View the step-by-step solution to:

Assignment 2: The data set provided below is 1,000 observations for the model Y=alpha+beta X + epsilon. Population parameters are alpha= 1 and beta...

Assignment 2:

The data set provided below is 1,000 observations for the model

Y=alpha+beta X + epsilon.

Population parameters are alpha= 1 and beta =5. Epsilon is distributed normal with zero mean and unitary variance.

1- Split the data into sizes of 5 observations (first 5 observations of (Y,X), next 5 observations of (Y,X), etc.) for a total of 200 different data sets. Calculate the beta hat of these data sets and plot their sampling distribution. Is your estimator biased/unbiased? Calculate the degree of bias by bias = average (beta hats) - beta. What is the mean squared error (MSE)? Calculate the MSE by MSE = var(beta hat) + bias squared (beta hat).

2- Repeat Question (1) by splitting the data into sizes of 20 observations for a total of 50 different data sets.

3- Repeat Question (1) by splitting the data into sizes of 40 observations for a total of 25 different data sets.

4- Repeat Question (1) by splitting the data into sizes of 50 observations for a total of 20 different data sets.

5- Illustrate consistency of beta hat by using your results from (1)-(4) graphically.


You can use Eviews, Stata, Excel or R as software.

The data set is:
Y X
1 2.758351791 -0.04503362
2 2.989603935 0.386025168
3 0.328154451 0.089103784
4 1.236011346 -0.070756065
5 0.70614413 0.249995487
6 -5.77302486 -1.158440409
7 0.896364614 -0.175224152
8 5.524250448 0.989686873
9 9.427908989 1.511941041
10 0.478388708 -0.355520185
11 -2.043636659 -0.369636406
12 6.34462259 1.023429461
13 5.199586138 0.747320217
14 -0.635408807 -0.028578803
15 -4.55264254 -0.843659328
16 5.607798618 1.002961387
17 -1.221680786 -0.531740202
18 -1.587406544 -0.702913944
19 -0.67433359 0.209221816
20 5.524367722 0.759335153
21 1.368280511 0.499685161
22 -6.137309765 -1.282761277
23 8.226436037 1.389327918
24 1.225705458 -0.021933952
25 4.52820334 0.610716998
26 1.886340895 0.298202312
27 -1.815201828 -0.405343775
28 2.695558863 0.17188337
29 -2.696328153 -1.011758419
30 -1.332321159 0.069315382
31 3.208899051 0.452837469
32 7.719018768 1.638555881
33 -0.136696719 -0.00568255
34 5.491174481 0.754087898
35 -2.300798983 -0.516327104
36 -4.114632414 -0.989074248
37 9.805014768 2.020744832
38 -2.64311066 -0.78140069
39 0.475005352 -0.007845276
40 -0.531994471 -0.176800688
41 0.430584625 -0.196977711
42 2.841669546 0.3430673
43 -6.20378778 -1.481843628
44 5.400712585 0.935459527
45 8.273240308 1.577114675
46 5.152835705 0.737552641
47 2.5149777 0.204068409
48 -5.292475762 -1.508702095
49 -0.606803808 -0.258586646
50 -6.504677648 -1.331016503
51 -7.291944316 -1.30385121
52 0.855845633 -0.206664032
53 -1.468494883 -0.368143027
54 -8.337786796 -1.930443731
55 -0.522115992 -0.011932002
56 -8.642389621 -1.540541664
57 -6.333547999 -1.42271834
58 2.971751272 0.275321298
59 2.594482124 0.420151423
60 -3.914816164 -0.774251434
61 -0.998750484 -0.550675846
62 3.704585988 0.619793435
63 -5.114613761 -1.167025311
64 1.779424011 -0.059656692
65 -3.609538015 -0.618354692
66 6.03417676 0.963281553
67 1.705061291 -0.280059326
68 -2.123614238 -0.445920109
69 9.227468837 1.335250978
70 -4.754896068 -1.185515575
71 11.57545153 2.007716182
72 -5.996729463 -1.497422091
73 -0.88663667 -0.518808284
74 2.588198529 0.332996539
75 -4.019536646 -0.793729955
76 3.789116183 0.26823511
77 -2.498337427 -0.371880201
78 4.537296328 0.600219952
79 0.373843207 0.475876422
80 3.739742198 0.410618148
81 -6.509381507 -1.655317456
82 4.105221942 0.707374695
83 9.312276123 1.539508889
84 4.631133399 0.81666181
85 -1.089274796 -0.729970947
86 0.036577543 -0.08490438
87 4.926408029 0.602133728
88 7.734861054 1.3693882
89 2.315687048 -0.038274422
