[Stata Program]
input id stot ntread ntmath ntwrt ntsci
20386 2533.33 2.00 1.00 1.00 3.00
20743 2700.00 1.00 2.00 1.00 3.00
39223 6500.00 3.00 3.00 3.00 3.00
9990 2000.00 2.00 1.00 1.00 2.00
20503 933.33 2.00 1.00 1.00 2.00
7223 4233.33 2.00 1.00 1.00 2.00
5096 2933.33 3.00 3.00 2.00 3.00
999999 . 2.00 3.00 2.00 3.00
50 . 1.00 1.00 1.00 1.00
999998 . 1.00 1.00 1.00 2.00
5920 666.67 1.00 1.00 1.00 2.00
42048 . 3.00 3.00 3.00 3.00
999997 . 1.00 1.00 1.00 2.00
5202 2666.67 3.00 3.00 2.00 3.00
6607 3400.00 3.00 3.00 3.00 3.00
6064 4700.00 3.00 3.00 2.00 3.00
548 566.67 1.00 1.00 1.00 2.00
4676 2600.00 2.00 2.00 2.00 3.00
6754 2466.67 2.00 3.00 2.00 3.00
40759 5066.67 2.00 3.00 3.00 3.00
999996 . 3.00 3.00 3.00 3.00
73 3766.67 2.00 1.00 1.00 2.00
38654 . 2.00 1.00 2.00 2.00
20308 3000.00 2.00 2.00 2.00 3.00
8049 2859.40 1.00 1.00 1.00 1.00
999995 . 2.00 1.00 1.00 2.00
6300 1866.67 1.00 2.00 1.00 2.00
6022 992.73 1.00 2.00 1.00 2.00
3328 1494.55 1.00 2.00 1.00 2.00
6480 3000.00 3.00 3.00 2.00 3.00
69064 . 3.00 3.00 3.00 3.00
5703 3000.00 2.00 1.00 1.00 2.00
999994 . 1.00 1.00 1.00 1.00
end
label variable stot "total standardized test score"
label variable ntread "teacher rating of student in reading"
label variable ntmath "teacher rating of student in math"
label variable ntwrt "teacher rating of student in writing"
label variable ntsci "teacher rating of student in science"
regress stot ntread ntmath ntwrt ntsci
vif
correlate stot ntread ntmath ntwrt ntsci if stot !=.
regress ntread ntmath ntwrt ntsci if stot !=.
regress ntmath ntwrt ntsci ntread if stot !=.
regress ntwrt ntsci ntread ntmath if stot !=.
regress ntsci ntread ntmath ntwrt if stot !=.
sw regress stot ntread ntmath ntwrt ntsci, pe(.05)
generate stotnew=stot
replace stotnew=1300.721*ntwrt + 744.3796 if stot ==.
generate group=2
replace group=1 if stot ==.
ttest stotnew, by(group)
ttest ntread, by(group)
ttest ntmath, by(group)
ttest ntwrt, by(group)
ttest ntsci, by(group)
[Stata Output]
regress stot ntread ntmath ntwrt ntsci
Source | SS df MS Number of obs = 23
-------------+------------------------------ F( 4, 18) = 4.56
Model | 22994242.6 4 5748560.66 Prob > F = 0.0102
Residual | 22679651.4 18 1259980.63 R-squared = 0.5034
-------------+------------------------------ Adj R-squared = 0.3931
Total | 45673894.0 22 2076086.09 Root MSE = 1122.5
------------------------------------------------------------------------------
stot | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ntread | 640.076 455.9313 1.40 0.177 -317.8002 1597.952
ntmath | -346.3548 519.7406 -0.67 0.514 -1438.289 745.5797
ntwrt | 1335.012 650.5975 2.05 0.055 -31.8431 2701.866
ntsci | -276.631 652.4119 -0.42 0.677 -1647.298 1094.036
_cons | 801.5994 1081.488 0.74 0.468 -1470.522 3073.721
------------------------------------------------------------------------------
vif
Variable | VIF 1/VIF
-------------+----------------------
ntwrt | 3.91 0.255465
ntmath | 3.64 0.275077
ntsci | 2.61 0.382497
ntread | 2.14 0.467818
-------------+----------------------
Mean VIF | 3.08
correlate stot ntread ntmath ntwrt ntsci if stot !=.
(obs=23)
| stot ntread ntmath ntwrt ntsci
-------------+---------------------------------------------
stot | 1.0000
ntread | 0.6098 1.0000
ntmath | 0.4655 0.6043 1.0000
ntwrt | 0.6570 0.6971 0.8228 1.0000
ntsci | 0.4321 0.6469 0.7401 0.7142 1.0000
regress ntread ntmath ntwrt ntsci if stot !=.
