Calculation from page 142 to page 143 based on data file duncan.
use https://stats.idre.ucla.edu/stat/stata/examples/ara/duncan, clear
(From Fox, Applied Regression Analysis. Use 'notes' command for source of data)
regress prestige educ income
Source | SS df MS Number of obs = 45
---------+------------------------------ F( 2, 42) = 101.22
Model | 36180.9458 2 18090.4729 Prob > F = 0.0000
Residual | 7506.69865 42 178.73092 R-squared = 0.8282
---------+------------------------------ Adj R-squared = 0.8200
Total | 43687.6444 44 992.90101 Root MSE = 13.369
------------------------------------------------------------------------------
prestige | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
educ | .5458339 .0982526 5.555 0.000 .3475521 .7441158
income | .5987328 .1196673 5.003 0.000 .3572343 .8402313
_cons | -6.064663 4.271941 -1.420 0.163 -14.68579 2.556463
------------------------------------------------------------------------------
sort occ_type
by occ_type: summarize(prestige)
-> occ_type= bc
Variable | Obs Mean Std. Dev. Min Max
---------+-----------------------------------------------------
prestige | 21 22.7619 18.05521 3 67
-> occ_type= prof
Variable | Obs Mean Std. Dev. Min Max
---------+-----------------------------------------------------
prestige | 18 80.44444 14.10558 45 97
-> occ_type= wc
Variable | Obs Mean Std. Dev. Min Max
---------+-----------------------------------------------------
prestige | 6 36.66667 11.79265 16 52
gen d1=0
gen d2=0
replace d1=1 if (occ_type==2)
(18 real changes made)
replace d2=1 if (occ_type==3)
(6 real changes made)
regress prestige income educ d1 d2
Source | SS df MS Number of obs = 45
---------+------------------------------ F( 4, 40) = 105.03
Model | 39889.6897 4 9972.42242 Prob > F = 0.0000
Residual | 3797.95474 40 94.9488686 R-squared = 0.9131
---------+------------------------------ Adj R-squared = 0.9044
Total | 43687.6444 44 992.90101 Root MSE = 9.7442
------------------------------------------------------------------------------
prestige | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
income | .5975465 .0893553 6.687 0.000 .4169527 .7781403
educ | .3453193 .1136089 3.040 0.004 .1157071 .5749315
d1 | 16.65751 6.993007 2.382 0.022 2.52412 30.79091
d2 | -14.66113 6.108774 -2.400 0.021 -27.00743 -2.314841
_cons | -.1850278 3.713771 -0.050 0.961 -7.690838 7.320782
------------------------------------------------------------------------------
test d1 d2
( 1) d1 = 0.0
( 2) d2 = 0.0
F( 2, 40) = 19.53
Prob > F = 0.0000
Calculation on page 150, Table 7.1 and Table 7.2 on page 151 based on data file duncan. In Table 7.2, the column of Sum of Squares come from the difference between the sum of squares of the models contrasted. The results from Stata for F-values in Table 7.2 is different from the book since the degree of freedom for residuals used in calculating the F-values is always 36 in the book whereas in Stata it depends on different models.