90 4.629202297 0.601132083
91 -0.093334091 -0.200978301
92 9.756232603 1.64666689
93 3.157413324 0.415388174
94 -6.551461575 -1.588290433
95 2.762789018 0.239675753
96 -4.542797872 -1.157628132
97 -3.433545248 -0.816915972
98 3.114939855 0.331863869
99 1.271520613 -0.223315511
100 1.035184192 0.295019249
101 -3.239847623 -0.833157509
102 2.953359102 0.686678516
103 -3.974203967 -0.818637023
104 3.274946718 0.21340772
105 11.24255522 1.84905405
106 2.517881778 0.668626496
107 1.168120308 0.250655454
108 -4.184840199 -0.660668883
109 7.866459325 0.840728952
110 1.413492864 -0.205893834
111 -4.148789603 -0.917354939
112 8.97108865 1.674007172
113 -2.807948358 -0.701769935
114 10.45190647 1.820516273
115 2.550515066 0.250436621
116 2.420129823 0.211691872
117 5.609183362 0.672593846
118 9.324388657 1.467100111
119 10.04238579 1.502089652
120 -2.87748076 -0.979444391
121 -2.102366686 -0.425856111
122 -6.745249786 -1.263712577
123 -6.283830118 -1.23435917
124 6.57912392 0.919757226
125 -2.527946543 -0.813563895
126 -2.450896757 -0.65533203
127 3.864304792 0.750740098
128 1.70928125 0.74357473
129 1.035235301 0.279786194
130 -2.952952344 -0.939270957
131 4.130007373 0.486400559
132 -6.624782307 -1.596474646
133 -2.188084423 -0.586813073
134 1.620199637 -0.159283013
135 9.569336496 1.730149902
136 2.407856948 0.663269874
137 0.29641319 -0.133455557
138 -5.623895654 -1.01921893
139 9.004296803 1.343958382
140 2.036798476 0.035087966
141 -2.585246022 -0.578084295
142 -0.428359974 -0.547223408
143 2.786445974 0.143931345
144 -3.795991802 -0.983475185
145 2.965902034 0.423698355
146 4.734469515 0.961722589
147 -2.311765905 -0.738879711
148 9.882638513 1.788142315
149 -1.577026927 -0.337164666
150 8.435721224 1.517619065
151 2.227679754 0.557949908
152 12.85962555 2.132302397
153 -4.426832362 -0.99812458
154 -5.214113568 -0.825094607
155 -2.667397357 -0.722869081
156 0.508073741 -0.200366288
157 3.916947419 0.660296352
158 -7.268289188 -1.830444983
159 -0.07938065 -0.233825129
160 4.594128477 0.801479462
161 6.091295097 0.63857266
162 -7.103377054 -1.258543598
163 1.399475832 0.355445291
164 -1.267150859 -0.353860915
165 5.057420899 0.79606668
166 -5.855320333 -1.292347419
167 6.692836886 0.806741017
168 15.83311458 2.528909181
169 2.319799073 0.320816297
170 -5.868213472 -0.814706995
171 5.00966873 0.963943725
172 1.191328739 0.25065598
173 6.83850887 1.550629148
174 5.847756644 0.886090212
175 4.731238541 0.456325693
176 -4.432076005 -0.906320535
177 18.7761436 3.376813285
178 4.549845071 0.579168989
179 -2.830415085 -0.497573582
180 3.046386572 0.482057898
181 1.347322551 0.171011107
182 1.175142268 -0.006762805
183 6.585700251 1.046350947
184 8.39063359 1.555911337
185 5.104387702 0.57752591
186 -0.017103757 -0.440600115
187 1.883911331 -0.143271722
188 -1.153908989 -0.600088308
189 5.626055689 0.481409803
190 -2.187311398 -0.573778965
191 -12.00832378 -2.419587119
192 -10.74857415 -2.050546547
193 -1.086004092 -0.698312388
194 9.821157208 1.967063166
195 1.050041999 -0.031663975
196 13.09557939 2.319781539
197 8.888420727 1.492371533
198 3.760582232 0.627931925
199 -3.2212331 -0.355469822
200 6.467308829 1.207431802
201 1.913561113 -0.003128137
202 9.846184712 1.83368799
203 -3.409886405 -0.8405283
204 6.314868766 0.896168186
205 -1.551177642 -0.840575956
206 5.313833838 0.666445143
207 6.671803679 1.116862726
208 -6.68954604 -1.321012936
209 2.057481067 0.523197945
210 9.490429649 1.635016955
211 5.206002254 0.650801194
212 1.807213964 0.126371701
213 4.535390467 0.59049563
214 0.415484197 -0.167227372
215 2.265168051 0.849938391
216 -0.525541339 -0.121243719
217 3.643998307 0.566295407
218 1.991879709 0.498638756
219 -2.667544855 -0.644279923
220 9.443771672 1.763745929
221 -5.335105835 -1.337264869
222 -0.337239931 -0.124472198
223 -11.69193726 -2.385055242
