[Emad Shehata]

clear all
input y x1 x2 x3
99.2  96.7  101  12
99  98.1  100.1  15
100  100  100  17
111.6  104.9  90.6  22
122.2  104.9  86.5  36
117.6  109.5  89.7  45
121.1  110.8  90.6  66
136  112.3  82.8  89
154.2  109.3  70.1  99
153.6  105.3  65.4  118
158.5  101.7  61.3  134
140.6  95.4  62.5  151
136.2  96.4  63.6  167
168  97.6  52.6  184
154.3  102.4  59.7  200
149  101.6  59.5  217
165.5  103.8  61.3  233
end
 reg y x1 x2 x3
 estat ovtest

 reg y x1 x2 x3
 predict double yh
 gen yh2 = yh^2
 gen yh3 = yh^3
 gen yh4 = yh^4

 reg y x1 x2 x3 yh2 yh3 yh4, noomitted
 test yh2 yh3 yh4

. reg y x1 x2 x3

Source | SS df MS Number of obs = 17
-------------+------------------------------ F( 3, 13) = 84.64
Model | 8461.08634 3 2820.36211 Prob > F = 0.0000
Residual | 433.163821 13 33.3202939 R-squared = 0.9513
-------------+------------------------------ Adj R-squared = 0.9401
Total | 8894.25016 16 555.890635 Root MSE = 5.7724

------------------------------------------------------------------------------
y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
x1 | 1.060841 .2769969 3.83 0.002 .4624256 1.659257
x2 | -1.397391 .2321721 -6.02 0.000 -1.898969 -.895814
x3 | -.0034456 .0514889 -0.07 0.948 -.1146807 .1077894
_cons | 132.2612 36.46863 3.63 0.003 53.47554 211.0469
------------------------------------------------------------------------------

. estat ovtest

Ramsey RESET test using powers of the fitted values of y
Ho: model has no omitted variables
F(3, 10) = 3.94
Prob > F = 0.0429

.  reg y x1 x2 x3

      Source |       SS       df       MS              Number of obs =      17
-------------+------------------------------           F(  3,    13) =   84.64
       Model |  8461.08634     3  2820.36211           Prob > F      =  0.0000
    Residual |  433.163821    13  33.3202939           R-squared     =  0.9513
-------------+------------------------------           Adj R-squared =  0.9401
       Total |  8894.25016    16  555.890635           Root MSE      =  5.7724

------------------------------------------------------------------------------
           y |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
          x1 |   1.060841   .2769969     3.83   0.002     .4624256    1.659257
          x2 |  -1.397391   .2321721    -6.02   0.000    -1.898969    -.895814
          x3 |  -.0034456   .0514889    -0.07   0.948    -.1146807    .1077894
       _cons |   132.2612   36.46863     3.63   0.003     53.47554    211.0469
------------------------------------------------------------------------------

.  predict double yh
(option xb assumed; fitted values)

.  gen yh2 = yh^2
.  gen yh3 = yh^3
.  gen yh4 = yh^4
.  reg y x1 x2 x3 yh2 yh3 yh4, noomitted

      Source |       SS       df       MS              Number of obs =      17
-------------+------------------------------           F(  6,    10) =   73.05
       Model |  8695.85007     6  1449.30835           Prob > F      =  0.0000
    Residual |  198.400089    10  19.8400089           R-squared     =  0.9777
-------------+------------------------------           Adj R-squared =  0.9643
       Total |  8894.25016    16  555.890635           Root MSE      =  4.4542

------------------------------------------------------------------------------
           y |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
          x1 |  -72.75485   106.4014    -0.68   0.510     -309.832    164.3223
          x2 |    96.4665   140.1559     0.69   0.507    -215.8203    408.7533
          x3 |   .2020127    .347275     0.58   0.574    -.5717642    .9757895
         yh2 |    .795382   1.182519     0.67   0.516    -1.839436      3.4302
         yh3 |  -.0040173   .0061253    -0.66   0.527    -.0176653    .0096306
         yh4 |   7.64e-06   .0000118     0.65   0.531    -.0000186    .0000339
       _cons |  -6875.445   10117.14    -0.68   0.512    -29417.84    15666.95
------------------------------------------------------------------------------

.  test yh2 yh3 yh4

 ( 1)  yh2 = 0
 ( 2)  yh3 = 0
 ( 3)  yh4 = 0

       F(  3,    10) =    3.94
            Prob > F =    0.0429

.

