Выполнение
1. Построить диаграмму рассеивания (корреляционное поле) двух случайных величин X и y.
2. Оценить выборочные средние, дисперсии, коэффициент корреляции выборки и коэффициенты линейной регрессии случайных величин, используя метод наименьших квадратов.
№ |
X |
Y |
Xi^2 |
Yi^2 |
XiYi |
Xi-X_ |
Yi-Y_ |
(Xi-X_)(Yi-Y_) |
Yx_ |
Xy_ |
Eps |
1 |
-50 |
-30,03 |
2500 |
901,8009 |
1501,5 |
-50 |
-30,67069 |
1533,53465 |
-32,6186 |
-45,05433 |
2,5886 |
2 |
-49 |
-34,95 |
2401 |
1221,5025 |
1712,55 |
-49 |
-35,59069 |
1743,94396 |
-31,95342 |
-52,28166 |
2,99658 |
3 |
-48 |
-34,82 |
2304 |
1212,4324 |
1671,36 |
-48 |
-35,46069 |
1702,11327 |
-31,28823 |
-52,0907 |
3,53177 |
4 |
-47 |
-33,94 |
2209 |
1151,9236 |
1595,18 |
-47 |
-34,58069 |
1625,29257 |
-30,62304 |
-50,798 |
3,31696 |
5 |
-46 |
-29,41 |
2116 |
864,9481 |
1352,86 |
-46 |
-30,05069 |
1382,33188 |
-29,95786 |
-44,14357 |
0,54786 |
6 |
-45 |
-23,86 |
2025 |
569,2996 |
1073,7 |
-45 |
-24,50069 |
1102,53119 |
-29,29267 |
-35,99078 |
5,43267 |
7 |
-44 |
-25,75 |
1936 |
663,0625 |
1133 |
-44 |
-26,39069 |
1161,1905 |
-28,62749 |
-38,76714 |
2,87749 |
8 |
-43 |
-31,63 |
1849 |
1000,4569 |
1360,09 |
-43 |
-32,27069 |
1387,6398 |
-27,9623 |
-47,40468 |
3,6677 |
9 |
-42 |
-25,63 |
1764 |
656,8969 |
1076,46 |
-42 |
-26,27069 |
1103,36911 |
-27,29711 |
-38,59086 |
1,66711 |
10 |
-41 |
-27,83 |
1681 |
774,5089 |
1141,03 |
-41 |
-28,47069 |
1167,29842 |
-26,63193 |
-41,82259 |
1,19807 |
11 |
-40 |
-23,46 |
1600 |
550,3716 |
938,4 |
-40 |
-24,10069 |
964,02772 |
-25,96674 |
-35,4032 |
2,50674 |
12 |
-39 |
-26,94 |
1521 |
725,7636 |
1050,66 |
-39 |
-27,58069 |
1075,64703 |
-25,30156 |
-40,51521 |
1,63844 |
13 |
-38 |
-22,85 |
1444 |
522,1225 |
868,3 |
-38 |
-23,49069 |
892,64634 |
-24,63637 |
-34,50712 |
1,78637 |
14 |
-37 |
-22,81 |
1369 |
520,2961 |
843,97 |
-37 |
-23,45069 |
867,67564 |
-23,97119 |
-34,44837 |
1,16119 |
15 |
-36 |
-27,11 |
1296 |
734,9521 |
975,96 |
-36 |
-27,75069 |
999,02495 |
-23,306 |
-40,76494 |
3,804 |
16 |
-35 |
-21,23 |
1225 |
450,7129 |
743,05 |
-35 |
-21,87069 |
765,47426 |
-22,64081 |
-32,12739 |
1,41081 |
17 |
-34 |
-26,58 |
1156 |
706,4964 |
903,72 |
-34 |
-27,22069 |
