TESTING FOR THE SIGNIFICANCE OF A SUBSET OF
COEFFICIENTS-THE WALD TEST
(UNRESTRICTED) MODEL
MODEL A
reg
price
sqft
bedrms
Source
Model
Residual
SS
df
MS
Number of obs
F (3, 10)
3. 28371.6473
Prob > F
10.1670.00687
R-squared
Adj R-squared
13 7831.9239
Root MSE
85114.94
16700.07
Total
101815
price
Coef.
sqft
bedrms
baths
_cons
baths
Std. Err.
0.1548 .0319404
-21.5875 27.02933
-12.1928 43.25
129.0616 88.30326
t
P>t
4.85
-0.80
-0.28
1.46
0.001
0.443
0.784
0.175
14
16.99
0.0003
0.836
0.7868
40.866
[95% Conf. Interval]
0.083632
-81.8126
-108.56
-67.6903
0.225968
38.63758
84.17425
325.8136
Wald Test:
test bedrms baths
( 1) bedrms = 0
( 2) baths = 0
F( 2, 10) = 0.47
Prob > F = 0.6375
EXPLANATION OF THE TEST: Wald test here is used to test the joint significance of a
subset of coefficients, namely, bedrms and baths. These two variables are individually
insignificant based on t-tests with very high p values. But before dropping them together,
we may want to test the joint significance of them using Wald test.
The command test bedrms baths tests whether baths and bedrms are insignificant
jointly. Since the null says they are, and F-stat’s p-value=0.6375, then we cannot reject
the null. DROP both baths and bedrms from the regression equation. They don’t belong
to the model.
SPECIAL WALD TEST: This is an F-test for the significance of all variables in the
model, i.e. sqft, bedrms and baths. Hence, the null states betas of all variables in the
model are set equal to zero.
Null H 0 :  sqft   bedrms   baths  0
Alternative H A : At least some are non zero.
test bedrms baths sqft
( 1) bedrms = 0
( 2) baths = 0
( 3) sqft = 0
F( 3, 10) = 16.99
Prob > F = 0.0003
Notice that F-test p-value is 0.0003, which is lower than 1% of  . Hence, we can reject
the null and at least some variables in this trio is significant. This variable is SQFT!
(based on the t-test).
RESTRICTED MODEL
MODEL B
reg
price sqft
Source
SS
df
Number of
obs
MS
F( 1,
12)
14
54.86
Model
83541.4429
1 83541.4429
Residual
18273.5678
12 1522.79731
R-squared
0.8205
Total
101815.011
13 7831.9239
Adj R-squared
Root MSE
0.8056
39.023
price
sqft
cons
Coef.
Std. Err.
0.1387503 .0187329
52.3509 37.28549
t
Prob > F
P>t
7.41
0
1.40 0.186
[95% Conf.
0
Interval]
0.0979349 0.179566
-28.88719 133.589