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R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Sat, 29 Nov 2014 14:36:26 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Nov/29/t1417271817nty0aul48mjmh3x.htm/, Retrieved Sun, 19 May 2024 14:46:05 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=261142, Retrieved Sun, 19 May 2024 14:46:05 +0000

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Estimated Impact

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

-       [Exponential Smoothing] [] [2014-11-29 14:36:26] [beda3c52974d0e45a2203fe962302ec0] [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	2 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net
R Framework error message	Warning: there are blank lines in the 'Data' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.

\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 & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
R Framework error message & Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values. \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261142&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261142&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261142&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	2 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net
R Framework error message	Warning: there are blank lines in the 'Data' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.00978900094391386
gamma	1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.00978900094391386 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261142&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]0.00978900094391386[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261142&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261142&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	0.00978900094391386
gamma	1

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	105.16	103.408632478633	1.75136752136748
14	105.16	105.180675606851	-0.0206756068512846
15	105.16	105.190889879983	-0.0308898799829365
16	105.16	105.237670832252	-0.0776708322519539
17	105.16	105.280660512402	-0.12066051240177
18	105.17	105.289896033199	-0.119896033198629
19	105.17	105.109139037483	0.0608609625168555
20	105.54	105.624734805503	-0.0847348055026629
21	106.9	106.968488669745	-0.0684886697449514
22	107.27	108.253651567425	-0.983651567425497
23	107.31	107.303605934637	0.00639406536315335
24	107.39	107.351168526149	0.0388314738513174
25	107.41	107.006131980816	0.403868019183776
26	107.46	107.420918778571	0.0390812214294414
27	113.14	107.481718011351	5.65828198864934
28	117	113.264190272412	3.73580972758818
29	119.28	117.204510117361	2.07548988263851
30	119.39	119.515243756448	-0.125243756448398
31	119.5	119.434434411865	0.0655655881350441
32	119.67	120.060076233469	-0.390076233469102
33	119.67	121.200841110185	-1.5308411101848
34	119.73	121.111689038446	-1.38168903844553
35	119.77	119.847747016477	-0.0777470164773746
36	119.77	119.89448595086	-0.124485950859651
37	119.78	119.467850691103	0.312149308897474
