[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