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Author's title

Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sun, 15 Jan 2012 09:02:21 -0500

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Jan/15/t1326636174fbot8wkj54drxn0.htm/, Retrieved Fri, 03 May 2024 12:37:16 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=161078, Retrieved Fri, 03 May 2024 12:37:16 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W102

Estimated Impact

131

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Exponential Smoothing] [] [2012-01-15 14:02:21] [76c30f62b7052b57088120e90a652e05] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161078&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161078&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161078&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.0725975572270489
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0725975572270489 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161078&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0725975572270489[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161078&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161078&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.0725975572270489
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	100.1	100.3	-0.200000000000017
4	100.2	100.685480488555	-0.485480488554586
5	100.1	100.750235791004	-0.65023579100415
6	100.4	100.603030260956	-0.203030260955629
7	99.8	100.888290759967	-1.08829075996709
8	99.7	100.209283509241	-0.509283509240703
9	99.4	100.072310770534	-0.672310770533812
10	100.2	99.7235026508956	0.476497349104363
11	100.5	100.558095194466	-0.0580951944657784
12	100.6	100.853877625261	-0.253877625260927
13	100.9	100.935446729832	-0.0354467298323584
14	101.9	101.232873383835	0.667126616165135
15	102.1	102.28130514653	-0.18130514652961
16	102.6	102.468142835779	0.131857164221145
17	103.5	102.977715343804	0.522284656195808
18	103.9	103.915631934021	-0.0156319340211724
19	103.7	104.314497093797	-0.614497093796516
20	103	104.069886105864	-1.06988610586376
21	103.1	103.292214988067	-0.192214988066894
22	103.2	103.378260649471	-0.178260649470801
23	103.2	103.46531936177	-0.265319361769528
24	103.1	103.44605782422	-0.346057824220026
25	103.7	103.320934871522	0.379065128477677
26	104.2	103.94845407388	0.25154592612023
27	104.4	104.466715693647	-0.0667156936465148
28	104.9	104.661872297259	0.238127702740925
29	105.4	105.179159786786	0.220840213213847
30	105.9	105.695192246803	0.204807753197031
31	105.5	106.210060789386	-0.710060789386247
32	106.1	105.758512110594	0.341487889405911
33	105.4	106.383303297188	-0.983303297187561
34	105.7	105.611917879798	0.0880821202015341
35	106.2	105.91831242656	0.281687573439527
36	106.7	106.438762256293	0.261237743706602
37	106.8	106.957727478342	-0.157727478342011
38	106.8	107.046276848707	-0.246276848706785
39	106.8	107.028397751089	-0.228397751089105
40	107.3	107.011816632284	0.288183367716115
41	107.3	107.532738040814	-0.23273804081353
42	107.5	107.515841827577	-0.015841827576665
43	107.4	107.714691749593	-0.314691749592583
44	106.9	107.591845897293	-0.691845897292652
45	108.1	107.041619575172	1.05838042482833
46	108.6	108.318455408631	0.281544591368885
47	108.2	108.838894858215	-0.638894858214982
48	108.3	108.392512652184	-0.0925126521836575
49	108.3	108.485796459623	-0.185796459622523
50	109.3	108.472308090512	0.827691909487498
51	109.2	109.532396501278	-0.33239650127787
52	109.4	109.408265327254	-0.00826532725429274
53	109.7	109.607665284686	0.0923347153140526
54	109.6	109.914368559465	-0.314368559465009
55	109.3	109.791546169979	-0.491546169978847
56	108.4	109.455861118774	-1.05586111877408
57	108.7	108.47920818078	0.22079181921994
58	109.4	108.795237127511	0.604762872488863
59	109	109.539141434755	-0.53914143475545
60	110.3	109.100001083592	1.19999891640768
61	109.5	110.487118073599	-0.987118073598623
62	109.7	109.615455712761	0.0845442872393107
63	109.5	109.821593421492	-0.32159342149177
64	110.9	109.598246524671	1.30175347532882
65	110.9	111.092750647092	-0.19275064709187
66	110.4	111.078757420959	-0.678757420959073
67	111.1	110.529481290248	0.570518709752278
68	110.8	111.270899554928	-0.470899554928053
69	111.3	110.936713397541	0.363286602459027
70	111.7	111.463087117453	0.236912882547202
71	112.2	111.880286414001	0.319713585998642
72	111.7	112.403496839357	-0.703496839357157
73	111.3	111.852424687303	-0.552424687302889
74	111.9	111.412320004453	0.487679995547239
75	111.7	112.047724380838	-0.347724380838002