38	119.78	119.871739654315	-0.0917396543153046
39	119.78	119.881258281419	-0.101258281419263
40	121.28	119.92735039734	1.3526496026598
41	122.44	121.484341485577	0.955658514422538
42	122.72	122.664113094344	0.0558869056561377
43	122.75	122.755076837983	-0.00507683798274172
44	122.8	123.300027140811	-0.500027140810943
45	122.81	124.319715707991	-1.50971570799088
46	122.83	124.240770432834	-1.41077043283364
47	122.83	122.936543733068	-0.106543733068364
48	122.83	122.943000776365	-0.113000776364743
49	122.84	122.516477944992	0.323522055008411
50	122.85	122.920478236027	-0.0704782360268013
51	123.61	122.940204991174	0.66979500882556
52	124.74	123.753844948481	0.986155051518594
53	125.1	124.937248421212	0.162751578788416
54	125.29	125.309258263237	-0.0192582632366367
55	125.45	125.309486410746	0.1405135892537
56	125.51	125.985861898404	-0.475861898404133
57	125.55	127.015787019165	-1.46578701916482
58	125.57	126.967271761984	-1.39727176198394
59	125.81	125.66317720072	0.146822799279661
60	127.41	125.912114449241	1.49788555075894
61	127.75	127.101360585645	0.648639414355344
62	127.76	127.838543450817	-0.0785434508173779
63	127.8	127.85819125557	-0.0581912555698381
64	128.23	127.944704954647	0.285295045352512
65	130.01	128.421247708116	1.58875229188425
66	130.07	130.227216672467	-0.157216672467314
67	130.17	130.096094344979	0.0739056550212069
68	130.21	130.711817807506	-0.501817807505518
69	130.22	131.721488845848	-1.50148884584755
70	130.23	131.642624103452	-1.41262410345158
71	130.23	130.328379258103	-0.0983792581028808
72	130.23	130.334916223452	-0.104916223452392
73	130.23	129.908472531775	0.321527468224673
74	130.24	130.302453297799	-0.0624532977986405
75	130.13	130.322258609074	-0.192258609074145
76	130.14	130.257459922702	-0.117459922701812
77	130.79	130.310060107408	0.47993989259237
78	131.38	130.975174906136	0.404825093864105
79	131.61	131.379554406028	0.230445593971524
80	131.72	132.126810238165	-0.406810238165434
81	131.89	133.207411305693	-1.31741130569335
82	131.89	133.290348498512	-1.4003484985117
83	131.96	131.966223819071	-0.0062238190713515
84	131.99	132.043662894101	-0.0536628941005404
85	132	131.647720921313	0.352279078687104
86	132.06	132.05200271488	0.00799728511995568
87	132.11	132.122497666978	-0.01249766697822
88	132.88	132.219458660638	0.660541339362254
89	135.48	133.039674700432	2.44032529956769
90	136.56	135.67397971376	0.886020286240125
91	136.96	136.573069633845	0.386930366155156
92	137.4	137.491857295564	-0.091857295564381
93	138.32	138.905541437745	-0.585541437744752
94	138.82	139.745642905391	-0.925642905391271
95	138.96	138.92616511945	0.0338348805499606
96	138.94	139.073996329128	-0.133996329127626
97	139	138.627267972269	0.372732027731331
98	139.19	139.081749979773	0.108250020226677
99	139.22	139.28322630599	-0.0632263059900993
100	139.37	139.359690716954	0.010309283045558
101	140.74	139.553541634536	1.18645836546406
102	141.17	140.945572543262	0.224427456737942
103	141.51	141.188186130515	0.321813869485482
104	142.94	142.046336366787	0.893663633213293
105	144.81	144.459667774269	0.350332225730909