224 7.255373846 0.796791632
225 2.510230707 0.71550936
226 0.157656942 -0.159523112
227 -2.67216543 -0.822567015
228 11.48222177 2.39110818
229 0.590315351 -0.381253319
230 0.08858587 -0.478331414
231 4.365912935 0.638090604
232 3.069181869 0.298918991
233 4.946010519 0.999487212
234 9.974736636 1.50832893
235 9.12977428 1.507009089
236 1.497371301 0.20764315
237 -2.130948223 -0.647995964
238 -2.997393006 -0.986777218
239 4.07174899 0.560837249
240 2.387054736 0.213953801
241 8.041183291 1.370469037
242 -7.892995053 -1.778969667
243 5.822606382 1.31402472
244 3.655144085 0.547027794
245 8.103912661 1.164445808
246 -6.703045819 -1.549243844
247 0.37052845 -0.355219668
248 -0.961637432 -0.571221415
249 0.663572653 -0.067760919
250 2.087729133 -0.143150539
251 -4.282696105 -1.069300311
252 -0.21078785 0.187847194
253 2.851732144 0.431620291
254 -1.972994464 -0.530272079
255 5.496630271 0.915050098
256 3.664471053 0.456683723
257 7.234830752 0.853849176
258 8.024081353 1.561870555
259 -0.796438395 -0.394397732
260 -6.409268116 -1.350235334
261 0.880822131 0.391797751
262 -2.982957417 -0.732416199
263 0.138379571 -0.259792859
264 -5.725530603 -1.253006217
265 -1.380051702 -0.505339239
266 2.376162564 0.219432484
267 0.815546454 0.01275093
268 1.090981274 -0.13437507
269 -5.941027937 -1.216069271
270 9.227700148 2.010534513
271 -2.762055325 -0.862662205
272 -6.117565795 -1.503258029
273 2.313049662 0.18542839
274 0.519763879 -0.130084909
275 2.14840181 -0.081293014
276 -7.439697549 -2.055343758
277 7.88378432 1.590370027
278 -3.446329854 -0.913347973
279 -0.595281883 -0.531628483
280 -3.701952191 -1.131314062
281 -8.56811936 -2.01013777
282 6.273294118 0.84058758
283 4.777473452 0.746274952
284 -6.665345437 -1.215717926
285 -7.943292288 -1.676582069
286 4.825010059 0.69799211
287 3.029467789 0.512301165
288 3.300580086 -0.061502023
289 -5.668126422 -1.589512539
290 -0.857101472 -0.119647741
291 0.728518724 -0.156370674
292 2.016800328 0.183600922
293 -2.11621188 -0.782775181
294 -4.869030007 -1.375344556
295 -2.072369692 -0.547296706
296 -5.045271094 -1.087881835
297 4.076024109 0.502715184
298 -2.518695516 -0.538874331
299 -5.336847493 -1.414258502
300 -0.18869808 -0.382357794
301 2.45987413 0.703428617
302 0.060756216 -0.216904092
303 -5.305711403 -1.184542765
304 -2.273630776 -0.808757938
305 10.23318706 1.644556254
306 6.424704068 0.873097883
307 -7.584711112 -1.493391578
308 1.61436997 -0.042703051
309 0.679639433 -0.01345257
310 -4.637985882 -1.167565217
311 -0.692295511 -0.516412271
312 -6.101933708 -1.062302915
313 12.58309192 2.270620698
314 -6.931473373 -1.420738741
315 1.564191371 -0.168930958
316 3.985357954 0.240475527
317 -4.395785918 -1.10863474
318 -3.547046529 -0.668647617
319 13.18807932 2.196592711
320 -3.378083786 -0.855443574
321 -4.734485935 -1.004339533
322 4.292571059 0.527045684
323 -1.190722954 -0.518190994
324 8.83470896 1.354165862
325 3.44250918 0.554463885
326 2.710051214 0.070567841
327 3.943786433 0.614515105
328 8.343671587 1.187218027
329 -0.019962222 -0.344456025
330 -4.180105888 -0.607273348
331 2.96287149 0.117379522
332 2.783602656 0.157391999
333 8.015941868 2.014288799
334 6.183484119 0.964826571
335 2.601400456 0.469995363
336 -5.316766746 -1.142027184
337 1.732837402 0.258454123
338 5.101802151 0.463542749
339 8.405104993 1.661277973
340 -2.678362343 -0.642212909
341 3.447825816 0.225628481
342 6.09550699 0.745729951
343 2.907251531 0.350234234
344 -6.195790723 -1.390964266
345 2.000156384 0.077719908
346 2.625616974 -0.037015053
347 -5.728252637 -1.15577657
348 -0.604000076 0.083819822
349 -1.94799658 -0.725480519
350 -0.95454295 -0.906971328
351 -1.410913716 -0.442134434
352 9.946313713 2.017239303
353 1.585912221 0.174552201
354 3.507394209 0.381023137
355 -1.089329586 -0.519737575
356 -4.557853384 -1.197947979
