F Test of Tobit model Coefficients _Testing Same Model in Different Data Sets

Yue Zhao

Join Date: Sep 2018

Posts: 8
#1

F Test of Tobit model Coefficients _Testing Same Model in Different Data Sets

10 Sep 2018, 21:22

Hi all,
I am running Tobit regressions which require the same model to be run for multiple datasets.
I need to do an F test to see if the differences in coefficients in different datasets are statistically significant. I have no clue about how to implement this in Stata.
Can anyone help me with it? Thanks!
Tags: None
Clyde Schechter

Join Date: Apr 2014

Posts: 29959
#2

10 Sep 2018, 22:00

Are the multiple data sets mutually exclusive? That is, could you imagine the data sets as all being subsets of a single combined data set with an additional variable designated the one and only subset any given observation came from?

If so, you can go about this in two ways. You can run the -tobit- models in each data set, and following each -tobit- command use -estimates store- to retain the results in memory. Once they are all done, you can use -suest- to combine them. Then you can run -test- commands following -suest- to do contrasts of specific coefficients, or sets of coefficients, or all the coefficients.

Read -help estimates store- and -help suest-.

An alternative approach is to actually combine all the data sets into a single large data set with a variable indicating which one each observation comes from. (-help append-) Then run the -tobit- model on the combined data set, but add to it interactions between that data set indicator variable and all the other variables in your model. Then you can test the estimates for the interaction terms individually, in subsets, or all together. The simplest way to add the interaction terms is with factor variable notation. -help fvvarlist-.

There is no particular reason to prefer either of approaches over the other. Well, the combined data set and interaction terms approach generalizes to all possible estimating commands, whereas -suest- cannot be used with some estimators, so perhaps the combined data set and interaction approach is more worth learning for future applications.

So, you've asked a fairly broad question that has a lengthy answer. You now have a substantial reading list to go through to learn the commands that will help you. If you get stuck trying to implement this, do post back showing the exact code you are running, the exact response(s) you are getting from Stata, including any messages. Wrap the code and output in code delimiters to assure that things align readably. (If you are not familiar with code delimiters, read Forum FAQ #12 for instructions.) And also show an example of your data using the -dataex- command. If you are running version 15.1 or a fully updated version 14.2, it is already part of your official Stata installation. If not, run -ssc install dataex- to get it. Either way, run -help dataex- to read the simple instructions for using it. -dataex- will save you time; it is easier and quicker than typing out tables. It includes complete information about aspects of the data that are often critical to answering your question but cannot be seen from tabular displays or screenshots. It also makes it possible for those who want to help you to create a faithful representation of your example to try out their code, which in turn makes it more likely that their answer will actually work in your data.

When asking for help with code, always show example data. When showing example data, always use -dataex-.
Comment

Yue Zhao

Join Date: Sep 2018
Posts: 8

11 Sep 2018, 13:39

Thank you very much for your answer, Clyde.
I am gonna divide the full dataset into two subsets based on whether the variable “norm” is above the average or not. If it is above the average, I call it “high_norm”. If it is below the average, I call it “low_norm”.
Then I run the tobit model for these two subsets. So I can get two coefficients of the variable “operation”, one from the “high_norm”, and the other from the “low_norm”. My goal is to compare the coefficients of the variable “operation” from these two subsets. So I need to take an F test. I am stuck in the last step.
Here is the code. I am not sure if I put the sample data in a correct way using -dataex-. Please let me knodoesn'tt doesnt work.
Really appreciate your help!

. dataex operation size cost PPP resource norm risk in 1/30

Code:

* Example generated by -dataex-. To install: ssc install dataex
clear
input double(operation size cost PPP resource norm risk)
18.399999618530273  -.3778327703475952  -.9071999192237854   .08188223838806152  -.1113569363951683    -.6199849247932434    -.624012291431427
18.399999618530273 -.40205010771751404  -.9117006063461304   -.3542981743812561    .223642498254776   -.47683894634246826    1.267051339149475
11.600000381469727 -.04139556363224983  -.9156386256217957 -.024021748453378677   .8689360618591309    -.6254710555076599    .8203957080841064
11.800000190734863  -.1249365359544754  -.9071999192237854   .08188223838806152    .657260537147522    -.5510783195495605   1.2482249736785889
11.199999809265137  -.2852507531642914  -.8400837779045105    .5147495865821838  .21688228845596313   -.14836332201957703     2.85198974609375
12.199999809265137  -.3442705571651459  -.8327139019966125    1.031813383102417  .23961099982261658   .055991631001234055    3.942247152328491
                11 -.41052982211112976  -.9156386256217957 -.024021748453378677   .2753913700580597    -.8822530508041382   1.9798166751861572
12.600000381469727  -.4124920070171356  -.9071999192237854   .08188223838806152 -.06872667372226715   -.47910258173942566     -.53339684009552
12.800000190734863  -.4138182997703552  -.9117006063461304   -.3542981743812561 -.24208040535449982    -.4821726679801941  -.39179888367652893
12.800000190734863 -.42479583621025085  -.8238251209259033   .07329901307821274  -.3674023151397705  .0034701505210250616  -.12726706266403198
12.800000190734863 -.42418625950813293  -.8400837779045105    .5147495865821838  -.6881850361824036   -.33259984850883484  -.06733386963605881
12.800000190734863 -.42827674746513367  -.8327139019966125    1.031813383102417 -.26216331124305725    -.3594644367694855 -.016053592786192894
                 6 -.36937758326530457  1.2356785535812378 -.024021748453378677  -.8310554623603821     -.824479341506958  -1.0755586624145508
                 6  -.3631949722766876  1.4623993635177612   .08188223838806152  -.9515716433525085   -1.0078279972076416   -1.021239161491394
                 6  -.3718755543231964    1.36282217502594   -.3542981743812561  -.9823076128959656    -.6889771819114685   -.7112607955932617
                 6 -.35925114154815674   1.254806399345398   .07329901307821274  -.9679455757141113     .3041660189628601   -.4853729009628296
 6.199999809265137  -.3353084921836853   1.456210970878601    .5147495865821838 -1.0663305521011353    .06059702858328819  -.20103222131729126
 7.800000190734863  -.3370598256587982  -.8965108394622803    1.031813383102417 -1.0470980405807495     .6091872453689575  -.11621597409248352
                 5  -.4523542821407318 -1.0934149026870728   -.3542981743812561   -.412740021944046     .5452356338500977    -.777881383895874
                 5  -.4565393626689911 -1.0765373706817627   .07329901307821274 -.20467467606067657      .677656888961792   -.5777859091758728
 4.800000190734863  -.4576379954814911 -1.0484082698822021    .5147495865821838  -.2314063310623169     .9116454124450684  -.43494001030921936
 4.599999904632568  -.4592602849006653  -1.025904893875122    1.031813383102417 .011350096203386784    .17719988524913788   -.5323051810264587
14.800000190734863  2.9494690895080566  -.8327139019966125    1.031813383102417 -1.3621976375579834    .37993356585502625   1.4040451049804688
 7.599999904632568 -.13403452932834625  1.2356785535812378 -.024021748453378677 -.23062898218631744   -.23050619661808014   -.1370173543691635
 8.800000190734863  -.2086687833070755  1.4623993635177612   .08188223838806152 .041160330176353455   -.09920760989189148   .22145545482635498
 9.800000190734863  -.2588375210762024    1.36282217502594   -.3542981743812561   .5523819327354431    -.1437295824289322   .21106936037540436
11.600000381469727 -.11891254782676697  1.0376492738723755   .07329901307821274 -.30747005343437195 -.0019190004095435143   .12498844414949417
12.399999618530273 -.17159172892570496  1.2204887866973877    .5147495865821838  -.6979902982711792   -.17532913386821747  -.16300901770591736
13.199999809265137 -.24584807455539703  .04283396154642105    1.031813383102417  -.3528188169002533   -.11198530346155167   .16346964240074158
21.600000381469727  -.3988196849822998  -.9156386256217957 -.024021748453378677  1.1261144876480103    -.7285856604576111  -1.1565927267074585
end

Code:

. sum norm, detail

                            norm
-------------------------------------------------------------
      Percentiles      Smallest
 1%    -2.610545      -2.888673
 5%    -1.494263      -2.757503
10%    -.9065234      -2.610545       Obs                 299
25%    -.5500375      -2.557424       Sum of Wgt.         299