106	145.41	146.258930510091	-0.848930510090781
107	146.11	145.54020366186	0.569796338140435
108	146.23	146.253281398751	-0.0232813987514362

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 105.16 & 103.408632478633 & 1.75136752136748 \tabularnewline
14 & 105.16 & 105.180675606851 & -0.0206756068512846 \tabularnewline
15 & 105.16 & 105.190889879983 & -0.0308898799829365 \tabularnewline
16 & 105.16 & 105.237670832252 & -0.0776708322519539 \tabularnewline
17 & 105.16 & 105.280660512402 & -0.12066051240177 \tabularnewline
18 & 105.17 & 105.289896033199 & -0.119896033198629 \tabularnewline
19 & 105.17 & 105.109139037483 & 0.0608609625168555 \tabularnewline
20 & 105.54 & 105.624734805503 & -0.0847348055026629 \tabularnewline
21 & 106.9 & 106.968488669745 & -0.0684886697449514 \tabularnewline
22 & 107.27 & 108.253651567425 & -0.983651567425497 \tabularnewline
23 & 107.31 & 107.303605934637 & 0.00639406536315335 \tabularnewline
24 & 107.39 & 107.351168526149 & 0.0388314738513174 \tabularnewline
25 & 107.41 & 107.006131980816 & 0.403868019183776 \tabularnewline
26 & 107.46 & 107.420918778571 & 0.0390812214294414 \tabularnewline
27 & 113.14 & 107.481718011351 & 5.65828198864934 \tabularnewline
28 & 117 & 113.264190272412 & 3.73580972758818 \tabularnewline
29 & 119.28 & 117.204510117361 & 2.07548988263851 \tabularnewline
30 & 119.39 & 119.515243756448 & -0.125243756448398 \tabularnewline
31 & 119.5 & 119.434434411865 & 0.0655655881350441 \tabularnewline
32 & 119.67 & 120.060076233469 & -0.390076233469102 \tabularnewline
33 & 119.67 & 121.200841110185 & -1.5308411101848 \tabularnewline
34 & 119.73 & 121.111689038446 & -1.38168903844553 \tabularnewline
35 & 119.77 & 119.847747016477 & -0.0777470164773746 \tabularnewline
36 & 119.77 & 119.89448595086 & -0.124485950859651 \tabularnewline
37 & 119.78 & 119.467850691103 & 0.312149308897474 \tabularnewline
38 & 119.78 & 119.871739654315 & -0.0917396543153046 \tabularnewline
39 & 119.78 & 119.881258281419 & -0.101258281419263 \tabularnewline
40 & 121.28 & 119.92735039734 & 1.3526496026598 \tabularnewline
41 & 122.44 & 121.484341485577 & 0.955658514422538 \tabularnewline
42 & 122.72 & 122.664113094344 & 0.0558869056561377 \tabularnewline
43 & 122.75 & 122.755076837983 & -0.00507683798274172 \tabularnewline
44 & 122.8 & 123.300027140811 & -0.500027140810943 \tabularnewline
45 & 122.81 & 124.319715707991 & -1.50971570799088 \tabularnewline
46 & 122.83 & 124.240770432834 & -1.41077043283364 \tabularnewline
47 & 122.83 & 122.936543733068 & -0.106543733068364 \tabularnewline
48 & 122.83 & 122.943000776365 & -0.113000776364743 \tabularnewline
49 & 122.84 & 122.516477944992 & 0.323522055008411 \tabularnewline
50 & 122.85 & 122.920478236027 & -0.0704782360268013 \tabularnewline
51 & 123.61 & 122.940204991174 & 0.66979500882556 \tabularnewline
52 & 124.74 & 123.753844948481 & 0.986155051518594 \tabularnewline
53 & 125.1 & 124.937248421212 & 0.162751578788416 \tabularnewline
54 & 125.29 & 125.309258263237 & -0.0192582632366367 \tabularnewline
55 & 125.45 & 125.309486410746 & 0.1405135892537 \tabularnewline