357 -1.550671543 -0.277201102
358 -2.942440762 -0.91601926
359 3.930819751 0.699184771
360 0.390738738 -0.04722079
361 3.694210096 0.254418037
362 9.770440839 1.746364533
363 1.1976582 0.097067496
364 0.191930745 -0.099954046
365 -8.116775571 -1.800030708
366 5.915194727 0.858137259
367 13.69155931 2.187824111
368 -5.354789687 -1.143306507
369 4.001331321 0.92181864
370 4.121269637 0.572729509
371 4.617714783 0.873491512
372 0.091715279 -0.093518965
373 3.595836267 0.785099609
374 0.078967366 -0.100071772
375 11.33950995 2.266425569
376 -0.510327907 -0.317635823
377 8.259003115 1.453761824
378 -1.07760477 -0.062666238
379 3.120128572 0.353311937
380 -2.656109063 -0.533371277
381 2.127157589 -0.080546068
382 5.177645933 0.522226568
383 -1.179022593 -0.34244083
384 -3.388705763 -0.816792013
385 -1.34769905 -0.415370897
386 10.68295677 2.018813054
387 3.014664199 0.210049842
388 -2.839725124 -1.138815584
389 -1.162565857 -0.372340647
390 4.81110165 0.924823097
391 4.105840794 0.596646394
392 -3.527897922 -0.824945973
393 4.556611698 0.889220482
394 8.464980122 1.844947169
395 3.691557212 0.290882125
396 7.454145823 1.460126474
397 1.16807286 -0.020758539
398 5.517524673 0.787858578
399 0.218993058 -0.328173486
400 15.0685077 2.643696869
401 0.332597812 0.057248615
402 5.760635926 1.122999578
403 3.701833621 0.332168531
404 4.769371874 0.94471031
405 9.938961539 1.818986777
406 -2.063600637 -0.786094941
407 -5.488014736 -1.337201259
408 3.804186364 0.707301162
409 0.142084593 -0.312254815
410 8.394761034 0.957272638
411 2.875329266 0.289333831
412 7.753421788 1.385570834
413 -4.046821098 -0.881446502
414 11.14300893 1.804946866
415 -0.877411699 -0.482395473
416 -5.182363253 -1.011875974
417 3.030251081 0.240814793
418 -2.103976409 -0.139286879
419 1.406889247 0.202631147
420 -1.621182478 -0.542707073
421 5.296060045 0.828231645
422 4.200312765 0.320696094
423 -1.93399182 -0.479363173
424 10.56153038 1.70304687
425 2.04777904 -0.299492237
426 8.840936965 1.581961676
427 6.59271924 1.370935714
428 0.9976196 0.28204182
429 2.225031498 0.611112208
430 7.240911105 1.281140912
431 -0.102188235 -0.138745897
432 1.792724062 0.289229146
433 3.892888947 0.565735552
434 9.191110807 1.93027481
435 -0.8141715 -0.317422959
436 7.588692581 1.124092182
437 12.7067882 2.280395086
438 -9.774964176 -2.116093005
439 3.657632259 0.639650807
440 -2.140832931 -0.757305066
441 -4.624105688 -1.190918397
442 2.333039181 -0.11650463
443 -2.446258918 -0.61592487
444 8.959740994 1.643710194
445 6.450686685 1.22489216
446 0.454846406 -0.015535889
447 4.035097192 0.814066817
448 2.247953873 0.43962549
449 9.980248922 1.590118454
450 -0.24096696 -0.381955809
451 13.82420478 2.380678055
452 2.036000083 0.081306546
453 -6.266594269 -1.404268054
454 3.187551558 0.254316422
455 -4.821601315 -1.680137992
456 -3.023594398 -0.623821545
457 0.386552745 -0.119431359
458 5.934795316 0.901149968
459 5.649810618 0.922915491
460 5.833330982 0.835418889
461 4.158657912 0.657117749
462 5.38118029 0.659575986
463 -0.027339015 -0.35042312
464 -0.042329635 -0.152510695
465 -3.920577587 -1.014496468
466 -3.419503053 -1.192090695
467 3.972260631 0.73889063
468 11.9029694 2.027990062
469 -5.793154583 -0.997436598
470 -1.638349294 -0.475678048
471 3.095511301 0.313981069
472 -4.307807871 -0.986883975
473 -5.380365447 -1.2884413
474 -5.762606349 -1.313958332
475 8.084442497 1.476890836
476 3.318134192 0.288597316
477 -5.98151205 -1.437391748
478 2.948522079 0.570161778
479 -4.814891961 -1.082798603
480 -2.804000192 -0.430424968
481 -0.945269036 -0.172796878
482 4.325954315 0.409972234
483 1.575372599 0.344268451
484 2.066564067 0.101293827
485 3.311851143 0.175519981
486 -4.266989165 -1.104335695
487 -2.920460371 -0.628684457
488 5.931108226 1.170177467
489 6.143835009 0.904296846
490 8.374874944 1.71128491
