Predicted scores are the values predicted from the linear regression model. Predicted scores are often denoted by Y' or Yhat. Residuals scores or just plain residuals for short, are the differences between the observed score and the predicted score. Residuals can be standardized in several different ways, including what are known as Studentized residuals.
Leverage has to do with how extreme scores are on the predictor variable and will be denoted as lev. When an observation has both a large residual and high leverage the observation is said to be influential. Cook's D is one measure of influence of an observation.
Here is how you can obtain predicted scores, residuals, leverage and Cook's D using Stata.
use http://www.philender.com/courses/data/hsbdemo, clear
regress science math
Source | SS df MS Number of obs = 200
-------------+------------------------------ F( 1, 198) = 130.81
Model | 7760.55791 1 7760.55791 Prob > F = 0.0000
Residual | 11746.9421 198 59.3279904 R-squared = 0.3978
-------------+------------------------------ Adj R-squared = 0.3948
Total | 19507.50 199 98.0276382 Root MSE = 7.7025
------------------------------------------------------------------------------
science | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
math | .66658 .0582822 11.44 0.000 .5516466 .7815135
_cons | 16.75789 3.116229 5.38 0.000 10.61264 22.90315
------------------------------------------------------------------------------
generate pre1 = 16.75789 + .66658*math
predict pre2
list pre1 pre2 in 1/20
pre1 pre2
1. 44.08767 44.08768
2. 52.08663 52.08664
3. 52.75321 52.75322
4. 48.08715 48.08715
5. 54.75295 54.75296
6. 50.75347 50.75348
7. 44.75425 44.75426
8. 46.75399 46.75399
9. 52.75321 52.75322
10. 51.42005 51.42006
11. 50.75347 50.75348
12. 50.75347 50.75348
13. 64.08507 64.08508
14. 54.75295 54.75296
15. 50.08689 50.08689
16. 45.42083 45.42084
17. 50.75347 50.75348
18. 56.75269 56.7527
19. 58.08585 58.08586
20. 54.75295 54.75296
corr pre1 pre2
(obs=200)
| pre1 pre2
-------------+------------------
pre1 | 1.0000
pre2 | 1.0000 1.0000
generate res1 = science - pre1
predict res2, resid
list res1 res2 in 1/20
res1 res2
1. 2.912331 2.912324
2. 10.91337 10.91336
3. 5.246792 5.246784
4. 4.912849 4.912844
5. -1.752949 -1.752956
6. 12.24653 12.24652
7. 8.24575 8.245745
8. -7.75399 -7.753996
9. 5.246792 5.246784
10. -1.420052 -1.420056
11. 2.246529 2.246524
12. 12.24653 12.24652
13. -3.085068 -3.085076
14. .2470512 .247044
15. -19.08689 -19.08689
16. 4.57917 4.579165
17. -.7534714 -.7534758
18. 1.247311 1.247304
19. -3.08585 -3.085856
20. -1.752949 -1.752956
predict rsta, rsta
predict rstu, rstu
list res1 res2 rsta rstu in 1/20
res1 res2 rsta rstu
1. 2.912331 2.912324 .3805392 .3797159
2. 10.91337 10.91336 1.420427 1.42411
3. 5.246792 5.246784 .6829278 .6820047
4. 4.912849 4.912844 .640015 .6390582
5. -1.752949 -1.752956 -.2282794 -.2277322
6. 12.24653 12.24652 1.594062 1.600334
7. 8.24575 8.245745 1.076735 1.077171
8. -7.75399 -7.753996 -1.010918 -1.010974
9. 5.246792 5.246784 .6829278 .6820047
10. -1.420052 -1.420056 -.1848286 -.1843772
11. 2.246529 2.246524 .2924176 .2917413
12. 12.24653 12.24652 1.594062 1.600334
13. -3.085068 -3.085076 -.4054857 -.4046285
14. .2470512 .247044 .0321714 .0320901
15. -19.08689 -19.08689 -2.484742 -2.518029
16. 4.57917 4.579165 .5975997 .596627
17. -.7534714 -.7534758 -.0980758 -.0978302
18. 1.247311 1.247304 .1625953 .162195
19. -3.08585 -3.085856 -.4026527 -.4017991
20. -1.752949 -1.752956 -.2282794 -.2277322
corr res1 res2 rsta rstu
(obs=200)
| res1 res2 rsta rstu
-------------+------------------------------------
res1 | 1.0000
res2 | 1.0000 1.0000
rsta | 1.0000 1.0000 1.0000
rstu | 1.0000 1.0000 1.0000 1.0000
predict lev, leverage
predict d, cooksd
sort d
list rsta lev d in -20/l
rsta lev d
181. -1.404299 .0114879 .011459
182. -1.662786 .0083463 .0116353
183. -1.576623 .009279 .0116406
184. 1.42586 .0127641 .013143
185. -2.137993 .0057607 .0132424
186. 2.158743 .0057607 .0135007
187. -1.53488 .0114879 .0136892
188. 2.246003 .0060859 .0154442
189. -2.484742 .0054006 .0167619
190. -1.796041 .0114879 .0187439
191. -1.495091 .0167983 .0190953
192. 2.420326 .0066418 .0195839
193. 1.733267 .01566 .0238973
194. -1.799162 .0152117 .0250004
195. -1.971433 .0127641 .0251248
196. -1.414706 .0264486 .027186
197. -2.620104 .009279 .0321482
198. 2.298569 .0141548 .0379298
199. -2.453299 .0152117 .0464843
200. 3.403156 .022826 .1352672