56 & 125.51 & 125.985861898404 & -0.475861898404133 \tabularnewline
57 & 125.55 & 127.015787019165 & -1.46578701916482 \tabularnewline
58 & 125.57 & 126.967271761984 & -1.39727176198394 \tabularnewline
59 & 125.81 & 125.66317720072 & 0.146822799279661 \tabularnewline
60 & 127.41 & 125.912114449241 & 1.49788555075894 \tabularnewline
61 & 127.75 & 127.101360585645 & 0.648639414355344 \tabularnewline
62 & 127.76 & 127.838543450817 & -0.0785434508173779 \tabularnewline
63 & 127.8 & 127.85819125557 & -0.0581912555698381 \tabularnewline
64 & 128.23 & 127.944704954647 & 0.285295045352512 \tabularnewline
65 & 130.01 & 128.421247708116 & 1.58875229188425 \tabularnewline
66 & 130.07 & 130.227216672467 & -0.157216672467314 \tabularnewline
67 & 130.17 & 130.096094344979 & 0.0739056550212069 \tabularnewline
68 & 130.21 & 130.711817807506 & -0.501817807505518 \tabularnewline
69 & 130.22 & 131.721488845848 & -1.50148884584755 \tabularnewline
70 & 130.23 & 131.642624103452 & -1.41262410345158 \tabularnewline
71 & 130.23 & 130.328379258103 & -0.0983792581028808 \tabularnewline
72 & 130.23 & 130.334916223452 & -0.104916223452392 \tabularnewline
73 & 130.23 & 129.908472531775 & 0.321527468224673 \tabularnewline
74 & 130.24 & 130.302453297799 & -0.0624532977986405 \tabularnewline
75 & 130.13 & 130.322258609074 & -0.192258609074145 \tabularnewline
76 & 130.14 & 130.257459922702 & -0.117459922701812 \tabularnewline
77 & 130.79 & 130.310060107408 & 0.47993989259237 \tabularnewline
78 & 131.38 & 130.975174906136 & 0.404825093864105 \tabularnewline
79 & 131.61 & 131.379554406028 & 0.230445593971524 \tabularnewline
80 & 131.72 & 132.126810238165 & -0.406810238165434 \tabularnewline
81 & 131.89 & 133.207411305693 & -1.31741130569335 \tabularnewline
82 & 131.89 & 133.290348498512 & -1.4003484985117 \tabularnewline
83 & 131.96 & 131.966223819071 & -0.0062238190713515 \tabularnewline
84 & 131.99 & 132.043662894101 & -0.0536628941005404 \tabularnewline
85 & 132 & 131.647720921313 & 0.352279078687104 \tabularnewline
86 & 132.06 & 132.05200271488 & 0.00799728511995568 \tabularnewline
87 & 132.11 & 132.122497666978 & -0.01249766697822 \tabularnewline
88 & 132.88 & 132.219458660638 & 0.660541339362254 \tabularnewline
89 & 135.48 & 133.039674700432 & 2.44032529956769 \tabularnewline
90 & 136.56 & 135.67397971376 & 0.886020286240125 \tabularnewline
91 & 136.96 & 136.573069633845 & 0.386930366155156 \tabularnewline
92 & 137.4 & 137.491857295564 & -0.091857295564381 \tabularnewline
93 & 138.32 & 138.905541437745 & -0.585541437744752 \tabularnewline
94 & 138.82 & 139.745642905391 & -0.925642905391271 \tabularnewline
95 & 138.96 & 138.92616511945 & 0.0338348805499606 \tabularnewline
96 & 138.94 & 139.073996329128 & -0.133996329127626 \tabularnewline
97 & 139 & 138.627267972269 & 0.372732027731331 \tabularnewline
98 & 139.19 & 139.081749979773 & 0.108250020226677 \tabularnewline
99 & 139.22 & 139.28322630599 & -0.0632263059900993 \tabularnewline
100 & 139.37 & 139.359690716954 & 0.010309283045558 \tabularnewline
101 & 140.74 & 139.553541634536 & 1.18645836546406 \tabularnewline