491 2.220562883 0.511849
492 0.230892236 -0.11391603
493 -3.813314793 -0.415583056
494 1.201880179 0.435062659
495 -2.818692093 -0.698489157
496 1.681736444 0.213654329
497 3.232667816 0.733092214
498 4.413576232 0.757083868
499 3.872985313 0.798627026
500 1.399808299 -0.055603302
501 -5.103410777 -1.219551257
502 -5.927839602 -1.201460177
503 -1.601231721 -0.496042549
504 -0.78125444 0.066931117
505 -0.283096059 -0.056949136
506 2.912021255 0.255580167
507 3.159908599 0.397590951
508 2.483120858 0.654840094
509 -4.204927689 -0.615050072
510 -1.169782917 0.006746079
511 -5.042506601 -1.351483389
512 11.09725265 2.293831778
513 0.732911973 -0.240718941
514 4.878814662 0.955598912
515 3.516567591 0.668960834
516 4.55518331 0.725985754
517 -4.535399761 -1.016158285
518 -9.76815045 -1.973862332
519 -7.612800688 -1.445192592
520 2.190166628 0.400545595
521 6.262512632 0.950350416
522 -6.071172681 -1.474604731
523 -2.287922873 -0.394849116
524 3.495397068 0.620601636
525 4.740404712 0.806497046
526 1.122149388 -0.105204922
527 3.224349166 0.280470195
528 6.863697943 1.330048807
529 4.814074521 0.731341065
530 4.685869161 0.739110565
531 1.563734957 -0.310764099
532 -3.648593289 -0.827693414
533 -1.118717791 -0.768108848
534 -0.869165693 -0.346077845
535 4.631714284 0.230186825
536 -5.09167449 -0.909285763
537 -3.490702436 -0.843514221
538 -1.579117379 -0.720152104
539 -1.960164621 -0.462759757
540 -3.934967337 -1.204934867
541 -3.344797709 -0.680895765
542 4.868423075 0.414348868
543 -4.250612271 -1.276476389
544 -6.343976358 -1.208093448
545 0.066340227 -0.056615765
546 3.783552571 0.502913536
547 -0.544066841 -0.642505995
548 4.081275346 0.598720587
549 -4.417549524 -1.248087197
550 -2.690729538 -0.880170072
551 -0.477250015 -0.397558024
552 3.002921328 0.545573021
553 8.55503861 1.314969975
554 -0.335650762 -0.541332615
555 -3.354231645 -0.419980669
556 -4.628720393 -1.124695684
557 -1.773687694 -0.703949258
558 7.810518566 1.209792728
559 3.732677423 0.674259895
560 3.193269353 0.4248916
561 -1.692512421 -0.264092817
562 7.629377389 1.167984553
563 -1.422996153 -0.674814871
564 0.308929463 0.065013517
565 5.046441101 0.339960618
566 0.432603894 -0.034196495
567 -0.688922737 -0.137618639
568 4.133747634 0.394433176
569 -7.003995313 -1.312866775
570 -7.431892261 -1.770766293
571 -2.784124688 -0.346905744
572 -2.018836568 -0.435093865
573 2.570058299 0.269771569
574 12.40679944 2.289700907
575 -2.412503942 -0.950282031
576 5.14722717 0.603429445
577 -0.224910576 -0.154289957
578 2.602088209 0.205370921
579 -13.59816304 -2.94200447
580 -2.215008741 -0.933470319
581 2.87014802 0.12820534
582 1.632690081 0.532200207
583 -2.934249684 -0.960479635
584 -5.027096346 -0.97384111
585 -2.607953911 -0.625750189
586 1.302341233 0.533560792
587 -7.282295055 -1.482301312
588 -6.54361176 -1.585348097
589 8.868314643 1.579502075
590 -0.02906323 -0.522371272
591 3.018826173 0.318323273
592 -1.619698998 -0.659882378
593 -2.312130901 -0.685785961
594 6.263683726 1.329639806
595 5.492741733 0.897015789
596 -2.408032883 -0.575109163
597 -1.657141948 -0.544010007
598 3.422546716 0.347653355
599 -3.33138919 -0.803198741
600 1.583070155 0.359636809
601 4.587579618 0.652290926
602 -8.507933114 -1.886787036
603 -10.61003133 -2.471974979
604 -8.508045779 -1.451799862
605 5.249941647 0.687308833
606 -0.331070844 -0.384837129
607 3.933842386 0.964536104
608 -4.047701457 -1.318073861
609 1.465172155 -0.11791362
610 -0.965606738 -0.462356271
611 2.213848017 0.492608562
612 -2.728189085 -0.828437633
613 3.069895153 0.514198065
614 1.998763706 0.623513515
615 4.268509186 0.800243653
616 11.10664066 1.865479306
617 -2.074481097 -0.746781439
618 0.231500205 -0.072657737
619 13.48895457 2.070892579
620 0.902518866 -0.042095103
621 -7.961533835 -2.175602652
622 -0.530105231 -0.218167824