gen incd1=income*d1
gen incd2=income*d2
gen edud1=educ*d1
gen edud2=educ*d2
regress prestige income educ d1 d2 incd1 edud1 incd2 edud2
Source | SS df MS Number of obs = 45
---------+------------------------------ F( 8, 36) = 54.17
Model | 40336.9993 8 5042.12491 Prob > F = 0.0000
Residual | 3350.64519 36 93.0734776 R-squared = 0.9233
---------+------------------------------ Adj R-squared = 0.9063
Total | 43687.6444 44 992.90101 Root MSE = 9.6475
------------------------------------------------------------------------------
prestige | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
income | .7834109 .1307364 5.992 0.000 .5182653 1.048557
educ | .3196229 .2797922 1.142 0.261 -.247822 .8870677
d1 | 32.00781 14.10923 2.269 0.029 3.39296 60.62265
d2 | -7.043203 20.63835 -0.341 0.735 -48.89971 34.81331
incd1 | -.3691426 .2038801 -1.811 0.079 -.7826306 .0443455
edud1 | .0185911 .3183687 0.058 0.954 -.6270905 .6642727
incd2 | -.3603084 .2595728 -1.388 0.174 -.8867465 .1661297
edud2 | .1067709 .3621628 0.295 0.770 -.6277293 .8412711
_cons | -3.950543 6.794024 -0.581 0.565 -17.72946 9.828376
------------------------------------------------------------------------------
regress prestige income educ d1 d2 incd1 incd2 edud1 edud2
Source | SS df MS Number of obs = 45
---------+------------------------------ F( 8, 36) = 54.17
Model | 40336.9993 8 5042.12491 Prob > F = 0.0000
Residual | 3350.64519 36 93.0734776 R-squared = 0.9233
---------+------------------------------ Adj R-squared = 0.9063
Total | 43687.6444 44 992.90101 Root MSE = 9.6475
------------------------------------------------------------------------------
prestige | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
income | .7834109 .1307364 5.992 0.000 .5182653 1.048557
educ | .3196229 .2797922 1.142 0.261 -.247822 .8870677
d1 | 32.00781 14.10923 2.269 0.029 3.39296 60.62265
d2 | -7.043203 20.63835 -0.341 0.735 -48.89971 34.81331
incd1 | -.3691426 .2038801 -1.811 0.079 -.7826306 .0443455
incd2 | -.3603084 .2595728 -1.388 0.174 -.8867465 .1661297
edud1 | .0185911 .3183687 0.058 0.954 -.6270905 .6642727
edud2 | .1067709 .3621628 0.295 0.770 -.6277293 .8412711
_cons | -3.950543 6.794024 -0.581 0.565 -17.72946 9.828376
------------------------------------------------------------------------------
testparm edud1 edud2
( 1) edud1 = 0.0
( 2) edud2 = 0.0
F( 2, 36) = 0.06
Prob > F = 0.9399
testparm incd1 incd2
( 1) incd1 = 0.0
( 2) incd2 = 0.0
F( 2, 36) = 2.00
Prob > F = 0.1502
regress prestige income educ d1 d2 edud1 edud2
Source | SS df MS Number of obs = 45
---------+------------------------------ F( 6, 38) = 67.99
Model | 39964.8263 6 6660.80439 Prob > F = 0.0000
Residual | 3722.81811 38 97.9688976 R-squared = 0.9148
---------+------------------------------ Adj R-squared = 0.9013
Total | 43687.6444 44 992.90101 Root MSE = 9.8979
------------------------------------------------------------------------------
prestige | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
income | .5968503 .0939507 6.353 0.000 .406657 .7870436
educ | .4843067 .2743359 1.765 0.086 -.0710574 1.039671
d1 | 26.56871 13.97144 1.902 0.065 -1.714991 54.85241
d2 | -17.30707 17.34143 -0.998 0.325 -52.41295 17.79881
edud1 | -.2172445 .3015031 -0.721 0.476 -.8276055 .3931165
edud2 | -.0384071 .3634739 -0.106 0.916 -.7742216 .6974073
_cons | -3.689497 6.969121 -0.529 0.600 -17.79774 10.41875
------------------------------------------------------------------------------
testparm income
( 1) income = 0.0
F( 1, 38) = 40.36
Prob > F = 0.0000
regress prestige income educ d1 d2 incd1 incd2
Source | SS df MS Number of obs = 45
---------+------------------------------ F( 6, 38) = 75.96
Model | 40325.4393 6 6720.90655 Prob > F = 0.0000
Residual | 3362.20513 38 88.4790824 R-squared = 0.9230
---------+------------------------------ Adj R-squared = 0.9109
Total | 43687.6444 44 992.90101 Root MSE = 9.4063
------------------------------------------------------------------------------
prestige | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