925,50356 |
-21,97563 |
-39,98638 |
4,60437 |
18 |
-33 |
-19,27 |
1089 |
371,3329 |
635,91 |
-33 |
-19,91069 |
657,05287 |
-21,31044 |
-29,24821 |
2,04044 |
19 |
-32 |
-18,52 |
1024 |
342,9904 |
592,64 |
-32 |
-19,16069 |
613,14218 |
-20,64526 |
-28,14648 |
2,12526 |
20 |
-31 |
-21,09 |
961 |
444,7881 |
653,79 |
-31 |
-21,73069 |
673,65149 |
-19,98007 |
-31,92174 |
1,10993 |
21 |
-30 |
-17,51 |
900 |
306,6001 |
525,3 |
-30 |
-18,15069 |
544,52079 |
-19,31488 |
-26,66282 |
1,80488 |
22 |
-29 |
-15,32 |
841 |
234,7024 |
444,28 |
-29 |
-15,96069 |
462,8601 |
-18,6497 |
-23,44578 |
3,3297 |
23 |
-28 |
-15,95 |
784 |
254,4025 |
446,6 |
-28 |
-16,59069 |
464,53941 |
-17,98451 |
-24,37123 |
2,03451 |
24 |
-27 |
-16,6 |
729 |
275,56 |
448,2 |
-27 |
-17,24069 |
465,49871 |
-17,31933 |
-25,32606 |
0,71933 |
25 |
-26 |
-14,8 |
676 |
219,04 |
384,8 |
-26 |
-15,44069 |
401,45802 |
-16,65414 |
-22,68192 |
1,85414 |
26 |
-25 |
-15,67 |
625 |
245,5489 |
391,75 |
-25 |
-16,31069 |
407,76733 |
-15,98895 |
-23,95992 |
0,31895 |
27 |
-24 |
-16,88 |
576 |
284,9344 |
405,12 |
-24 |
-17,52069 |
420,49663 |
-15,32377 |
-25,73737 |
1,55623 |
28 |
-23 |
-17,86 |
529 |
318,9796 |
410,78 |
-23 |
-18,50069 |
425,51594 |
-14,65858 |
-27,17696 |
3,20142 |
29 |
-22 |
-12,65 |
484 |
160,0225 |
278,3 |
-22 |
-13,29069 |
292,39525 |
-13,9934 |
-19,52363 |
1,3434 |
30 |
-21 |
-14,12 |
441 |
199,3744 |
296,52 |
-21 |
-14,76069 |
309,97455 |
-13,32821 |
-21,68302 |
0,79179 |
31 |
-20 |
-15,46 |
400 |
239,0116 |
309,2 |
-20 |
-16,10069 |
322,01386 |
-12,66303 |
-23,65144 |
2,79697 |
32 |
-19 |
-18,03 |
361 |
325,0809 |
342,57 |
-19 |
-18,67069 |
354,74317 |
-11,99784 |
-27,42669 |
6,03216 |
33 |
-18 |
-12,07 |
324 |
145,6849 |
217,26 |
-18 |
-12,71069 |
228,79248 |
-11,33265 |
-18,67163 |
0,73735 |
34 |
-17 |
-8,7 |
289 |
75,69 |
147,9 |
-17 |
-9,34069 |
158,79178 |
-10,66747 |
-13,7212 |
1,96747 |
35 |
-16 |
-9,37 |
256 |
87,7969 |
149,92 |
-16 |
-10,01069 |
160,17109 |
-10,00228 |
-14,70541 |
0,63228 |
36 |
-15 |
-13,99 |
225 |
195,7201 |
209,85 |
-15 |
-14,63069 |
219,4604 |
-9,3371 |
-21,49205 |
4,6529 |
37 |
-14 |
-18,45 |
196 |
340,4025 |
258,3 |
-14 |
-19,09069 |
267,2697 |