50%    -.1043692                      Mean           .0054955
                        Largest       Std. Dev.      .9719611
75%     .4200296       2.557417
90%     1.420565       2.651641       Variance       .9447083
95%     2.170326       2.660218       Skewness       .5614073
99%     2.651641       2.706151       Kurtosis       4.073483

. 
. egen normmean=mean(norm)

. 
. gen high_norm=0 if norm<normmean
(121 missing values generated)

. 
. replace high_norm=1 if missing(high_norm)
(121 real changes made)

. 
. 
. 
. *test low_norm sample*

. 
. tobit risk size PPP resource cost operation, ll(0), if high_norm==0

Refining starting values:

Grid node 0:   log likelihood = -237.44543

Fitting full model:

Iteration 0:   log likelihood = -237.44543  
Iteration 1:   log likelihood = -181.37746  
Iteration 2:   log likelihood = -166.77426  
Iteration 3:   log likelihood = -163.53825  
Iteration 4:   log likelihood =  -163.4372  
Iteration 5:   log likelihood = -163.43661  
Iteration 6:   log likelihood = -163.43661  

Tobit regression                                Number of obs     =        178
                                                   Uncensored     =         60
Limits: lower = 0                                  Left-censored  =        118
        upper = +inf                               Right-censored =          0

                                                LR chi2(5)        =      11.37
                                                Prob > chi2       =     0.0445
Log likelihood = -163.43661                     Pseudo R2         =     0.0336

------------------------------------------------------------------------------
        risk |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        size |  -.0026304   .1157768    -0.02   0.982    -.2311473    .2258865
         PPP |   .5396431   .2640573     2.04   0.043     .0184545    1.060832
    resource |   .0163501   .1661216     0.10   0.922    -.3115361    .3442362
        cost |   .0887001   .1340803     0.66   0.509    -.1759437    .3533439
   operation |  -.0405574   .0199937    -2.03   0.044    -.0800203   -.0010945
       _cons |  -.1874862   .2580408    -0.73   0.468    -.6967996    .3218273
-------------+----------------------------------------------------------------
  var(e.risk)|    1.95699   .4083789                      1.296317    2.954379
------------------------------------------------------------------------------

. 
. estimates store low_norm

. 
. 
. 
. *test high_norm sample*

. 
. tobit risk size PPP resource cost operation, ll(0), if high_norm==1

Refining starting values:

Grid node 0:   log likelihood = -156.85432

Fitting full model:

Iteration 0:   log likelihood = -156.85432  
Iteration 1:   log likelihood = -95.555607  
Iteration 2:   log likelihood = -76.075133  
Iteration 3:   log likelihood = -68.898554  
Iteration 4:   log likelihood = -67.660773  
Iteration 5:   log likelihood = -67.628196  
Iteration 6:   log likelihood = -67.628119  
Iteration 7:   log likelihood = -67.628119  

Tobit regression                                Number of obs     =        121
                                                   Uncensored     =         22
Limits: lower = 0                                  Left-censored  =         99
        upper = +inf                               Right-censored =          0

                                                LR chi2(5)        =      24.15
                                                Prob > chi2       =     0.0002
Log likelihood = -67.628119                     Pseudo R2         =     0.1515

------------------------------------------------------------------------------
        risk |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        size |  -.5782509   .2917932    -1.98   0.050    -1.156184   -.0003177
         PPP |    1.24688   .5128526     2.43   0.017     .2311106    2.262649
    resource |    -.99764   .4593527    -2.17   0.032    -1.907446    -.087834
        cost |  -.5675052   .3072405    -1.85   0.067    -1.176034    .0410234
   operation |   -.023021   .0363105    -0.63   0.527    -.0949385    .0488965
       _cons |  -2.064819   .6955159    -2.97   0.004    -3.442376   -.6872625
-------------+----------------------------------------------------------------
  var(e.risk)|   2.629274   .9171524                       1.31761    5.246685
------------------------------------------------------------------------------