income | .7761539 .1181297 6.570 0.000 .5370128 1.015295
educ | .3572765 .1125671 3.174 0.003 .1293962 .5851567
d1 | 31.71204 10.1657 3.120 0.003 11.13265 52.29142
d2 | -1.637165 13.22173 -0.124 0.902 -28.40317 25.12884
incd1 | -.3697649 .183357 -2.017 0.051 -.7409517 .0014219
incd2 | -.3604304 .2486993 -1.449 0.155 -.8638958 .143035
_cons | -4.731993 4.157457 -1.138 0.262 -13.14832 3.684338
------------------------------------------------------------------------------
test educ
( 1) educ = 0.0
F( 1, 38) = 10.07
Prob > F = 0.0030
regress prestige income educ d1 d2
Source | SS df MS Number of obs = 45
---------+------------------------------ F( 4, 40) = 105.03
Model | 39889.6897 4 9972.42242 Prob > F = 0.0000
Residual | 3797.95474 40 94.9488686 R-squared = 0.9131
---------+------------------------------ Adj R-squared = 0.9044
Total | 43687.6444 44 992.90101 Root MSE = 9.7442
------------------------------------------------------------------------------
prestige | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
income | .5975465 .0893553 6.687 0.000 .4169527 .7781403
educ | .3453193 .1136089 3.040 0.004 .1157071 .5749315
d1 | 16.65751 6.993007 2.382 0.022 2.52412 30.79091
d2 | -14.66113 6.108774 -2.400 0.021 -27.00743 -2.314841
_cons | -.1850278 3.713771 -0.050 0.961 -7.690838 7.320782
------------------------------------------------------------------------------
test d1 d2
( 1) x = 0.0
( 2) x1 = 0.0
F( 2, 40) = 19.53
Prob > F = 0.0000
regress prestige educ income
Source | SS df MS Number of obs = 45
---------+------------------------------ F( 2, 42) = 101.22
Model | 36180.9458 2 18090.4729 Prob > F = 0.0000
Residual | 7506.69865 42 178.73092 R-squared = 0.8282
---------+------------------------------ Adj R-squared = 0.8200
Total | 43687.6444 44 992.90101 Root MSE = 13.369
------------------------------------------------------------------------------
prestige | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
educ | .5458339 .0982526 5.555 0.000 .3475521 .7441158
income | .5987328 .1196673 5.003 0.000 .3572343 .8402313
_cons | -6.064663 4.271941 -1.420 0.163 -14.68579 2.556463
------------------------------------------------------------------------------
regress prestige educ d1 d2 edud1 edud2
Source | SS df MS Number of obs = 45
---------+------------------------------ F( 5, 39) = 36.59
Model | 36010.99 5 7202.198 Prob > F = 0.0000
Residual | 7676.65446 39 196.837294 R-squared = 0.8243
---------+------------------------------ Adj R-squared = 0.8018
Total | 43687.6444 44 992.90101 Root MSE = 14.03
------------------------------------------------------------------------------
prestige | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
educ | 1.011168 .3706646 2.728 0.010 .2614281 1.760908
d1 | 42.66032 19.47572 2.190 0.035 3.26697 82.05367
d2 | 16.21902 23.41483 0.693 0.493 -31.14193 63.57998
edud1 | -.5115146 .4222935 -1.211 0.233 -1.365684 .3426546
edud2 | -.6322738 .4978774 -1.270 0.212 -1.639326 .3747783
_cons | -2.854351 9.876664 -0.289 0.774 -22.83179 17.12309
------------------------------------------------------------------------------
regress prestige income d1 d2 incd1 incd2
Source | SS df MS Number of obs = 45
---------+------------------------------ F( 5, 39) = 72.31
Model | 39434.1346 5 7886.82691 Prob > F = 0.0000
Residual | 4253.50988 39 109.064356 R-squared = 0.9026
---------+------------------------------ Adj R-squared = 0.8902
Total | 43687.6444 44 992.90101 Root MSE = 10.443
------------------------------------------------------------------------------
prestige | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
income | .8450123 .1289228 6.554 0.000 .5842414 1.105783
d1 | 44.48683 10.36413 4.292 0.000 23.52339 65.45027
d2 | 14.85314 13.49857 1.100 0.278 -12.45029 42.15657
incd1 | -.2909451 .2016964 -1.442 0.157 -.6989147 .1170244
incd2 | -.4674322 .2735699 -1.709 0.095 -1.02078 .0859151
_cons | 2.682804 3.81815 0.703 0.486 -5.040133 10.40574
------------------------------------------------------------------------------