-8,67191 |
-28,04366 |
9,77809 |
38 |
-13 |
-11,72 |
169 |
137,3584 |
152,36 |
-13 |
-12,36069 |
160,68901 |
-8,00672 |
-18,15749 |
3,71328 |
39 |
-12 |
-7,04 |
144 |
49,5616 |
84,48 |
-12 |
-7,68069 |
92,16832 |
-7,34154 |
-11,28271 |
0,30154 |
40 |
-11 |
-6,21 |
121 |
38,5641 |
68,31 |
-11 |
-6,85069 |
75,35762 |
-6,67635 |
-10,06346 |
0,46635 |
41 |
-10 |
-4,73 |
100 |
22,3729 |
47,3 |
-10 |
-5,37069 |
53,70693 |
-6,01117 |
-7,88939 |
1,28117 |
42 |
-9 |
-3,6 |
81 |
12,96 |
32,4 |
-9 |
-4,24069 |
38,16624 |
-5,34598 |
-6,22945 |
1,74598 |
43 |
-8 |
-6,89 |
64 |
47,4721 |
55,12 |
-8 |
-7,53069 |
60,24554 |
-4,68079 |
-11,06236 |
2,20921 |
44 |
-7 |
-2,6 |
49 |
6,76 |
18,2 |
-7 |
-3,24069 |
22,68485 |
-4,01561 |
-4,76048 |
1,41561 |
45 |
-6 |
-2,6 |
36 |
6,76 |
15,6 |
-6 |
-3,24069 |
19,44416 |
-3,35042 |
-4,76048 |
0,75042 |
46 |
-5 |
-4,7 |
25 |
22,09 |
23,5 |
-5 |
-5,34069 |
26,70347 |
-2,68524 |
-7,84532 |
2,01476 |
47 |
-4 |
-2,44 |
16 |
5,9536 |
9,76 |
-4 |
-3,08069 |
12,32277 |
-2,02005 |
-4,52545 |
0,41995 |
48 |
-3 |
0,67 |
9 |
0,4489 |
-2,01 |
-3 |
0,02931 |
-0,08792 |
-1,35486 |
0,04305 |
2,02486 |
49 |
-2 |
3,86 |
4 |
14,8996 |
-7,72 |
-2 |
3,21931 |
-6,43861 |
-0,68968 |
4,72907 |
4,54968 |
50 |
-1 |
5,57 |
1 |
31,0249 |
-5,57 |
-1 |
4,92931 |
-4,92931 |
-0,02449 |
7,241 |
5,59449 |
51 |
0 |
4,89 |
0 |
23,9121 |
0 |
0 |
4,24931 |
0 |
0,64069 |
6,2421 |
4,24931 |
52 |
1 |
4,51 |
1 |
20,3401 |
4,51 |
1 |
3,86931 |
3,86931 |
1,30588 |
5,6839 |
3,20412 |
53 |
2 |
2,57 |
4 |
6,6049 |
5,14 |
2 |
1,92931 |
3,85861 |
1,97106 |
2,83409 |
0,59894 |
54 |
3 |
-2,26 |
9 |
5,1076 |
-6,78 |
3 |
-2,90069 |
-8,70208 |
2,63625 |
-4,26103 |
4,89625 |
55 |
4 |
-0,02 |
16 |
0,0004 |
-0,08 |
4 |
-0,66069 |
-2,64277 |
3,30144 |
-0,97054 |
3,32144 |
56 |
5 |
1,81 |
25 |
3,2761 |
9,05 |
5 |
1,16931 |
5,84653 |
3,96662 |
1,71768 |
2,15662 |
57 |
6 |
2,68 |
36 |
7,1824 |
16,08 |
6 |
2,03931 |
12,23584 |
4,63181 |
2,99568 |
1,95181 |
58 |
7 |
4,6 |
49 |
21,16 |
32,2 |
7 |
3,95931 |
27,71515 |
5,29699 |
5,8161 |
0,69699 |
59 |
8 |
10,95 |
64 |
119,9025 |
87,6 |
8 |
10,30931 |
82,47446 |
5,96218 |
15,14406 |
4,98782 |
60 |
9 |
6,57 |
81 |
43,1649 |
59,13 |
9 |