. 
. estimates store high_norm

. 
. 
. 
. suest low_norm high_norm

Simultaneous results for low_norm, high_norm

                                                Number of obs     =        299

------------------------------------------------------------------------------
             |               Robust
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
low_norm_r~k |
        size |  -.0026304   .0932446    -0.03   0.977    -.1853864    .1801256
         PPP |   .5396431   .2183594     2.47   0.013     .1116666    .9676197
    resource |   .0163501   .1612246     0.10   0.919    -.2996442    .3323444
        cost |   .0887001    .149196     0.59   0.552    -.2037188    .3811189
   operation |  -.0405574   .0172625    -2.35   0.019    -.0743912   -.0067236
       _cons |  -.1874862   .2351246    -0.80   0.425    -.6483218    .2733495
-------------+----------------------------------------------------------------
/low_norm    |
  var(e.risk)|    1.95699   .3952685                       1.31724    2.907451
-------------+----------------------------------------------------------------
high_norm_~k |
        size |  -.5782509   .3228464    -1.79   0.073    -1.211018    .0545165
         PPP |    1.24688   .4877586     2.56   0.011     .2908905    2.202869
    resource |    -.99764   .3374877    -2.96   0.003    -1.659104   -.3361763
        cost |  -.5675052   .2345439    -2.42   0.016    -1.027203   -.1078076
   operation |   -.023021   .0316937    -0.73   0.468    -.0851395    .0390975
       _cons |  -2.064819   .6467878    -3.19   0.001      -3.3325   -.7971385
-------------+----------------------------------------------------------------
/high_norm   |
  var(e.risk)|   2.629274   1.120319                      1.140627    6.060772
------------------------------------------------------------------------------

. 
. test low_norm_operation high_norm_operation
low_norm_operation not found
r(111);

Comment

Clyde Schechter

Join Date: Apr 2014
Posts: 29959

11 Sep 2018, 14:57

Your -dataex- was perfect. Thank you. Actually, your code is quite good until your very last line. This will work:

Code:

* Example generated by -dataex-. To install: ssc install dataex
clear
input double(operation size cost PPP resource norm risk)
18.399999618530273  -.3778327703475952  -.9071999192237854   .08188223838806152  -.1113569363951683    -.6199849247932434    -.624012291431427
18.399999618530273 -.40205010771751404  -.9117006063461304   -.3542981743812561    .223642498254776   -.47683894634246826    1.267051339149475
11.600000381469727 -.04139556363224983  -.9156386256217957 -.024021748453378677   .8689360618591309    -.6254710555076599    .8203957080841064
11.800000190734863  -.1249365359544754  -.9071999192237854   .08188223838806152    .657260537147522    -.5510783195495605   1.2482249736785889
11.199999809265137  -.2852507531642914  -.8400837779045105    .5147495865821838  .21688228845596313   -.14836332201957703     2.85198974609375
12.199999809265137  -.3442705571651459  -.8327139019966125    1.031813383102417  .23961099982261658   .055991631001234055    3.942247152328491
                11 -.41052982211112976  -.9156386256217957 -.024021748453378677   .2753913700580597    -.8822530508041382   1.9798166751861572
12.600000381469727  -.4124920070171356  -.9071999192237854   .08188223838806152 -.06872667372226715   -.47910258173942566     -.53339684009552
12.800000190734863  -.4138182997703552  -.9117006063461304   -.3542981743812561 -.24208040535449982    -.4821726679801941  -.39179888367652893
12.800000190734863 -.42479583621025085  -.8238251209259033   .07329901307821274  -.3674023151397705  .0034701505210250616  -.12726706266403198
12.800000190734863 -.42418625950813293  -.8400837779045105    .5147495865821838  -.6881850361824036   -.33259984850883484  -.06733386963605881
12.800000190734863 -.42827674746513367  -.8327139019966125    1.031813383102417 -.26216331124305725    -.3594644367694855 -.016053592786192894
                 6 -.36937758326530457  1.2356785535812378 -.024021748453378677  -.8310554623603821     -.824479341506958  -1.0755586624145508
                 6  -.3631949722766876  1.4623993635177612   .08188223838806152  -.9515716433525085   -1.0078279972076416   -1.021239161491394
                 6  -.3718755543231964    1.36282217502594   -.3542981743812561  -.9823076128959656    -.6889771819114685   -.7112607955932617
                 6 -.35925114154815674   1.254806399345398   .07329901307821274  -.9679455757141113     .3041660189628601   -.4853729009628296
 6.199999809265137  -.3353084921836853   1.456210970878601    .5147495865821838 -1.0663305521011353    .06059702858328819  -.20103222131729126
 7.800000190734863  -.3370598256587982  -.8965108394622803    1.031813383102417 -1.0470980405807495     .6091872453689575  -.11621597409248352
                 5  -.4523542821407318 -1.0934149026870728   -.3542981743812561   -.412740021944046     .5452356338500977    -.777881383895874
                 5  -.4565393626689911 -1.0765373706817627   .07329901307821274 -.20467467606067657      .677656888961792   -.5777859091758728
 4.800000190734863  -.4576379954814911 -1.0484082698822021    .5147495865821838  -.2314063310623169     .9116454124450684  -.43494001030921936
 4.599999904632568  -.4592602849006653  -1.025904893875122    1.031813383102417 .011350096203386784    .17719988524913788   -.5323051810264587
14.800000190734863  2.9494690895080566  -.8327139019966125    1.031813383102417 -1.3621976375579834    .37993356585502625   1.4040451049804688
 7.599999904632568 -.13403452932834625  1.2356785535812378 -.024021748453378677 -.23062898218631744   -.23050619661808014   -.1370173543691635
 8.800000190734863  -.2086687833070755  1.4623993635177612   .08188223838806152 .041160330176353455   -.09920760989189148   .22145545482635498
 9.800000190734863  -.2588375210762024    1.36282217502594   -.3542981743812561   .5523819327354431    -.1437295824289322   .21106936037540436
11.600000381469727 -.11891254782676697  1.0376492738723755   .07329901307821274 -.30747005343437195 -.0019190004095435143   .12498844414949417
12.399999618530273 -.17159172892570496  1.2204887866973877    .5147495865821838  -.6979902982711792   -.17532913386821747  -.16300901770591736
13.199999809265137 -.24584807455539703  .04283396154642105    1.031813383102417  -.3528188169002533   -.11198530346155167   .16346964240074158
21.600000381469727  -.3988196849822998  -.9156386256217957 -.024021748453378677  1.1261144876480103    -.7285856604576111  -1.1565927267074585
end

