerance of ambiguity 63