76	111.8	111.822480440201	-0.02248044020088
77	111.5	111.920848415157	-0.420848415156897
78	112.9	111.590295848254	1.30970415174637
79	112	113.085377170361	-1.08537717036054
80	112.4	112.106581439122	0.29341856087764
81	111.1	112.527882909887	-1.42788290988716
82	111.7	111.124222098623	0.57577790137691
83	111.4	111.766022167768	-0.366022167768378
84	112.2	111.439449852497	0.760550147502556
85	112.5	112.294663935355	0.205336064645195
86	113.2	112.609570832059	0.590429167941352
87	114.7	113.352434547367	1.34756545263321
88	115.2	114.950264507432	0.249735492568462
89	114.1	115.468394694145	-1.36839469414491
90	113.7	114.269052582028	-0.56905258202751
91	115.5	113.827740754639	1.67225924536142
92	115	115.749142690902	-0.749142690902161
93	115.4	115.194756761528	0.205243238471837
94	115	115.609656919279	-0.609656919278606
95	114.6	115.165397316192	-0.565397316192403
96	114.6	114.724350852174	-0.124350852174103
97	114.5	114.715323284067	-0.215323284067154
98	115.2	114.59969133963	0.600308660370217
99	116.3	115.343272281955	0.956727718045101
100	116.5	116.512728377216	-0.0127283772163764
101	118.4	116.711804328123	1.688195671877
102	118.5	118.734363210023	-0.234363210022565
103	118.7	118.817349013471	-0.117349013471028
104	119.2	119.00882976175	0.191170238249967
105	119.5	119.522708254061	-0.0227082540614845
106	118.5	119.821059690288	-1.32105969028773
107	118.6	118.725153983822	-0.125153983821733
108	118.2	118.816068110319	-0.61606811031902
109	118.6	118.371343070424	0.228656929575607
110	120.6	118.787943004955	1.81205699504538
111	124.5	120.919493916351	3.58050608364891
112	124.6	125.079429911661	-0.479429911660603
113	126.5	125.144624471212	1.35537552878755
114	126	127.143021423728	-1.14302142372775
115	126.3	126.560040860507	-0.260040860506933
116	126.3	126.841162529255	-0.541162529254905
117	125.1	126.801875451568	-1.7018754515682
118	126.7	125.47832345108	1.22167654892036
119	123.9	127.167014184253	-3.26701418425284
120	123.6	124.12983693505	-0.529836935049985
121	124.9	123.791372067837	1.10862793216333
122	126.2	125.171855747585	1.02814425241459
123	126.3	126.546496508788	-0.246496508787743
124	126.4	126.628601464385	-0.228601464384738
125	126.2	126.712005556492	-0.5120055564919
126	125.8	126.474835203804	-0.674835203803909
127	124.9	126.025843816477	-1.12584381647692
128	126.2	125.044110305582	1.15588969441848
129	125.9	126.42802507382	-0.528025073820217
130	124.6	126.089691743306	-1.48969174330625
131	122.9	124.681543761721	-1.7815437617209
132	119.9	122.852208036527	-2.95220803652688

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 100.1 & 100.3 & -0.200000000000017 \tabularnewline
4 & 100.2 & 100.685480488555 & -0.485480488554586 \tabularnewline
5 & 100.1 & 100.750235791004 & -0.65023579100415 \tabularnewline
6 & 100.4 & 100.603030260956 & -0.203030260955629 \tabularnewline
7 & 99.8 & 100.888290759967 & -1.08829075996709 \tabularnewline
8 & 99.7 & 100.209283509241 & -0.509283509240703 \tabularnewline
9 & 99.4 & 100.072310770534 & -0.672310770533812 \tabularnewline
10 & 100.2 & 99.7235026508956 & 0.476497349104363 \tabularnewline
11 & 100.5 & 100.558095194466 & -0.0580951944657784 \tabularnewline
12 & 100.6 & 100.853877625261 & -0.253877625260927 \tabularnewline
13 & 100.9 & 100.935446729832 & -0.0354467298323584 \tabularnewline
14 & 101.9 & 101.232873383835 & 0.667126616165135 \tabularnewline
15 & 102.1 & 102.28130514653 & -0.18130514652961 \tabularnewline
16 & 102.6 & 102.468142835779 & 0.131857164221145 \tabularnewline
17 & 103.5 & 102.977715343804 & 0.522284656195808 \tabularnewline
18 & 103.9 & 103.915631934021 & -0.0156319340211724 \tabularnewline
19 & 103.7 & 104.314497093797 & -0.614497093796516 \tabularnewline
20 & 103 & 104.069886105864 & -1.06988610586376 \tabularnewline
21 & 103.1 & 103.292214988067 & -0.192214988066894 \tabularnewline
22 & 103.2 & 103.378260649471 & -0.178260649470801 \tabularnewline
23 & 103.2 & 103.46531936177 & -0.265319361769528 \tabularnewline
24 & 103.1 & 103.44605782422 & -0.346057824220026 \tabularnewline
25 & 103.7 & 103.320934871522 & 0.379065128477677 \tabularnewline
26 & 104.2 & 103.94845407388 & 0.25154592612023 \tabularnewline
27 & 104.4 & 104.466715693647 & -0.0667156936465148 \tabularnewline
28 & 104.9 & 104.661872297259 & 0.238127702740925 \tabularnewline
29 & 105.4 & 105.179159786786 & 0.220840213213847 \tabularnewline
30 & 105.9 & 105.695192246803 & 0.204807753197031 \tabularnewline
31 & 105.5 & 106.210060789386 & -0.710060789386247 \tabularnewline