Source | SS df MS Number of obs = 23
-------------+------------------------------ F( 3, 19) = 7.20
Model | 6.89523278 3 2.29841093 Prob > F = 0.0020
Residual | 6.06128896 19 .319015209 R-squared = 0.5322
-------------+------------------------------ Adj R-squared = 0.4583
Total | 12.9565217 22 .588932806 Root MSE = .56481
------------------------------------------------------------------------------
ntread | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ntmath | -.0497051 .2612746 -0.19 0.851 -.5965592 .4971489
ntwrt | .5419124 .3028424 1.79 0.090 -.091944 1.175769
ntsci | .4165965 .3140605 1.33 0.200 -.2407398 1.073933
_cons | .1731255 .5427322 0.32 0.753 -.9628261 1.309077
------------------------------------------------------------------------------
regress ntmath ntwrt ntsci ntread if stot !=.
Source | SS df MS Number of obs = 23
-------------+------------------------------ F( 3, 19) = 16.69
Model | 12.2921781 3 4.09739271 Prob > F = 0.0000
Residual | 4.6643436 19 .245491768 R-squared = 0.7249
-------------+------------------------------ Adj R-squared = 0.6815
Total | 16.9565217 22 .770750988 Root MSE = .49547
------------------------------------------------------------------------------
ntmath | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ntwrt | .7437601 .2309885 3.22 0.005 .2602957 1.227225
ntsci | .4756888 .2664986 1.78 0.090 -.0820992 1.033477
ntread | -.0382496 .2010586 -0.19 0.851 -.4590702 .382571
_cons | -.3116694 .4719882 -0.66 0.517 -1.299552 .6762132
------------------------------------------------------------------------------
regress ntwrt ntsci ntread ntmath if stot !=.
Source | SS df MS Number of obs = 23
-------------+------------------------------ F( 3, 19) = 18.46
Model | 8.67544657 3 2.89181552 Prob > F = 0.0000
Residual | 2.97672735 19 .15666986 R-squared = 0.7445
-------------+------------------------------ Adj R-squared = 0.7042
Total | 11.6521739 22 .529644269 Root MSE = .39582
------------------------------------------------------------------------------
ntwrt | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ntsci | .1336367 .2280035 0.59 0.565 -.3435801 .6108536
ntread | .2661357 .1487273 1.79 0.090 -.0451541 .5774255
ntmath | .4746587 .147414 3.22 0.005 .1661176 .7831998
_cons | -.2153496 .378144 -0.57 0.576 -1.006814 .5761148
------------------------------------------------------------------------------
regress ntsci ntread ntmath ntwrt if stot !=.
Source | SS df MS Number of obs = 23
-------------+------------------------------ F( 3, 19) = 10.22
Model | 4.77893706 3 1.59297902 Prob > F = 0.0003
Residual | 2.96019338 19 .155799651 R-squared = 0.6175
-------------+------------------------------ Adj R-squared = 0.5571
Total | 7.73913043 22 .351778656 Root MSE = .39471
------------------------------------------------------------------------------
ntsci | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ntread | .2034561 .1533799 1.33 0.200 -.1175717 .5244839
ntmath | .3018926 .1691315 1.78 0.090 -.0521037 .6558889
ntwrt | .1328945 .2267371 0.59 0.565 -.3416718 .6074607
_cons | 1.281526 .2412229 5.31 0.000 .7766411 1.786412
------------------------------------------------------------------------------
collin ntread ntmath ntwrt ntsci if stot!=. /* user written program: findit collin */
Collinearity Diagnostics
SQRT Cond R-
Variable VIF VIF Tolerance Eigenval Index Squared
------------------------------------------------------------------------
ntread 2.14 1.46 0.4678 3.1168 1.0000 0.5322
ntmath 3.64 1.91 0.2751 0.4202 2.7235 0.7249
ntwrt 3.91 1.98 0.2555 0.3048 3.1979 0.7445
ntsci 2.61 1.62 0.3825 0.1582 4.4382 0.6175
------------------------------------------------------------------------
Mean VIF 3.08 Condition Number 4.4382
Determinant of correlation matrix 0.0632
sw regress stot ntread ntmath ntwrt ntsci, pe(.05)
begin with empty model
p = 0.0007 < 0.0500 adding ntwrt
Source | SS df MS Number of obs = 23
-------------+------------------------------ F( 1, 21) = 15.95
Model | 19714026.3 1 19714026.3 Prob > F = 0.0007
Residual | 25959867.7 21 1236184.18 R-squared = 0.4316
-------------+------------------------------ Adj R-squared = 0.4046
Total | 45673894.0 22 2076086.09 Root MSE = 1111.8
------------------------------------------------------------------------------
stot | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ntwrt | 1300.721 325.7153 3.99 0.001 623.3591 1978.083
_cons | 744.3796 560.0524 1.33 0.198 -420.3131 1909.072
------------------------------------------------------------------------------
generate stotnew=stot
replace stotnew=1300.721*ntwrt + 744.3796 if stot ==.