623 9.540333973 1.98788444
624 -10.52197253 -1.966727552
625 -4.952538666 -0.981627633
626 -5.288413344 -0.797318928
627 -4.115289701 -1.069256615
628 0.843331175 -0.046472372
629 -0.172060324 -0.412198372
630 6.695986924 1.24028689
631 6.979265411 1.26102775
632 -8.199731827 -1.545425234
633 1.784792503 -0.048046801
634 -6.386167693 -1.470428004
635 -3.112207322 -0.854539554
636 3.153603253 0.775701476
637 -2.236663693 -0.088639263
638 2.898284985 0.271159494
639 -0.417470053 -0.391452881
640 -7.046227663 -1.692621536
641 -4.69798154 -1.033550108
642 0.963822382 0.087572142
643 2.425812415 -0.024845792
644 6.257400135 1.122861546
645 2.318025042 0.366048184
646 0.930208063 -0.119342683
647 -1.207025991 -0.679787756
648 0.80706757 0.01051387
649 3.080190974 0.255103183
650 -3.194390088 -0.717945387
651 -0.106809262 -0.420854203
652 4.000473724 0.870379508
653 -2.999044222 -1.045352976
654 1.557415477 0.170607671
655 6.214160821 1.015779759
656 1.04124421 -0.174654458
657 -0.267927771 -0.125136828
658 3.792879501 0.5368738
659 0.740394291 0.084243094
660 -0.994571491 -0.537670596
661 -3.093728437 -1.12854466
662 0.381342281 0.000104012
663 -2.637945205 -0.45205534
664 0.793713268 -0.00927198
665 -2.497123968 -0.677502731
666 2.720661593 0.135104879
667 -1.912811535 -0.571987342
668 4.852336614 0.73100002
669 5.974107062 1.013644306
670 -3.531778591 -0.957708537
671 7.852045984 1.380803646
672 3.307508711 0.662484837
673 4.969946752 0.531934492
674 -7.522610099 -1.819628947
675 7.446209161 1.318304463
676 1.394846202 0.052241857
677 5.429271113 0.946503396
678 -5.662247993 -1.320887101
679 -4.736967824 -1.146233253
680 3.590409055 0.775484432
681 4.553689063 0.840620902
682 0.721943795 0.092646646
683 12.32623611 2.129176432
684 8.070547328 1.360718608
685 -4.878154858 -0.79269156
686 5.853839028 1.182341617
687 0.641133287 0.469691177
688 7.230951701 1.518307173
689 0.115976849 -0.342760514
690 2.158693635 -0.056809339
691 -6.05405607 -1.181016258
692 -10.39206367 -2.161399685
693 5.853306939 1.08158371
694 7.450902992 1.200154374
695 1.039119595 0.078664787
696 3.07346022 0.327030618
697 -0.796392025 -0.262362514
698 -4.330571321 -1.230891499
699 2.171675433 0.386197199
700 3.056942281 0.378094213
701 -0.815393717 -0.566701742
702 -4.157115314 -1.003863558
703 0.175774534 -0.285390013
704 -0.563936426 -0.376261813
705 -1.311468223 -0.35689628
706 0.893438114 -0.013850004
707 7.180376814 1.166126088
708 0.911302086 -0.081219251
709 1.562921739 -0.23986166
710 -5.21194366 -1.223201625
711 8.982013937 1.693796145
712 3.269160056 0.465063574
713 6.269000286 1.233304414
714 2.856646936 0.383182423
715 1.201664898 -0.183016837
716 0.892977529 0.047458852
717 -3.270761515 -0.902813365
718 7.112495033 1.196225982
719 -7.178270084 -1.567561132
720 3.592056752 0.488524174
721 3.791092515 0.087471576
722 1.228450402 0.141437346
723 -5.052069969 -1.091994108
724 -1.521298203 -0.509026945
725 0.295130766 -0.136164334
726 4.939716953 0.842378851
727 0.245967171 -0.240400901
728 5.384982281 0.61198723
729 3.1929949 0.631582505
730 -0.96384538 -0.513028803
731 -9.136525687 -2.074588116
732 6.895458092 0.97695423
733 4.673045867 0.975102015
734 1.479905239 0.145001722
735 0.800480151 0.169742492
736 -1.820763931 -0.670030229
737 -1.937398233 -0.497263062
738 8.019526219 1.497383984
739 -1.362539618 -0.510163192
740 5.645365782 0.56018223
741 2.327854256 0.541995595
742 6.043451047 0.976833
743 5.292102968 0.89890863
744 1.362275881 0.180609303
745 2.792776867 -0.053300062
746 1.953754854 0.408173312
747 1.167334077 0.152696958
748 0.950520056 -0.059028105
749 9.941867711 2.168593769
750 9.539880729 1.52162992
751 -6.151943845 -1.226488157
752 2.012943536 0.2813383
753 2.694397366 0.481071062
754 4.560573333 0.647909785
755 0.008040779 -0.263983442