32 & 106.1 & 105.758512110594 & 0.341487889405911 \tabularnewline
33 & 105.4 & 106.383303297188 & -0.983303297187561 \tabularnewline
34 & 105.7 & 105.611917879798 & 0.0880821202015341 \tabularnewline
35 & 106.2 & 105.91831242656 & 0.281687573439527 \tabularnewline
36 & 106.7 & 106.438762256293 & 0.261237743706602 \tabularnewline
37 & 106.8 & 106.957727478342 & -0.157727478342011 \tabularnewline
38 & 106.8 & 107.046276848707 & -0.246276848706785 \tabularnewline
39 & 106.8 & 107.028397751089 & -0.228397751089105 \tabularnewline
40 & 107.3 & 107.011816632284 & 0.288183367716115 \tabularnewline
41 & 107.3 & 107.532738040814 & -0.23273804081353 \tabularnewline
42 & 107.5 & 107.515841827577 & -0.015841827576665 \tabularnewline
43 & 107.4 & 107.714691749593 & -0.314691749592583 \tabularnewline
44 & 106.9 & 107.591845897293 & -0.691845897292652 \tabularnewline
45 & 108.1 & 107.041619575172 & 1.05838042482833 \tabularnewline
46 & 108.6 & 108.318455408631 & 0.281544591368885 \tabularnewline
47 & 108.2 & 108.838894858215 & -0.638894858214982 \tabularnewline
48 & 108.3 & 108.392512652184 & -0.0925126521836575 \tabularnewline
49 & 108.3 & 108.485796459623 & -0.185796459622523 \tabularnewline
50 & 109.3 & 108.472308090512 & 0.827691909487498 \tabularnewline
51 & 109.2 & 109.532396501278 & -0.33239650127787 \tabularnewline
52 & 109.4 & 109.408265327254 & -0.00826532725429274 \tabularnewline
53 & 109.7 & 109.607665284686 & 0.0923347153140526 \tabularnewline
54 & 109.6 & 109.914368559465 & -0.314368559465009 \tabularnewline
55 & 109.3 & 109.791546169979 & -0.491546169978847 \tabularnewline
56 & 108.4 & 109.455861118774 & -1.05586111877408 \tabularnewline
57 & 108.7 & 108.47920818078 & 0.22079181921994 \tabularnewline
58 & 109.4 & 108.795237127511 & 0.604762872488863 \tabularnewline
59 & 109 & 109.539141434755 & -0.53914143475545 \tabularnewline
60 & 110.3 & 109.100001083592 & 1.19999891640768 \tabularnewline
61 & 109.5 & 110.487118073599 & -0.987118073598623 \tabularnewline
62 & 109.7 & 109.615455712761 & 0.0845442872393107 \tabularnewline
63 & 109.5 & 109.821593421492 & -0.32159342149177 \tabularnewline
64 & 110.9 & 109.598246524671 & 1.30175347532882 \tabularnewline
65 & 110.9 & 111.092750647092 & -0.19275064709187 \tabularnewline
66 & 110.4 & 111.078757420959 & -0.678757420959073 \tabularnewline
67 & 111.1 & 110.529481290248 & 0.570518709752278 \tabularnewline
68 & 110.8 & 111.270899554928 & -0.470899554928053 \tabularnewline
69 & 111.3 & 110.936713397541 & 0.363286602459027 \tabularnewline
70 & 111.7 & 111.463087117453 & 0.236912882547202 \tabularnewline
71 & 112.2 & 111.880286414001 & 0.319713585998642 \tabularnewline
72 & 111.7 & 112.403496839357 & -0.703496839357157 \tabularnewline
73 & 111.3 & 111.852424687303 & -0.552424687302889 \tabularnewline
74 & 111.9 & 111.412320004453 & 0.487679995547239 \tabularnewline
75 & 111.7 & 112.047724380838 & -0.347724380838002 \tabularnewline
76 & 111.8 & 111.822480440201 & -0.02248044020088 \tabularnewline
77 & 111.5 & 111.920848415157 & -0.420848415156897 \tabularnewline
78 & 112.9 & 111.590295848254 & 1.30970415174637 \tabularnewline
79 & 112 & 113.085377170361 & -1.08537717036054 \tabularnewline
80 & 112.4 & 112.106581439122 & 0.29341856087764 \tabularnewline
81 & 111.1 & 112.527882909887 & -1.42788290988716 \tabularnewline
82 & 111.7 & 111.124222098623 & 0.57577790137691 \tabularnewline
83 & 111.4 & 111.766022167768 & -0.366022167768378 \tabularnewline
84 & 112.2 & 111.439449852497 & 0.760550147502556 \tabularnewline
85 & 112.5 & 112.294663935355 & 0.205336064645195 \tabularnewline
86 & 113.2 & 112.609570832059 & 0.590429167941352 \tabularnewline
87 & 114.7 & 113.352434547367 & 1.34756545263321 \tabularnewline
88 & 115.2 & 114.950264507432 & 0.249735492568462 \tabularnewline
89 & 114.1 & 115.468394694145 & -1.36839469414491 \tabularnewline
90 & 113.7 & 114.269052582028 & -0.56905258202751 \tabularnewline
91 & 115.5 & 113.827740754639 & 1.67225924536142 \tabularnewline
92 & 115 & 115.749142690902 & -0.749142690902161 \tabularnewline
93 & 115.4 & 115.194756761528 & 0.205243238471837 \tabularnewline
94 & 115 & 115.609656919279 & -0.609656919278606 \tabularnewline
95 & 114.6 & 115.165397316192 & -0.565397316192403 \tabularnewline
96 & 114.6 & 114.724350852174 & -0.124350852174103 \tabularnewline
97 & 114.5 & 114.715323284067 & -0.215323284067154 \tabularnewline
98 & 115.2 & 114.59969133963 & 0.600308660370217 \tabularnewline
99 & 116.3 & 115.343272281955 & 0.956727718045101 \tabularnewline