[Emad Shehata]

any how the last code is not the optimal solution, the way to get the same results as Stata did is:

clear all
 sysuse auto.dta
*** Manual RESET
 gen double y = price
 gen double x1 = mpg
 reg y x1
 scalar r2=e(r2)
 predict double yh
 gen double yh2=yh^2
 gen double yh3=yh^3
 gen double yh4=yh^4
 reg y x1 yh2 yh3 yh4 , noomitted
 predict yhm4 , xb
 correlate yhm4 y
 scalar rho2=r(rho)*r(rho)
 scalar resetf4=(e(N)-e(df_m)-1)*(rho2-r2)/((4-1)*(1-rho2))
 scalar resetf4p= Ftail((4-1), (e(N)-e(df_m)-1), resetf4)
 scalar resetf4df= (e(N)-e(df_m)-1)
 
 reg y x1
 estat ovtest
 scalar list resetf4 resetf4df resetf4p

[Emad Shehata]

. clear all

.
.  sysuse auto.dta
(1978 Automobile Data)

.
. *** Manual RESET

.
.  gen double y = price

.
.  gen double x1 = mpg

.
.  reg y x1

      Source |       SS       df       MS              Number of obs =      74
-------------+------------------------------           F(  1,    72) =   20.26
       Model |   139449474     1   139449474           Prob > F      =  0.0000
    Residual |   495615923    72  6883554.48           R-squared     =  0.2196
-------------+------------------------------           Adj R-squared =  0.2087
       Total |   635065396    73  8699525.97           Root MSE      =  2623.7

------------------------------------------------------------------------------
           y |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
          x1 |  -238.8943   53.07669    -4.50   0.000    -344.7008   -133.0879
       _cons |   11253.06   1170.813     9.61   0.000     8919.088    13587.03
------------------------------------------------------------------------------

.
.  scalar r2=e(r2)

.
.  predict double yh
(option xb assumed; fitted values)

.
.  gen double yh2=yh^2

.
.  gen double yh3=yh^3

.
.  gen double yh4=yh^4

.
.  reg y x1 yh2 yh3 yh4 , noomitted

      Source |       SS       df       MS              Number of obs =      74
-------------+------------------------------           F(  4,    69) =   12.27
       Model |   263997367     4  65999341.7           Prob > F      =  0.0000
    Residual |   371068029    69  5377797.53           R-squared     =  0.4157
-------------+------------------------------           Adj R-squared =  0.3818
       Total |   635065396    73  8699525.97           Root MSE      =    2319

------------------------------------------------------------------------------
           y |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
          x1 |   4321.748   2876.026     1.50   0.137    -1415.767    10059.26
         yh2 |   .0067004   .0040298     1.66   0.101    -.0013388    .0147396
         yh3 |  -1.02e-06   5.56e-07    -1.83   0.072    -2.13e-06    9.20e-08
         yh4 |   5.52e-11   2.71e-11     2.04   0.046     1.12e-12    1.09e-10
       _cons |  -182923.9   123551.7    -1.48   0.143    -429402.7    63555.01
------------------------------------------------------------------------------

.
.  predict yhm4 , xb

.
.  correlate yhm4 y
(obs=74)

             |     yhm4        y
-------------+------------------
        yhm4 |   1.0000
           y |   0.6447   1.0000


.
.  scalar rho2=r(rho)*r(rho)

.
.  scalar resetf4=(e(N)-e(df_m)-1)*(rho2-r2)/((4-1)*(1-rho2))

.
.  scalar resetf4p= Ftail((4-1), (e(N)-e(df_m)-1), resetf4)

.
.  scalar resetf4df= (e(N)-e(df_m)-1)

.
.   reg y x1

      Source |       SS       df       MS              Number of obs =      74
-------------+------------------------------           F(  1,    72) =   20.26
       Model |   139449474     1   139449474           Prob > F      =  0.0000
    Residual |   495615923    72  6883554.48           R-squared     =  0.2196
-------------+------------------------------           Adj R-squared =  0.2087
       Total |   635065396    73  8699525.97           Root MSE      =  2623.7

------------------------------------------------------------------------------
           y |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
          x1 |  -238.8943   53.07669    -4.50   0.000    -344.7008   -133.0879
       _cons |   11253.06   1170.813     9.61   0.000     8919.088    13587.03
------------------------------------------------------------------------------

.
.  estat ovtest

Ramsey RESET test using powers of the fitted values of y
       Ho:  model has no omitted variables
                  F(3, 69) =      7.72
                  Prob > F =      0.0002

.
.  scalar list resetf4 resetf4df resetf4p
   resetf4 =  7.7198817
 resetf4df =         69
  resetf4p =  .00016106

.

[Emad Shehata]