756 -3.340311664 -1.165045954
757 5.007685848 0.910287319
758 10.15620506 1.519682215
759 7.784947557 1.431208273
760 -7.893526713 -1.276414988
761 -2.141489969 -0.497941584
762 6.293586236 1.415318894
763 -4.178709184 -1.105338854
764 7.527088112 1.383228041
765 4.493339615 0.583449607
766 -2.882802482 -0.890744426
767 5.539661315 0.808494216
768 8.033306442 1.336350612
769 11.17976894 1.90689286
770 3.437526964 0.933448191
771 -10.27251592 -2.148571624
772 -3.115630548 -0.735768299
773 2.399722526 0.176784544
774 -0.623312262 -0.264038927
775 0.416025634 -0.26745353
776 2.993723464 0.026946378
777 -1.377805017 -0.365773024
778 -1.976334561 -0.449631368
779 -4.018792901 -0.881698308
780 -1.798307167 -0.501415509
781 -7.528094333 -1.560943986
782 2.902915674 0.192405251
783 7.837371464 1.278197467
784 6.043690113 0.996087828
785 -8.972990117 -1.95047905
786 0.974530745 -0.049750125
787 -8.998238363 -2.217754377
788 7.274640759 1.3309397
789 -5.813702454 -1.163446724
790 -2.11032239 -0.377287092
791 2.372698058 0.195406083
792 -1.534272523 -0.408885007
793 2.95065762 0.571081867
794 3.662091031 0.452271996
795 -3.891523882 -0.813337397
796 1.222314055 -0.000961247
797 -10.54041099 -2.35521175
798 -0.09760739 -0.519598655
799 -2.685514789 -0.521646916
800 7.288539429 1.077666109
801 4.693267379 0.704293095
802 -4.82623783 -1.152323499
803 3.226063422 0.517926289
804 2.381231219 0.488742444
805 4.878589666 0.773190861
806 -3.916515808 -0.78286933
807 1.392496353 0.256206908
808 6.330480842 1.410862726
809 -2.60913595 -0.961188165
810 3.994260424 0.632158157
811 0.864560185 0.101998378
812 4.285947617 0.28073047
813 -6.34433278 -1.543502966
814 -14.99285715 -3.348784867
815 5.514402617 0.891138855
816 1.125656503 -0.027774357
817 -3.497128454 -0.885381797
818 3.92655176 0.535864275
819 -0.29268797 -0.406228313
820 3.034242292 0.364915584
821 13.22895141 2.529856462
822 -7.05822892 -1.501275845
823 -4.568411888 -0.983404697
824 3.319149032 0.542703269
825 8.057422596 1.285790112
826 9.060211928 1.61096359
827 8.552733391 1.573384981
828 -4.277761092 -1.08403822
829 5.721905388 0.840688442
830 -3.53390511 -1.391774432
831 0.630611919 0.350333909
832 6.190018781 0.995143589
833 0.85433048 -0.184952879
834 -1.768009945 -0.516167345
835 1.420947529 0.030018261
836 5.724318108 0.768195659
837 6.11831777 1.317510767
838 0.938368203 -0.262741958
839 -1.369224379 -0.448464098
840 1.603076436 0.238711517
841 0.801377906 0.082014991
842 -0.103180772 0.482419057
843 -7.212204932 -1.99288628
844 1.302736731 -0.110402958
845 1.102519831 -0.030151455
846 4.014945687 0.479939997
847 6.94598952 1.121791652
848 -2.359973841 -0.691665064
849 -1.358690926 -0.47362564
850 -6.036018886 -1.169637018
851 3.465135399 0.086355177
852 13.39009008 2.358559266
853 -2.602911563 -0.497104236
854 -14.21806622 -2.813366662
855 5.451083248 1.001241445
856 1.403163207 -0.139153196
857 3.84181451 0.60374918
858 -1.050338613 -0.434240473
859 -2.061835009 -0.736629946
860 -6.846051046 -1.513641687
861 4.342672327 0.800769659
862 -3.448977053 -0.817572264
863 1.644735046 -0.021526368
864 5.625452159 0.819962228
865 5.346899884 0.905564757
866 4.93740311 0.99670665
867 5.319682728 1.048354137
868 -0.698070424 -0.264618093
869 6.606189358 0.931224832
870 7.86791646 1.550296482
871 2.831410604 0.460543833
872 2.406245669 0.71053116
873 6.893442084 1.168181957
874 9.873606101 1.720721485
875 -4.734210827 -1.232310451
876 8.141553105 1.453847748
877 -1.239222865 -0.304811601
878 2.869916561 0.66835239
879 3.750362451 0.290809728
880 -1.082150804 -0.566059531
881 -5.846140996 -1.535197362
882 -2.456463961 -0.223783402
883 -7.000821331 -1.178204092
884 7.636271975 1.345815229
885 6.242668247 0.944182047
886 8.576686294 1.367343605
887 -0.145476331 -0.130729517
888 -1.849060349 -0.393448816