100 & 116.5 & 116.512728377216 & -0.0127283772163764 \tabularnewline
101 & 118.4 & 116.711804328123 & 1.688195671877 \tabularnewline
102 & 118.5 & 118.734363210023 & -0.234363210022565 \tabularnewline
103 & 118.7 & 118.817349013471 & -0.117349013471028 \tabularnewline
104 & 119.2 & 119.00882976175 & 0.191170238249967 \tabularnewline
105 & 119.5 & 119.522708254061 & -0.0227082540614845 \tabularnewline
106 & 118.5 & 119.821059690288 & -1.32105969028773 \tabularnewline
107 & 118.6 & 118.725153983822 & -0.125153983821733 \tabularnewline
108 & 118.2 & 118.816068110319 & -0.61606811031902 \tabularnewline
109 & 118.6 & 118.371343070424 & 0.228656929575607 \tabularnewline
110 & 120.6 & 118.787943004955 & 1.81205699504538 \tabularnewline
111 & 124.5 & 120.919493916351 & 3.58050608364891 \tabularnewline
112 & 124.6 & 125.079429911661 & -0.479429911660603 \tabularnewline
113 & 126.5 & 125.144624471212 & 1.35537552878755 \tabularnewline
114 & 126 & 127.143021423728 & -1.14302142372775 \tabularnewline
115 & 126.3 & 126.560040860507 & -0.260040860506933 \tabularnewline
116 & 126.3 & 126.841162529255 & -0.541162529254905 \tabularnewline
117 & 125.1 & 126.801875451568 & -1.7018754515682 \tabularnewline
118 & 126.7 & 125.47832345108 & 1.22167654892036 \tabularnewline
119 & 123.9 & 127.167014184253 & -3.26701418425284 \tabularnewline
120 & 123.6 & 124.12983693505 & -0.529836935049985 \tabularnewline
121 & 124.9 & 123.791372067837 & 1.10862793216333 \tabularnewline
122 & 126.2 & 125.171855747585 & 1.02814425241459 \tabularnewline
123 & 126.3 & 126.546496508788 & -0.246496508787743 \tabularnewline
124 & 126.4 & 126.628601464385 & -0.228601464384738 \tabularnewline
125 & 126.2 & 126.712005556492 & -0.5120055564919 \tabularnewline
126 & 125.8 & 126.474835203804 & -0.674835203803909 \tabularnewline
127 & 124.9 & 126.025843816477 & -1.12584381647692 \tabularnewline
128 & 126.2 & 125.044110305582 & 1.15588969441848 \tabularnewline
129 & 125.9 & 126.42802507382 & -0.528025073820217 \tabularnewline
130 & 124.6 & 126.089691743306 & -1.48969174330625 \tabularnewline
131 & 122.9 & 124.681543761721 & -1.7815437617209 \tabularnewline
132 & 119.9 & 122.852208036527 & -2.95220803652688 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161078&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]100.1[/C][C]100.3[/C][C]-0.200000000000017[/C][/ROW]
[ROW][C]4[/C][C]100.2[/C][C]100.685480488555[/C][C]-0.485480488554586[/C][/ROW]
[ROW][C]5[/C][C]100.1[/C][C]100.750235791004[/C][C]-0.65023579100415[/C][/ROW]
[ROW][C]6[/C][C]100.4[/C][C]100.603030260956[/C][C]-0.203030260955629[/C][/ROW]
[ROW][C]7[/C][C]99.8[/C][C]100.888290759967[/C][C]-1.08829075996709[/C][/ROW]
[ROW][C]8[/C][C]99.7[/C][C]100.209283509241[/C][C]-0.509283509240703[/C][/ROW]
[ROW][C]9[/C][C]99.4[/C][C]100.072310770534[/C][C]-0.672310770533812[/C][/ROW]
[ROW][C]10[/C][C]100.2[/C][C]99.7235026508956[/C][C]0.476497349104363[/C][/ROW]
[ROW][C]11[/C][C]100.5[/C][C]100.558095194466[/C][C]-0.0580951944657784[/C][/ROW]
[ROW][C]12[/C][C]100.6[/C][C]100.853877625261[/C][C]-0.253877625260927[/C][/ROW]
[ROW][C]13[/C][C]100.9[/C][C]100.935446729832[/C][C]-0.0354467298323584[/C][/ROW]
[ROW][C]14[/C][C]101.9[/C][C]101.232873383835[/C][C]0.667126616165135[/C][/ROW]
[ROW][C]15[/C][C]102.1[/C][C]102.28130514653[/C][C]-0.18130514652961[/C][/ROW]
[ROW][C]16[/C][C]102.6[/C][C]102.468142835779[/C][C]0.131857164221145[/C][/ROW]
[ROW][C]17[/C][C]103.5[/C][C]102.977715343804[/C][C]0.522284656195808[/C][/ROW]
[ROW][C]18[/C][C]103.9[/C][C]103.915631934021[/C][C]-0.0156319340211724[/C][/ROW]
[ROW][C]19[/C][C]103.7[/C][C]104.314497093797[/C][C]-0.614497093796516[/C][/ROW]
[ROW][C]20[/C][C]103[/C][C]104.069886105864[/C][C]-1.06988610586376[/C][/ROW]
[ROW][C]21[/C][C]103.1[/C][C]103.292214988067[/C][C]-0.192214988066894[/C][/ROW]
[ROW][C]22[/C][C]103.2[/C][C]103.378260649471[/C][C]-0.178260649470801[/C][/ROW]
[ROW][C]23[/C][C]103.2[/C][C]103.46531936177[/C][C]-0.265319361769528[/C][/ROW]
[ROW][C]24[/C][C]103.1[/C][C]103.44605782422[/C][C]-0.346057824220026[/C][/ROW]
[ROW][C]25[/C][C]103.7[/C][C]103.320934871522[/C][C]0.379065128477677[/C][/ROW]
[ROW][C]26[/C][C]104.2[/C][C]103.94845407388[/C][C]0.25154592612023[/C][/ROW]
[ROW][C]27[/C][C]104.4[/C][C]104.466715693647[/C][C]-0.0667156936465148[/C][/ROW]
[ROW][C]28[/C][C]104.9[/C][C]104.661872297259[/C][C]0.238127702740925[/C][/ROW]
[ROW][C]29[/C][C]105.4[/C][C]105.179159786786[/C][C]0.220840213213847[/C][/ROW]
[ROW][C]30[/C][C]105.9[/C][C]105.695192246803[/C][C]0.204807753197031[/C][/ROW]