generate group=2
replace group=1 if stot ==.
ttest stotnew, by(group)
Two-sample t test with equal variances
------------------------------------------------------------------------------
Group | Obs Mean Std. Err. Std. Dev. [95% Conf. Interval]
---------+--------------------------------------------------------------------
1 | 10 3085.677 377.9807 1195.28 2230.625 3940.729
2 | 23 2780.291 300.4407 1440.863 2157.215 3403.367
---------+--------------------------------------------------------------------
combined | 33 2872.832 236.7355 1359.942 2390.618 3355.047
---------+--------------------------------------------------------------------
diff | 305.3865 520.4864 -756.1526 1366.926
------------------------------------------------------------------------------
Degrees of freedom: 31
Ho: mean(1) - mean(2) = diff = 0
Ha: diff < 0 Ha: diff ~= 0 Ha: diff > 0
t = 0.5867 t = 0.5867 t = 0.5867
P < t = 0.7192 P > |t| = 0.5616 P > t = 0.2808
ttest ntread, by(group)
Two-sample t test with equal variances
------------------------------------------------------------------------------
Group | Obs Mean Std. Err. Std. Dev. [95% Conf. Interval]
---------+--------------------------------------------------------------------
1 | 10 1.9 .2768875 .875595 1.273637 2.526363
2 | 23 1.956522 .160018 .7674196 1.624665 2.288379
---------+--------------------------------------------------------------------
combined | 33 1.939394 .1372028 .7881701 1.659921 2.218867
---------+--------------------------------------------------------------------
diff | -.0565217 .3031543 -.6748091 .5617656
------------------------------------------------------------------------------
Degrees of freedom: 31
Ho: mean(1) - mean(2) = diff = 0
Ha: diff < 0 Ha: diff ~= 0 Ha: diff > 0
t = -0.1864 t = -0.1864 t = -0.1864
P < t = 0.4267 P > |t| = 0.8533 P > t = 0.5733
ttest ntmath, by(group)
Two-sample t test with equal variances
------------------------------------------------------------------------------
Group | Obs Mean Std. Err. Std. Dev. [95% Conf. Interval]
---------+--------------------------------------------------------------------
1 | 10 1.8 .3265986 1.032796 1.061183 2.538817
2 | 23 1.956522 .1830599 .8779242 1.576879 2.336165
---------+--------------------------------------------------------------------
combined | 33 1.909091 .1590909 .9139077 1.585033 2.233148
---------+--------------------------------------------------------------------
diff | -.1565217 .3505886 -.8715519 .5585084
------------------------------------------------------------------------------
Degrees of freedom: 31
Ho: mean(1) - mean(2) = diff = 0
Ha: diff < 0 Ha: diff ~= 0 Ha: diff > 0
t = -0.4465 t = -0.4465 t = -0.4465
P < t = 0.3292 P > |t| = 0.6584 P > t = 0.6708
ttest ntwrt, by(group)
Two-sample t test with equal variances
------------------------------------------------------------------------------
Group | Obs Mean Std. Err. Std. Dev. [95% Conf. Interval]
---------+--------------------------------------------------------------------
1 | 10 1.8 .2905933 .9189366 1.142632 2.457368
2 | 23 1.565217 .1517498 .7277666 1.250508 1.879927
---------+--------------------------------------------------------------------
combined | 33 1.636364 .1363636 .7833495 1.3586 1.914127
---------+--------------------------------------------------------------------
diff | .2347826 .2985053 -.374023 .8435882
------------------------------------------------------------------------------
Degrees of freedom: 31
Ho: mean(1) - mean(2) = diff = 0
Ha: diff < 0 Ha: diff ~= 0 Ha: diff > 0
t = 0.7865 t = 0.7865 t = 0.7865
P < t = 0.7812 P > |t| = 0.4375 P > t = 0.2188
ttest ntsci, by(group)
Two-sample t test with equal variances
------------------------------------------------------------------------------
Group | Obs Mean Std. Err. Std. Dev. [95% Conf. Interval]
---------+--------------------------------------------------------------------
1 | 10 2.2 .2494438 .7888106 1.635719 2.764281
2 | 23 2.478261 .1236718 .5931093 2.221781 2.734741
---------+--------------------------------------------------------------------
combined | 33 2.393939 .114642 .6585682 2.160421 2.627458
---------+--------------------------------------------------------------------
diff | -.2782609 .2484711 -.7850211 .2284994
------------------------------------------------------------------------------
Degrees of freedom: 31
Ho: mean(1) - mean(2) = diff = 0
Ha: diff < 0 Ha: diff ~= 0 Ha: diff > 0
t = -1.1199 t = -1.1199 t = -1.1199
P < t = 0.1357 P > |t| = 0.2714 P > t = 0.8643