5,92931 |
53,36376 |
6,62737 |
8,70997 |
0,05737 |
61 |
10 |
4,9 |
100 |
24,01 |
49 |
10 |
4,25931 |
42,59307 |
7,29255 |
6,25679 |
2,39255 |
62 |
11 |
8,16 |
121 |
66,5856 |
89,76 |
11 |
7,51931 |
82,71238 |
7,95774 |
11,04564 |
0,20226 |
63 |
12 |
11,4 |
144 |
129,96 |
136,8 |
12 |
10,75931 |
129,11168 |
8,62292 |
15,8051 |
2,77708 |
64 |
13 |
17,87 |
169 |
319,3369 |
232,31 |
13 |
17,22931 |
223,98099 |
9,28811 |
25,30934 |
8,58189 |
65 |
14 |
11,17 |
196 |
124,7689 |
156,38 |
14 |
10,52931 |
147,4103 |
9,9533 |
15,46724 |
1,2167 |
66 |
15 |
11,19 |
225 |
125,2161 |
167,85 |
15 |
10,54931 |
158,2396 |
10,61848 |
15,49662 |
0,57152 |
67 |
16 |
10,91 |
256 |
119,0281 |
174,56 |
16 |
10,26931 |
164,30891 |
11,28367 |
15,0853 |
0,37367 |
68 |
17 |
11,78 |
289 |
138,7684 |
200,26 |
17 |
11,13931 |
189,36822 |
11,94885 |
16,36331 |
0,16885 |
69 |
18 |
15,43 |
324 |
238,0849 |
277,74 |
18 |
14,78931 |
266,20752 |
12,61404 |
21,72505 |
2,81596 |
70 |
19 |
18,41 |
361 |
338,9281 |
349,79 |
19 |
17,76931 |
337,61683 |
13,27923 |
26,10258 |
5,13077 |
71 |
20 |
19,37 |
400 |
375,1969 |
387,4 |
20 |
18,72931 |
374,58614 |
13,94441 |
27,51279 |
5,42559 |
72 |
21 |
17,37 |
441 |
301,7169 |
364,77 |
21 |
16,72931 |
351,31545 |
14,6096 |
24,57485 |
2,7604 |
73 |
22 |
15,35 |
484 |
235,6225 |
337,7 |
22 |
14,70931 |
323,60475 |
15,27478 |
21,60753 |
0,07522 |
74 |
23 |
16,03 |
529 |
256,9609 |
368,69 |
23 |
15,38931 |
353,95406 |
15,93997 |
22,60643 |
0,09003 |
75 |
24 |
16,55 |
576 |
273,9025 |
397,2 |
24 |
15,90931 |
381,82337 |
16,60515 |
23,3703 |
0,05515 |
76 |
25 |
18,14 |
625 |
329,0596 |
453,5 |
25 |
17,49931 |
437,48267 |
17,27034 |
25,70596 |
0,86966 |
77 |
26 |
20,79 |
676 |
432,2241 |
540,54 |
26 |
20,14931 |
523,88198 |
17,93553 |
29,59873 |
2,85447 |
78 |
27 |
18,82 |
729 |
354,1924 |
508,14 |
27 |
18,17931 |
490,84129 |
18,60071 |
26,70486 |
0,21929 |
79 |
28 |
18,33 |
784 |
335,9889 |
513,24 |
28 |
17,68931 |
495,30059 |
19,2659 |
25,98506 |
0,9359 |
80 |
29 |
15,98 |
841 |
255,3604 |
463,42 |
29 |
15,33931 |
444,8399 |
19,93108 |
22,53298 |
3,95108 |
81 |
30 |
20,54 |
900 |
421,8916 |
616,2 |
30 |
19,89931 |
596,97921 |
20,59627 |
29,23149 |