[ROW][C]31[/C][C]105.5[/C][C]106.210060789386[/C][C]-0.710060789386247[/C][/ROW]
[ROW][C]32[/C][C]106.1[/C][C]105.758512110594[/C][C]0.341487889405911[/C][/ROW]
[ROW][C]33[/C][C]105.4[/C][C]106.383303297188[/C][C]-0.983303297187561[/C][/ROW]
[ROW][C]34[/C][C]105.7[/C][C]105.611917879798[/C][C]0.0880821202015341[/C][/ROW]
[ROW][C]35[/C][C]106.2[/C][C]105.91831242656[/C][C]0.281687573439527[/C][/ROW]
[ROW][C]36[/C][C]106.7[/C][C]106.438762256293[/C][C]0.261237743706602[/C][/ROW]
[ROW][C]37[/C][C]106.8[/C][C]106.957727478342[/C][C]-0.157727478342011[/C][/ROW]
[ROW][C]38[/C][C]106.8[/C][C]107.046276848707[/C][C]-0.246276848706785[/C][/ROW]
[ROW][C]39[/C][C]106.8[/C][C]107.028397751089[/C][C]-0.228397751089105[/C][/ROW]
[ROW][C]40[/C][C]107.3[/C][C]107.011816632284[/C][C]0.288183367716115[/C][/ROW]
[ROW][C]41[/C][C]107.3[/C][C]107.532738040814[/C][C]-0.23273804081353[/C][/ROW]
[ROW][C]42[/C][C]107.5[/C][C]107.515841827577[/C][C]-0.015841827576665[/C][/ROW]
[ROW][C]43[/C][C]107.4[/C][C]107.714691749593[/C][C]-0.314691749592583[/C][/ROW]
[ROW][C]44[/C][C]106.9[/C][C]107.591845897293[/C][C]-0.691845897292652[/C][/ROW]
[ROW][C]45[/C][C]108.1[/C][C]107.041619575172[/C][C]1.05838042482833[/C][/ROW]
[ROW][C]46[/C][C]108.6[/C][C]108.318455408631[/C][C]0.281544591368885[/C][/ROW]
[ROW][C]47[/C][C]108.2[/C][C]108.838894858215[/C][C]-0.638894858214982[/C][/ROW]
[ROW][C]48[/C][C]108.3[/C][C]108.392512652184[/C][C]-0.0925126521836575[/C][/ROW]
[ROW][C]49[/C][C]108.3[/C][C]108.485796459623[/C][C]-0.185796459622523[/C][/ROW]
[ROW][C]50[/C][C]109.3[/C][C]108.472308090512[/C][C]0.827691909487498[/C][/ROW]
[ROW][C]51[/C][C]109.2[/C][C]109.532396501278[/C][C]-0.33239650127787[/C][/ROW]
[ROW][C]52[/C][C]109.4[/C][C]109.408265327254[/C][C]-0.00826532725429274[/C][/ROW]
[ROW][C]53[/C][C]109.7[/C][C]109.607665284686[/C][C]0.0923347153140526[/C][/ROW]
[ROW][C]54[/C][C]109.6[/C][C]109.914368559465[/C][C]-0.314368559465009[/C][/ROW]
[ROW][C]55[/C][C]109.3[/C][C]109.791546169979[/C][C]-0.491546169978847[/C][/ROW]
[ROW][C]56[/C][C]108.4[/C][C]109.455861118774[/C][C]-1.05586111877408[/C][/ROW]
[ROW][C]57[/C][C]108.7[/C][C]108.47920818078[/C][C]0.22079181921994[/C][/ROW]
[ROW][C]58[/C][C]109.4[/C][C]108.795237127511[/C][C]0.604762872488863[/C][/ROW]
[ROW][C]59[/C][C]109[/C][C]109.539141434755[/C][C]-0.53914143475545[/C][/ROW]
[ROW][C]60[/C][C]110.3[/C][C]109.100001083592[/C][C]1.19999891640768[/C][/ROW]
[ROW][C]61[/C][C]109.5[/C][C]110.487118073599[/C][C]-0.987118073598623[/C][/ROW]
[ROW][C]62[/C][C]109.7[/C][C]109.615455712761[/C][C]0.0845442872393107[/C][/ROW]
[ROW][C]63[/C][C]109.5[/C][C]109.821593421492[/C][C]-0.32159342149177[/C][/ROW]
[ROW][C]64[/C][C]110.9[/C][C]109.598246524671[/C][C]1.30175347532882[/C][/ROW]
[ROW][C]65[/C][C]110.9[/C][C]111.092750647092[/C][C]-0.19275064709187[/C][/ROW]
[ROW][C]66[/C][C]110.4[/C][C]111.078757420959[/C][C]-0.678757420959073[/C][/ROW]
[ROW][C]67[/C][C]111.1[/C][C]110.529481290248[/C][C]0.570518709752278[/C][/ROW]
[ROW][C]68[/C][C]110.8[/C][C]111.270899554928[/C][C]-0.470899554928053[/C][/ROW]
[ROW][C]69[/C][C]111.3[/C][C]110.936713397541[/C][C]0.363286602459027[/C][/ROW]
[ROW][C]70[/C][C]111.7[/C][C]111.463087117453[/C][C]0.236912882547202[/C][/ROW]
[ROW][C]71[/C][C]112.2[/C][C]111.880286414001[/C][C]0.319713585998642[/C][/ROW]
[ROW][C]72[/C][C]111.7[/C][C]112.403496839357[/C][C]-0.703496839357157[/C][/ROW]
[ROW][C]73[/C][C]111.3[/C][C]111.852424687303[/C][C]-0.552424687302889[/C][/ROW]
[ROW][C]74[/C][C]111.9[/C][C]111.412320004453[/C][C]0.487679995547239[/C][/ROW]
[ROW][C]75[/C][C]111.7[/C][C]112.047724380838[/C][C]-0.347724380838002[/C][/ROW]
[ROW][C]76[/C][C]111.8[/C][C]111.822480440201[/C][C]-0.02248044020088[/C][/ROW]
[ROW][C]77[/C][C]111.5[/C][C]111.920848415157[/C][C]-0.420848415156897[/C][/ROW]
[ROW][C]78[/C][C]112.9[/C][C]111.590295848254[/C][C]1.30970415174637[/C][/ROW]
[ROW][C]79[/C][C]112[/C][C]113.085377170361[/C][C]-1.08537717036054[/C][/ROW]
[ROW][C]80[/C][C]112.4[/C][C]112.106581439122[/C][C]0.29341856087764[/C][/ROW]
[ROW][C]81[/C][C]111.1[/C][C]112.527882909887[/C][C]-1.42788290988716[/C][/ROW]
[ROW][C]82[/C][C]111.7[/C][C]111.124222098623[/C][C]0.57577790137691[/C][/ROW]
[ROW][C]83[/C][C]111.4[/C][C]111.766022167768[/C][C]-0.366022167768378[/C][/ROW]
[ROW][C]84[/C][C]112.2[/C][C]111.439449852497[/C][C]0.760550147502556[/C][/ROW]
[ROW][C]85[/C][C]112.5[/C][C]112.294663935355[/C][C]0.205336064645195[/C][/ROW]
[ROW][C]86[/C][C]113.2[/C][C]112.609570832059[/C][C]0.590429167941352[/C][/ROW]