102 & 141.17 & 140.945572543262 & 0.224427456737942 \tabularnewline
103 & 141.51 & 141.188186130515 & 0.321813869485482 \tabularnewline
104 & 142.94 & 142.046336366787 & 0.893663633213293 \tabularnewline
105 & 144.81 & 144.459667774269 & 0.350332225730909 \tabularnewline
106 & 145.41 & 146.258930510091 & -0.848930510090781 \tabularnewline
107 & 146.11 & 145.54020366186 & 0.569796338140435 \tabularnewline
108 & 146.23 & 146.253281398751 & -0.0232813987514362 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261142&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]13[/C][C]105.16[/C][C]103.408632478633[/C][C]1.75136752136748[/C][/ROW]
[ROW][C]14[/C][C]105.16[/C][C]105.180675606851[/C][C]-0.0206756068512846[/C][/ROW]
[ROW][C]15[/C][C]105.16[/C][C]105.190889879983[/C][C]-0.0308898799829365[/C][/ROW]
[ROW][C]16[/C][C]105.16[/C][C]105.237670832252[/C][C]-0.0776708322519539[/C][/ROW]
[ROW][C]17[/C][C]105.16[/C][C]105.280660512402[/C][C]-0.12066051240177[/C][/ROW]
[ROW][C]18[/C][C]105.17[/C][C]105.289896033199[/C][C]-0.119896033198629[/C][/ROW]
[ROW][C]19[/C][C]105.17[/C][C]105.109139037483[/C][C]0.0608609625168555[/C][/ROW]
[ROW][C]20[/C][C]105.54[/C][C]105.624734805503[/C][C]-0.0847348055026629[/C][/ROW]
[ROW][C]21[/C][C]106.9[/C][C]106.968488669745[/C][C]-0.0684886697449514[/C][/ROW]
[ROW][C]22[/C][C]107.27[/C][C]108.253651567425[/C][C]-0.983651567425497[/C][/ROW]
[ROW][C]23[/C][C]107.31[/C][C]107.303605934637[/C][C]0.00639406536315335[/C][/ROW]
[ROW][C]24[/C][C]107.39[/C][C]107.351168526149[/C][C]0.0388314738513174[/C][/ROW]
[ROW][C]25[/C][C]107.41[/C][C]107.006131980816[/C][C]0.403868019183776[/C][/ROW]
[ROW][C]26[/C][C]107.46[/C][C]107.420918778571[/C][C]0.0390812214294414[/C][/ROW]
[ROW][C]27[/C][C]113.14[/C][C]107.481718011351[/C][C]5.65828198864934[/C][/ROW]
[ROW][C]28[/C][C]117[/C][C]113.264190272412[/C][C]3.73580972758818[/C][/ROW]
[ROW][C]29[/C][C]119.28[/C][C]117.204510117361[/C][C]2.07548988263851[/C][/ROW]
[ROW][C]30[/C][C]119.39[/C][C]119.515243756448[/C][C]-0.125243756448398[/C][/ROW]
[ROW][C]31[/C][C]119.5[/C][C]119.434434411865[/C][C]0.0655655881350441[/C][/ROW]
[ROW][C]32[/C][C]119.67[/C][C]120.060076233469[/C][C]-0.390076233469102[/C][/ROW]
[ROW][C]33[/C][C]119.67[/C][C]121.200841110185[/C][C]-1.5308411101848[/C][/ROW]
[ROW][C]34[/C][C]119.73[/C][C]121.111689038446[/C][C]-1.38168903844553[/C][/ROW]
[ROW][C]35[/C][C]119.77[/C][C]119.847747016477[/C][C]-0.0777470164773746[/C][/ROW]
[ROW][C]36[/C][C]119.77[/C][C]119.89448595086[/C][C]-0.124485950859651[/C][/ROW]
[ROW][C]37[/C][C]119.78[/C][C]119.467850691103[/C][C]0.312149308897474[/C][/ROW]
[ROW][C]38[/C][C]119.78[/C][C]119.871739654315[/C][C]-0.0917396543153046[/C][/ROW]
[ROW][C]39[/C][C]119.78[/C][C]119.881258281419[/C][C]-0.101258281419263[/C][/ROW]
[ROW][C]40[/C][C]121.28[/C][C]119.92735039734[/C][C]1.3526496026598[/C][/ROW]
[ROW][C]41[/C][C]122.44[/C][C]121.484341485577[/C][C]0.955658514422538[/C][/ROW]
[ROW][C]42[/C][C]122.72[/C][C]122.664113094344[/C][C]0.0558869056561377[/C][/ROW]
[ROW][C]43[/C][C]122.75[/C][C]122.755076837983[/C][C]-0.00507683798274172[/C][/ROW]