889 -0.35463501 -0.184855745
890 -2.497146136 -0.540402047
891 2.807494123 0.657468424
892 2.643134818 0.226627624
893 -4.106022965 -1.175250854
894 0.219465392 -0.454834199
895 13.49848046 2.367810577
896 -5.860509211 -1.289409454
897 1.221308939 0.144564424
898 5.748205781 1.031235735
899 -5.22253227 -1.388801067
900 -1.433064961 -0.461324603
901 -7.824947256 -1.643840456
902 5.118272198 0.84654128
903 1.62789305 0.256080004
904 6.970601946 1.549099034
905 5.510608673 0.879339548
906 3.35726528 0.438837617
907 -4.892304736 -0.887645526
908 -7.779263829 -1.927757456
909 3.617611189 0.614226623
910 8.214419989 1.196076311
911 11.43321209 2.219511247
912 -4.709020758 -0.770089179
913 3.756781649 0.642970103
914 -5.858227345 -1.090142033
915 -1.03543803 -0.434160197
916 1.581348177 -0.235030254
917 -1.500811294 -0.461322557
918 4.964208883 0.7129712
919 -1.01040908 -0.413334885
920 0.563851778 -0.336403847
921 4.781694715 0.637532936
922 -5.074097567 -1.161331648
923 2.153582027 0.557481715
924 -0.81017399 -0.735884486
925 10.22946169 1.613106574
926 3.247185353 1.032755024
927 -0.321609847 -0.232754306
928 3.029735672 0.527232908
929 0.80128345 0.32093169
930 -0.49535914 -0.003226066
931 2.363094736 0.242383427
932 -4.078080521 -1.021374416
933 2.857076778 0.63595232
934 -1.286818532 -0.818541388
935 3.804451566 0.262159445
936 8.387420495 1.190105471
937 2.146442727 0.198904377
938 -2.995933681 -0.423334351
939 -2.565726045 -0.867221199
940 -4.029170263 -1.305971828
941 3.442747987 0.511743251
942 11.4604844 1.752009254
943 2.237522613 0.283711155
944 3.16838533 0.561941917
945 0.205803849 -0.027081744
946 2.3633998 0.102400176
947 -4.309025703 -1.11647952
948 -7.252207478 -1.513889079
949 4.617780454 0.707025079
950 -9.061864339 -1.645340614
951 -7.294374418 -1.680985421
952 -2.846118667 -0.727805949
953 12.92923277 2.332200377
954 1.169565458 -0.180209972
955 -1.71549004 -0.292009846
956 11.89083071 1.832444757
957 3.702290358 0.679417633
958 1.129412982 -0.312140454
959 5.556960744 1.13826041
960 7.011796165 0.783841882
961 1.29774919 -0.152004815
962 1.93971579 -0.150461806
963 2.849270098 0.293256336
964 -4.527524934 -1.096881135
965 2.094907278 0.29866806
966 5.345288233 0.83069013
967 -2.2270005 -0.874588361
968 -2.601219963 -0.477716003
969 -4.569716461 -1.14381292
970 7.083867821 1.389977149
971 -5.402240344 -1.326884596
972 4.424077423 0.497595649
973 -0.128754103 -0.291331087
974 6.361729495 0.652351911
975 5.704678354 0.549893249
976 -2.615096757 -0.946350719
977 1.699438344 0.271533847
978 -4.344009627 -1.031212297
979 3.124933415 0.269894847
980 -4.724205477 -1.170085467
981 -0.364341548 -0.453762084
982 6.297810586 0.580654749
983 10.38102987 1.863584073
984 4.056196876 0.541629598
985 -2.677564624 -0.554969286
986 7.160202655 1.052857392
987 -7.37142811 -1.706173944
988 -1.366515882 -0.052251579
989 -1.553588145 -0.396289835
990 8.141835164 1.22613601
991 -0.082290119 -0.091619109
992 -5.511782991 -0.984072147
993 -2.200185586 -0.741165924
994 8.304293393 1.760300909
995 3.53779542 0.364509572
996 3.131055105 0.612946954
997 -0.028288598 -0.203577492
998 0.930325771 0.117134568
999 -1.079793744 -0.274147647
1000 1.798406587 0.158997035

Recently Asked Questions

Why Join Course Hero?

Course Hero has all the homework and study help you need to succeed! We’ve got course-specific notes, study guides, and practice tests along with expert tutors.

-

Educational Resources
  • -

    Study Documents

    Find the best study resources around, tagged to your specific courses. Share your own to gain free Course Hero access.

    Browse Documents
  • -

    Question & Answers

    Get one-on-one homework help from our expert tutors—available online 24/7. Ask your own questions or browse existing Q&A threads. Satisfaction guaranteed!

    Ask a Question