[ROW][C]87[/C][C]114.7[/C][C]113.352434547367[/C][C]1.34756545263321[/C][/ROW]
[ROW][C]88[/C][C]115.2[/C][C]114.950264507432[/C][C]0.249735492568462[/C][/ROW]
[ROW][C]89[/C][C]114.1[/C][C]115.468394694145[/C][C]-1.36839469414491[/C][/ROW]
[ROW][C]90[/C][C]113.7[/C][C]114.269052582028[/C][C]-0.56905258202751[/C][/ROW]
[ROW][C]91[/C][C]115.5[/C][C]113.827740754639[/C][C]1.67225924536142[/C][/ROW]
[ROW][C]92[/C][C]115[/C][C]115.749142690902[/C][C]-0.749142690902161[/C][/ROW]
[ROW][C]93[/C][C]115.4[/C][C]115.194756761528[/C][C]0.205243238471837[/C][/ROW]
[ROW][C]94[/C][C]115[/C][C]115.609656919279[/C][C]-0.609656919278606[/C][/ROW]
[ROW][C]95[/C][C]114.6[/C][C]115.165397316192[/C][C]-0.565397316192403[/C][/ROW]
[ROW][C]96[/C][C]114.6[/C][C]114.724350852174[/C][C]-0.124350852174103[/C][/ROW]
[ROW][C]97[/C][C]114.5[/C][C]114.715323284067[/C][C]-0.215323284067154[/C][/ROW]
[ROW][C]98[/C][C]115.2[/C][C]114.59969133963[/C][C]0.600308660370217[/C][/ROW]
[ROW][C]99[/C][C]116.3[/C][C]115.343272281955[/C][C]0.956727718045101[/C][/ROW]
[ROW][C]100[/C][C]116.5[/C][C]116.512728377216[/C][C]-0.0127283772163764[/C][/ROW]
[ROW][C]101[/C][C]118.4[/C][C]116.711804328123[/C][C]1.688195671877[/C][/ROW]
[ROW][C]102[/C][C]118.5[/C][C]118.734363210023[/C][C]-0.234363210022565[/C][/ROW]
[ROW][C]103[/C][C]118.7[/C][C]118.817349013471[/C][C]-0.117349013471028[/C][/ROW]
[ROW][C]104[/C][C]119.2[/C][C]119.00882976175[/C][C]0.191170238249967[/C][/ROW]
[ROW][C]105[/C][C]119.5[/C][C]119.522708254061[/C][C]-0.0227082540614845[/C][/ROW]
[ROW][C]106[/C][C]118.5[/C][C]119.821059690288[/C][C]-1.32105969028773[/C][/ROW]
[ROW][C]107[/C][C]118.6[/C][C]118.725153983822[/C][C]-0.125153983821733[/C][/ROW]
[ROW][C]108[/C][C]118.2[/C][C]118.816068110319[/C][C]-0.61606811031902[/C][/ROW]
[ROW][C]109[/C][C]118.6[/C][C]118.371343070424[/C][C]0.228656929575607[/C][/ROW]
[ROW][C]110[/C][C]120.6[/C][C]118.787943004955[/C][C]1.81205699504538[/C][/ROW]
[ROW][C]111[/C][C]124.5[/C][C]120.919493916351[/C][C]3.58050608364891[/C][/ROW]
[ROW][C]112[/C][C]124.6[/C][C]125.079429911661[/C][C]-0.479429911660603[/C][/ROW]
[ROW][C]113[/C][C]126.5[/C][C]125.144624471212[/C][C]1.35537552878755[/C][/ROW]
[ROW][C]114[/C][C]126[/C][C]127.143021423728[/C][C]-1.14302142372775[/C][/ROW]
[ROW][C]115[/C][C]126.3[/C][C]126.560040860507[/C][C]-0.260040860506933[/C][/ROW]
[ROW][C]116[/C][C]126.3[/C][C]126.841162529255[/C][C]-0.541162529254905[/C][/ROW]
[ROW][C]117[/C][C]125.1[/C][C]126.801875451568[/C][C]-1.7018754515682[/C][/ROW]
[ROW][C]118[/C][C]126.7[/C][C]125.47832345108[/C][C]1.22167654892036[/C][/ROW]
[ROW][C]119[/C][C]123.9[/C][C]127.167014184253[/C][C]-3.26701418425284[/C][/ROW]
[ROW][C]120[/C][C]123.6[/C][C]124.12983693505[/C][C]-0.529836935049985[/C][/ROW]
[ROW][C]121[/C][C]124.9[/C][C]123.791372067837[/C][C]1.10862793216333[/C][/ROW]
[ROW][C]122[/C][C]126.2[/C][C]125.171855747585[/C][C]1.02814425241459[/C][/ROW]
[ROW][C]123[/C][C]126.3[/C][C]126.546496508788[/C][C]-0.246496508787743[/C][/ROW]
[ROW][C]124[/C][C]126.4[/C][C]126.628601464385[/C][C]-0.228601464384738[/C][/ROW]
[ROW][C]125[/C][C]126.2[/C][C]126.712005556492[/C][C]-0.5120055564919[/C][/ROW]
[ROW][C]126[/C][C]125.8[/C][C]126.474835203804[/C][C]-0.674835203803909[/C][/ROW]
[ROW][C]127[/C][C]124.9[/C][C]126.025843816477[/C][C]-1.12584381647692[/C][/ROW]
[ROW][C]128[/C][C]126.2[/C][C]125.044110305582[/C][C]1.15588969441848[/C][/ROW]
[ROW][C]129[/C][C]125.9[/C][C]126.42802507382[/C][C]-0.528025073820217[/C][/ROW]
[ROW][C]130[/C][C]124.6[/C][C]126.089691743306[/C][C]-1.48969174330625[/C][/ROW]
[ROW][C]131[/C][C]122.9[/C][C]124.681543761721[/C][C]-1.7815437617209[/C][/ROW]
[ROW][C]132[/C][C]119.9[/C][C]122.852208036527[/C][C]-2.95220803652688[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161078&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161078&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	100.1	100.3	-0.200000000000017
4	100.2	100.685480488555	-0.485480488554586
5	100.1	100.750235791004	-0.65023579100415
6	100.4	100.603030260956	-0.203030260955629
7	99.8	100.888290759967	-1.08829075996709
8	99.7	100.209283509241	-0.509283509240703
9	99.4	100.072310770534	-0.672310770533812
10	100.2	99.7235026508956	0.476497349104363
11	100.5	100.558095194466	-0.0580951944657784
12	100.6	100.853877625261	-0.253877625260927
13	100.9	100.935446729832	-0.0354467298323584
14	101.9	101.232873383835	0.667126616165135
15	102.1	102.28130514653	-0.18130514652961
16	102.6	102.468142835779	0.131857164221145
17	103.5	102.977715343804	0.522284656195808