// egen normmean=mean(norm)
// gen high_norm=0 if norm<normmean
// replace high_norm=1 if missing(high_norm)

//    THE ABOVE CODE WORKS, BUT THIS IS SHORTER, CLEARER
//    AND ALSO FASTER IN A LARGE DATA SET
summ norm, meanonly
gen high_norm = norm >= r(mean)

*test low_norm sample*


tobit risk size PPP resource cost operation, ll(0), if high_norm==0

estimates store low_norm


*test high_norm sample*


tobit risk size PPP resource cost operation, ll(0), if high_norm==1

estimates store high_norm

suest low_norm high_norm

test _b[high_norm_risk:operation] = _b[low_norm_risk:operation]

Notes;

1. I slightly streamlined the code for creating the high_norm variable. What you had is fine, but this is shorter, clearer, and, if run on a large data set, faster.

2. You may be wondering how I knew what to write for the -test- command. Here's a general tip. If you want to use -test- or -lincom- after a Stata estimation command, you have to know exactly how that command has named the coefficients you want to work with. And, unfortunately, different commands, reflecting the complexity of the models they estimate, do it somewhat differently. The way to know is, after running the estimation command (in this case, -suest-), rerun it with the -coefl- option specified. When you do that, the estimation itself is not repeated. Rather the results are "replayed," and instead of the standard errors and test statistics and CIs, Stata shows you the names it has assigned to the different coefficients. You can then use those (I recommend doing it by copying and pasting into your do-file) in -test- or -lincom-. Here's what -suest, coefl- produces when run after the commands you provided in #3, other than the -test- command, using your -dataex- example as input:

Code:

. suest, coefl

Simultaneous results for low_norm, high_norm

                                                Number of obs     =         30

--------------------------------------------------------------------------------
               |      Coef.  Legend
---------------+----------------------------------------------------------------
low_norm_risk  |
          size |  -3.660367  _b[low_norm_risk:size]
           PPP |  -4.610978  _b[low_norm_risk:PPP]
      resource |   2.910845  _b[low_norm_risk:resource]
          cost |  -1.700188  _b[low_norm_risk:cost]
     operation |  -.3555047  _b[low_norm_risk:operation]
         _cons |   1.179534  _b[low_norm_risk:_cons]
---------------+----------------------------------------------------------------
/low_norm      |
    var(e.risk)|   .8922328  _b[/low_norm:var(e.risk)]
---------------+----------------------------------------------------------------
high_norm_risk |
          size |   1.161779  _b[high_norm_risk:size]
           PPP |   1.495203  _b[high_norm_risk:PPP]
      resource |   4.180792  _b[high_norm_risk:resource]
          cost |  -.2176855  _b[high_norm_risk:cost]
     operation |   .3746816  _b[high_norm_risk:operation]
         _cons |  -3.536634  _b[high_norm_risk:_cons]
---------------+----------------------------------------------------------------
/high_norm     |
    var(e.risk)|   .5674422  _b[/high_norm:var(e.risk)]
--------------------------------------------------------------------------------