. reset y x1
==============================================================================
* Ordinary Least Squares (OLS)
==============================================================================
  y = x1
------------------------------------------------------------------------------
  Sample Size       =          74
  Wald Test         =     20.2584   |   P-Value > Chi2(1)       =      0.0000
  F-Test            =     20.2584   |   P-Value > F(1 , 72)     =      0.0000
 (Buse 1973) R2     =      0.2196   |   Raw Moments R2          =      0.8563
 (Buse 1973) R2 Adj =      0.2087   |   Raw Moments R2 Adj      =      0.8543
  Root MSE (Sigma)  =   2623.6529   |   Log Likelihood Function =   -686.5396
------------------------------------------------------------------------------
- R2h= 0.2196   R2h Adj= 0.2087  F-Test =   20.26 P-Value > F(1 , 72)  0.0000
- R2v= 0.2196   R2v Adj= 0.2087  F-Test =   20.26 P-Value > F(1 , 72)  0.0000
------------------------------------------------------------------------------
           y |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
          x1 |  -238.8943   53.07669    -4.50   0.000    -344.7008   -133.0879
       _cons |   11253.06   1170.813     9.61   0.000     8919.088    13587.03
------------------------------------------------------------------------------
==============================================================================
*** REgression Specification Error Tests (RESET)
==============================================================================
 Ho: Model is Specified  -  Ha: Model is Misspecified
------------------------------------------------------------------------------
* Ramsey Specification ResetF Test
- Ramsey RESETF1 Test: Y= X Yh2         =  12.937  P-Value > F(1,  71) 0.0006
- Ramsey RESETF2 Test: Y= X Yh2 Yh3     =   9.098  P-Value > F(2,  70) 0.0003
- Ramsey RESETF3 Test: Y= X Yh2 Yh3 Yh4 =   7.720  P-Value > F(3,  69) 0.0002
------------------------------------------------------------------------------
* DeBenedictis-Giles Specification ResetL Test
- Debenedictis-Giles ResetL1 Test       =   6.328  P-Value > F(2, 70)  0.0030
- Debenedictis-Giles ResetL2 Test       =   6.707  P-Value > F(4, 68)  0.0001
- Debenedictis-Giles ResetL3 Test       =   4.520  P-Value > F(6, 66)  0.0007
------------------------------------------------------------------------------
* DeBenedictis-Giles Specification ResetS Test
- Debenedictis-Giles ResetS1 Test       =   5.910  P-Value > F(2, 70)  0.0042
- Debenedictis-Giles ResetS2 Test       =   3.845  P-Value > F(4, 68)  0.0071
- Debenedictis-Giles ResetS3 Test       =   3.350  P-Value > F(6, 66)  0.0061
------------------------------------------------------------------------------
- White Functional Form Test: E2= X X2  =   7.310  P-Value > Chi2(1)   0.0259
------------------------------------------------------------------------------
.

So, the following commands are not good idea to calculate Ramsey RESET test
reg y x1 x2 x3 yh2 yh3 yh4
test yh2 yh3 yh4
Thanks for all

[Richard Williams]

I think this is the critical section of ovtest.ado:

                        tempvar yh2 yh3 yh4
                        summ `yh'
                        replace `yh' = (`yh'-r(min))/(r(max)-r(min))
                        gen float `yh2' = `yh'*`yh'
                        gen float `yh3' = `yh'*`yh'*`yh'
                        gen float `yh4' = `yh'*`yh'*`yh'*`yh'
                        local rhs "`yh2' `yh3' `yh4'"

The resulting variables then range between 0 and 1. Adapting that to the auto example,

sysuse auto.dta, clear
reg price mpg
estat ovtest
predict double price_hat if e(sample)
sum price_hat
replace price_hat = (price_hat-r(min))/(r(max)-r(min))
gen float price_hat2 = price_hat^2
gen float price_hat3 = price_hat^3
gen float price_hat4 = price_hat^4
reg price mpg price_hat2 price_hat3 price_hat4
test price_hat2 price_hat3 price_hat4

At this point I would just trust ovtest rather than try to replicate by hand.

[Joao Santos Silva]

Dear Richard,

I am afraid I disagree. As far as I know, the -ovtest- command does not allow us to choose the number of powers to use (3 is generally too much!) and does not allow us to perform the test using robust standard errors (which is generally desirable).

Moreover, the RESET can be used in binary models (here is has nice interpretations), count data models, Tobit, and in all other models based on a linear index. There are no "ovtests" for all these models.

What I find troubling is Stata's sensitivity to the scale of the dependent variable. For example, in many models you can get convergence or non-convergence simply by changing the scale of the dependent variable.

All the best,

Joao

[Emad Shehata]

if we want to use test after regression , as mention of Prof. Richard
We need some modification to be done in the predicted variable (yh)
So, the following comands can be followed:

*** Manual RESET
 clear all
 sysuse auto.dta
 gen double y = price
 gen double x1 = mpg
 reg y x1
 estat ovtest

 predict double yh
 summ yh
 replace yh = (yh-r(min))/(r(max)-r(min))
 gen double yh2=yh^2
 gen double yh3=yh^3
 gen double yh4=yh^4
 reg y x1 yh2 yh3 yh4
 test yh2 yh3 yh4

 *** Manual RESET
. qui {
.  clear all
.  sysuse auto.dta
.  gen double y = price
.  gen double x1 = mpg
.  reg y x1
.  }

.  estat ovtest

Ramsey RESET test using powers of the fitted values of y
       Ho:  model has no omitted variables
                  F(3, 69) =      7.72
                  Prob > F =      0.0002
. qui {
.  predict double yh
.  summ yh
.  replace yh = (yh-r(min))/(r(max)-r(min))
.  gen double yh2=yh^2
.  gen double yh3=yh^3
.  gen double yh4=yh^4
.  reg y x1 yh2 yh3 yh4
.  }

.  test yh2 yh3 yh4
 ( 1)  yh2 = 0
 ( 2)  yh3 = 0
 ( 3)  yh4 = 0

       F(  3,    69) =    7.72
            Prob > F =    0.0002