18	103.9	103.915631934021	-0.0156319340211724
19	103.7	104.314497093797	-0.614497093796516
20	103	104.069886105864	-1.06988610586376
21	103.1	103.292214988067	-0.192214988066894
22	103.2	103.378260649471	-0.178260649470801
23	103.2	103.46531936177	-0.265319361769528
24	103.1	103.44605782422	-0.346057824220026
25	103.7	103.320934871522	0.379065128477677
26	104.2	103.94845407388	0.25154592612023
27	104.4	104.466715693647	-0.0667156936465148
28	104.9	104.661872297259	0.238127702740925
29	105.4	105.179159786786	0.220840213213847
30	105.9	105.695192246803	0.204807753197031
31	105.5	106.210060789386	-0.710060789386247
32	106.1	105.758512110594	0.341487889405911
33	105.4	106.383303297188	-0.983303297187561
34	105.7	105.611917879798	0.0880821202015341
35	106.2	105.91831242656	0.281687573439527
36	106.7	106.438762256293	0.261237743706602
37	106.8	106.957727478342	-0.157727478342011
38	106.8	107.046276848707	-0.246276848706785
39	106.8	107.028397751089	-0.228397751089105
40	107.3	107.011816632284	0.288183367716115
41	107.3	107.532738040814	-0.23273804081353
42	107.5	107.515841827577	-0.015841827576665
43	107.4	107.714691749593	-0.314691749592583
44	106.9	107.591845897293	-0.691845897292652
45	108.1	107.041619575172	1.05838042482833
46	108.6	108.318455408631	0.281544591368885
47	108.2	108.838894858215	-0.638894858214982
48	108.3	108.392512652184	-0.0925126521836575
49	108.3	108.485796459623	-0.185796459622523
50	109.3	108.472308090512	0.827691909487498
51	109.2	109.532396501278	-0.33239650127787
52	109.4	109.408265327254	-0.00826532725429274
53	109.7	109.607665284686	0.0923347153140526
54	109.6	109.914368559465	-0.314368559465009
55	109.3	109.791546169979	-0.491546169978847
56	108.4	109.455861118774	-1.05586111877408
57	108.7	108.47920818078	0.22079181921994
58	109.4	108.795237127511	0.604762872488863
59	109	109.539141434755	-0.53914143475545
60	110.3	109.100001083592	1.19999891640768
61	109.5	110.487118073599	-0.987118073598623
62	109.7	109.615455712761	0.0845442872393107
63	109.5	109.821593421492	-0.32159342149177
64	110.9	109.598246524671	1.30175347532882
65	110.9	111.092750647092	-0.19275064709187
66	110.4	111.078757420959	-0.678757420959073
67	111.1	110.529481290248	0.570518709752278
68	110.8	111.270899554928	-0.470899554928053
69	111.3	110.936713397541	0.363286602459027
70	111.7	111.463087117453	0.236912882547202
71	112.2	111.880286414001	0.319713585998642
72	111.7	112.403496839357	-0.703496839357157
73	111.3	111.852424687303	-0.552424687302889
74	111.9	111.412320004453	0.487679995547239
75	111.7	112.047724380838	-0.347724380838002
76	111.8	111.822480440201	-0.02248044020088
77	111.5	111.920848415157	-0.420848415156897
78	112.9	111.590295848254	1.30970415174637
79	112	113.085377170361	-1.08537717036054
80	112.4	112.106581439122	0.29341856087764
81	111.1	112.527882909887	-1.42788290988716
82	111.7	111.124222098623	0.57577790137691
83	111.4	111.766022167768	-0.366022167768378
84	112.2	111.439449852497	0.760550147502556
85	112.5	112.294663935355	0.205336064645195
86	113.2	112.609570832059	0.590429167941352
87	114.7	113.352434547367	1.34756545263321
88	115.2	114.950264507432	0.249735492568462
89	114.1	115.468394694145	-1.36839469414491
90	113.7	114.269052582028	-0.56905258202751
91	115.5	113.827740754639	1.67225924536142
92	115	115.749142690902	-0.749142690902161
93	115.4	115.194756761528	0.205243238471837
94	115	115.609656919279	-0.609656919278606
95	114.6	115.165397316192	-0.565397316192403
96	114.6	114.724350852174	-0.124350852174103
97	114.5	114.715323284067	-0.215323284067154
98	115.2	114.59969133963	0.600308660370217
99	116.3	115.343272281955	0.956727718045101
100	116.5	116.512728377216	-0.0127283772163764
101	118.4	116.711804328123	1.688195671877
102	118.5	118.734363210023	-0.234363210022565
103	118.7	118.817349013471	-0.117349013471028
104	119.2	119.00882976175	0.191170238249967
105	119.5	119.522708254061	-0.0227082540614845
106	118.5	119.821059690288	-1.32105969028773
107	118.6	118.725153983822	-0.125153983821733
108	118.2	118.816068110319	-0.61606811031902
109	118.6	118.371343070424	0.228656929575607
110	120.6	118.787943004955	1.81205699504538
111	124.5	120.919493916351	3.58050608364891
112	124.6	125.079429911661	-0.479429911660603
113	126.5	125.144624471212	1.35537552878755
114	126	127.143021423728	-1.14302142372775
115	126.3	126.560040860507	-0.260040860506933
116	126.3	126.841162529255	-0.541162529254905
117	125.1	126.801875451568	-1.7018754515682
118	126.7	125.47832345108	1.22167654892036
119	123.9	127.167014184253	-3.26701418425284