Added: It dawns on me that you specified in #1 that you are looking for an F-test here. But the -suest- method gives you a chi square test. Now, in the broadest sense, a chi square test is, in fact, an F-test where the denominator degrees of freedom is infinite. This similar to a z-test being a t-test with infinite degrees of freedom. In each case you are using inferences that are asymptotically correct. (With the -dataex- sample of 30 observations, asymptotically correct inferences are, of course, dicey, as 30 is pretty far from infinity, and 19 df is even more dubious. But in your real sample of > 400 observations, there should be no problem relying on the asymptotic chi-square test.)

If, however, you literally need an F test, the interaction method will give it to you:

Code:

. tobit risk i.high_norm##c.(size PPP resource cost operation), ll(0)

Refining starting values:

Grid node 0:   log likelihood = -35.511708

Fitting full model:

Iteration 0:   log likelihood = -35.511708  
Iteration 1:   log likelihood = -20.539587  
Iteration 2:   log likelihood = -17.143342  
Iteration 3:   log likelihood = -16.393964  
Iteration 4:   log likelihood = -16.354811  
Iteration 5:   log likelihood = -16.354426  
Iteration 6:   log likelihood =  -16.35442  
Iteration 7:   log likelihood =  -16.35442  

Tobit regression                                Number of obs     =         30
                                                   Uncensored     =         11
Limits: lower = 0                                  Left-censored  =         19
        upper = +inf                               Right-censored =          0

                                                LR chi2(11)       =      34.62
                                                Prob > chi2       =     0.0003
Log likelihood =  -16.35442                     Pseudo R2         =     0.5142

---------------------------------------------------------------------------------------
                 risk |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------------+----------------------------------------------------------------
          1.high_norm |  -4.932081   4.584822    -1.08   0.296    -14.52822    4.664062
                 size |  -3.616291   4.556935    -0.79   0.437    -13.15407    5.921484
                  PPP |  -4.246077   3.528965    -1.20   0.244    -11.63228     3.14013
             resource |   2.742099   2.089211     1.31   0.205     -1.63067    7.114869
                 cost |  -1.522629   4.467367    -0.34   0.737    -10.87294    7.827677
            operation |  -.3362266   .2086791    -1.61   0.124    -.7729969    .1005437
                      |
     high_norm#c.size |
                   1  |   4.804326   4.588378     1.05   0.308     -4.79926    14.40791
                      |
      high_norm#c.PPP |
                   1  |   5.790556   3.676782     1.57   0.132    -1.905036    13.48615
                      |
 high_norm#c.resource |
                   1  |   1.513964    2.35983     0.64   0.529    -3.425216    6.453145
                      |
     high_norm#c.cost |
                   1  |   1.340103   4.498024     0.30   0.769    -8.074369    10.75457
                      |
high_norm#c.operation |
                   1  |   .7216254   .2649616     2.72   0.013     .1670544    1.276196
                      |
                _cons |   1.241976   4.207516     0.30   0.771    -7.564456    10.04841
----------------------+----------------------------------------------------------------
           var(e.risk)|   .6725008   .3063014                      .2592263    1.744643
---------------------------------------------------------------------------------------

The nice thing here is that you don't even have to go on to a -test- command to just compare the two coefficients: you can read it right off of the regression output in the high_norm#c.operation line. The t-statistic is 2.72 with 19 df (df = 30 - 11). To translate that to an F statistic all you have to do it is take the square: F = 2.72² = 7.4, df = (1, 19).

Last edited by Clyde Schechter; 11 Sep 2018, 15:09.

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Yue Zhao

Join Date: Sep 2018

Posts: 8
#5

12 Sep 2018, 09:08

Thank you very much, Clyde!!!
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