0,05627 |
82 |
31 |
21,14 |
961 |
446,8996 |
655,34 |
31 |
20,49931 |
635,47851 |
21,26146 |
30,11287 |
0,12146 |
83 |
32 |
17,02 |
1024 |
289,6804 |
544,64 |
32 |
16,37931 |
524,13782 |
21,92664 |
24,06071 |
4,90664 |
84 |
33 |
23,01 |
1089 |
529,4601 |
759,33 |
33 |
22,36931 |
738,18713 |
22,59183 |
32,85984 |
0,41817 |
85 |
34 |
23,96 |
1156 |
574,0816 |
814,64 |
34 |
23,31931 |
792,85644 |
23,25701 |
34,25536 |
0,70299 |
86 |
35 |
21,59 |
1225 |
466,1281 |
755,65 |
35 |
20,94931 |
733,22574 |
23,9222 |
30,7739 |
2,3322 |
87 |
36 |
21,37 |
1296 |
456,6769 |
769,32 |
36 |
20,72931 |
746,25505 |
24,58739 |
30,45073 |
3,21739 |
88 |
37 |
19,37 |
1369 |
375,1969 |
716,69 |
37 |
18,72931 |
692,98436 |
25,25257 |
27,51279 |
5,88257 |
89 |
38 |
25,7 |
1444 |
660,49 |
976,6 |
38 |
25,05931 |
952,25366 |
25,91776 |
36,81137 |
0,21776 |
90 |
39 |
24,05 |
1521 |
578,4025 |
937,95 |
39 |
23,40931 |
912,96297 |
26,58294 |
34,38757 |
2,53294 |
91 |
40 |
24,91 |
1600 |
620,5081 |
996,4 |
40 |
24,26931 |
970,77228 |
27,24813 |
35,65088 |
2,33813 |
92 |
41 |
34,15 |
1681 |
1166,2225 |
1400,15 |
41 |
33,50931 |
1373,88158 |
27,91332 |
49,22417 |
6,23668 |
93 |
42 |
25,82 |
1764 |
666,6724 |
1084,44 |
42 |
25,17931 |
1057,53089 |
28,5785 |
36,98765 |
2,7585 |
94 |
43 |
30,55 |
1849 |
933,3025 |
1313,65 |
43 |
29,90931 |
1286,1002 |
29,24369 |
43,93588 |
1,30631 |
95 |
44 |
27,08 |
1936 |
733,3264 |
1191,52 |
44 |
26,43931 |
1163,3295 |
29,90887 |
38,83855 |
2,82887 |
96 |
45 |
30,65 |
2025 |
939,4225 |
1379,25 |
45 |
30,00931 |
1350,41881 |
30,57406 |
44,08277 |
0,07594 |
97 |
46 |
33,24 |
2116 |
1104,8976 |
1529,04 |
46 |
32,59931 |
1499,56812 |
31,23924 |
47,8874 |
2,00076 |
98 |
47 |
28,71 |
2209 |
824,2641 |
1349,37 |
47 |
28,06931 |
1319,25743 |
31,90443 |
41,23297 |
3,19443 |
99 |
48 |
33,71 |
2304 |
1136,3641 |
1618,08 |
48 |
33,06931 |
1587,32673 |
32,56962 |
48,57782 |
1,14038 |
100 |
49 |
33,46 |
2401 |
1119,5716 |
1639,54 |
49 |
32,81931 |
1608,14604 |
33,2348 |
48,21058 |
0,2252 |
101 |
50 |
34 |
2500 |
1156 |
1700 |
50 |
33,35931 |
1667,96535 |
33,89999 |
49,00382 |
0,10001 |
Суммы |
0 |
64,71 |
85850 |
38916,4593 |
57106,21 |
|
|
57106,21 |
|
|
|