120	123.6	124.12983693505	-0.529836935049985
121	124.9	123.791372067837	1.10862793216333
122	126.2	125.171855747585	1.02814425241459
123	126.3	126.546496508788	-0.246496508787743
124	126.4	126.628601464385	-0.228601464384738
125	126.2	126.712005556492	-0.5120055564919
126	125.8	126.474835203804	-0.674835203803909
127	124.9	126.025843816477	-1.12584381647692
128	126.2	125.044110305582	1.15588969441848
129	125.9	126.42802507382	-0.528025073820217
130	124.6	126.089691743306	-1.48969174330625
131	122.9	124.681543761721	-1.7815437617209
132	119.9	122.852208036527	-2.95220803652688

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
133	119.637884944649	117.953708581719	121.322061307579
134	119.375769889298	116.906015251751	121.845524526845
135	119.113654833947	115.980028767035	122.247280900859
136	118.851539778596	115.106393376032	122.59668618116
137	118.589424723245	114.259399988854	122.919449457636
138	118.327309667894	113.426443552484	123.228175783304
139	118.065194612543	112.600385054892	123.530004170193
140	117.803079557192	111.776805655051	123.829353459332
141	117.540964501841	110.952801776892	124.129127226789
142	117.27884944649	110.126383100936	124.431315792043
143	117.016734391139	109.296142715122	124.737326067156
144	116.754619335788	108.461063428731	125.048175242844

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
133 & 119.637884944649 & 117.953708581719 & 121.322061307579 \tabularnewline
134 & 119.375769889298 & 116.906015251751 & 121.845524526845 \tabularnewline
135 & 119.113654833947 & 115.980028767035 & 122.247280900859 \tabularnewline
136 & 118.851539778596 & 115.106393376032 & 122.59668618116 \tabularnewline
137 & 118.589424723245 & 114.259399988854 & 122.919449457636 \tabularnewline
138 & 118.327309667894 & 113.426443552484 & 123.228175783304 \tabularnewline
139 & 118.065194612543 & 112.600385054892 & 123.530004170193 \tabularnewline
140 & 117.803079557192 & 111.776805655051 & 123.829353459332 \tabularnewline
141 & 117.540964501841 & 110.952801776892 & 124.129127226789 \tabularnewline
142 & 117.27884944649 & 110.126383100936 & 124.431315792043 \tabularnewline
143 & 117.016734391139 & 109.296142715122 & 124.737326067156 \tabularnewline
144 & 116.754619335788 & 108.461063428731 & 125.048175242844 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161078&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]133[/C][C]119.637884944649[/C][C]117.953708581719[/C][C]121.322061307579[/C][/ROW]
[ROW][C]134[/C][C]119.375769889298[/C][C]116.906015251751[/C][C]121.845524526845[/C][/ROW]
[ROW][C]135[/C][C]119.113654833947[/C][C]115.980028767035[/C][C]122.247280900859[/C][/ROW]
[ROW][C]136[/C][C]118.851539778596[/C][C]115.106393376032[/C][C]122.59668618116[/C][/ROW]
[ROW][C]137[/C][C]118.589424723245[/C][C]114.259399988854[/C][C]122.919449457636[/C][/ROW]
[ROW][C]138[/C][C]118.327309667894[/C][C]113.426443552484[/C][C]123.228175783304[/C][/ROW]
[ROW][C]139[/C][C]118.065194612543[/C][C]112.600385054892[/C][C]123.530004170193[/C][/ROW]
[ROW][C]140[/C][C]117.803079557192[/C][C]111.776805655051[/C][C]123.829353459332[/C][/ROW]
[ROW][C]141[/C][C]117.540964501841[/C][C]110.952801776892[/C][C]124.129127226789[/C][/ROW]
[ROW][C]142[/C][C]117.27884944649[/C][C]110.126383100936[/C][C]124.431315792043[/C][/ROW]
[ROW][C]143[/C][C]117.016734391139[/C][C]109.296142715122[/C][C]124.737326067156[/C][/ROW]
[ROW][C]144[/C][C]116.754619335788[/C][C]108.461063428731[/C][C]125.048175242844[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161078&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161078&T=3

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
133	119.637884944649	117.953708581719	121.322061307579
134	119.375769889298	116.906015251751	121.845524526845
135	119.113654833947	115.980028767035	122.247280900859
136	118.851539778596	115.106393376032	122.59668618116
137	118.589424723245	114.259399988854	122.919449457636
138	118.327309667894	113.426443552484	123.228175783304
139	118.065194612543	112.600385054892	123.530004170193
140	117.803079557192	111.776805655051	123.829353459332
141	117.540964501841	110.952801776892	124.129127226789
142	117.27884944649	110.126383100936	124.431315792043
143	117.016734391139	109.296142715122	124.737326067156
144	116.754619335788	108.461063428731	125.048175242844

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Double ; par3 = multiplicative ;

R code (references can be found in the software module):

par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code