[ROW][C]44[/C][C]122.8[/C][C]123.300027140811[/C][C]-0.500027140810943[/C][/ROW]
[ROW][C]45[/C][C]122.81[/C][C]124.319715707991[/C][C]-1.50971570799088[/C][/ROW]
[ROW][C]46[/C][C]122.83[/C][C]124.240770432834[/C][C]-1.41077043283364[/C][/ROW]
[ROW][C]47[/C][C]122.83[/C][C]122.936543733068[/C][C]-0.106543733068364[/C][/ROW]
[ROW][C]48[/C][C]122.83[/C][C]122.943000776365[/C][C]-0.113000776364743[/C][/ROW]
[ROW][C]49[/C][C]122.84[/C][C]122.516477944992[/C][C]0.323522055008411[/C][/ROW]
[ROW][C]50[/C][C]122.85[/C][C]122.920478236027[/C][C]-0.0704782360268013[/C][/ROW]
[ROW][C]51[/C][C]123.61[/C][C]122.940204991174[/C][C]0.66979500882556[/C][/ROW]
[ROW][C]52[/C][C]124.74[/C][C]123.753844948481[/C][C]0.986155051518594[/C][/ROW]
[ROW][C]53[/C][C]125.1[/C][C]124.937248421212[/C][C]0.162751578788416[/C][/ROW]
[ROW][C]54[/C][C]125.29[/C][C]125.309258263237[/C][C]-0.0192582632366367[/C][/ROW]
[ROW][C]55[/C][C]125.45[/C][C]125.309486410746[/C][C]0.1405135892537[/C][/ROW]
[ROW][C]56[/C][C]125.51[/C][C]125.985861898404[/C][C]-0.475861898404133[/C][/ROW]
[ROW][C]57[/C][C]125.55[/C][C]127.015787019165[/C][C]-1.46578701916482[/C][/ROW]
[ROW][C]58[/C][C]125.57[/C][C]126.967271761984[/C][C]-1.39727176198394[/C][/ROW]
[ROW][C]59[/C][C]125.81[/C][C]125.66317720072[/C][C]0.146822799279661[/C][/ROW]
[ROW][C]60[/C][C]127.41[/C][C]125.912114449241[/C][C]1.49788555075894[/C][/ROW]
[ROW][C]61[/C][C]127.75[/C][C]127.101360585645[/C][C]0.648639414355344[/C][/ROW]
[ROW][C]62[/C][C]127.76[/C][C]127.838543450817[/C][C]-0.0785434508173779[/C][/ROW]
[ROW][C]63[/C][C]127.8[/C][C]127.85819125557[/C][C]-0.0581912555698381[/C][/ROW]
[ROW][C]64[/C][C]128.23[/C][C]127.944704954647[/C][C]0.285295045352512[/C][/ROW]
[ROW][C]65[/C][C]130.01[/C][C]128.421247708116[/C][C]1.58875229188425[/C][/ROW]
[ROW][C]66[/C][C]130.07[/C][C]130.227216672467[/C][C]-0.157216672467314[/C][/ROW]
[ROW][C]67[/C][C]130.17[/C][C]130.096094344979[/C][C]0.0739056550212069[/C][/ROW]
[ROW][C]68[/C][C]130.21[/C][C]130.711817807506[/C][C]-0.501817807505518[/C][/ROW]
[ROW][C]69[/C][C]130.22[/C][C]131.721488845848[/C][C]-1.50148884584755[/C][/ROW]
[ROW][C]70[/C][C]130.23[/C][C]131.642624103452[/C][C]-1.41262410345158[/C][/ROW]
[ROW][C]71[/C][C]130.23[/C][C]130.328379258103[/C][C]-0.0983792581028808[/C][/ROW]
[ROW][C]72[/C][C]130.23[/C][C]130.334916223452[/C][C]-0.104916223452392[/C][/ROW]
[ROW][C]73[/C][C]130.23[/C][C]129.908472531775[/C][C]0.321527468224673[/C][/ROW]
[ROW][C]74[/C][C]130.24[/C][C]130.302453297799[/C][C]-0.0624532977986405[/C][/ROW]
[ROW][C]75[/C][C]130.13[/C][C]130.322258609074[/C][C]-0.192258609074145[/C][/ROW]
[ROW][C]76[/C][C]130.14[/C][C]130.257459922702[/C][C]-0.117459922701812[/C][/ROW]
[ROW][C]77[/C][C]130.79[/C][C]130.310060107408[/C][C]0.47993989259237[/C][/ROW]
[ROW][C]78[/C][C]131.38[/C][C]130.975174906136[/C][C]0.404825093864105[/C][/ROW]
[ROW][C]79[/C][C]131.61[/C][C]131.379554406028[/C][C]0.230445593971524[/C][/ROW]
[ROW][C]80[/C][C]131.72[/C][C]132.126810238165[/C][C]-0.406810238165434[/C][/ROW]
[ROW][C]81[/C][C]131.89[/C][C]133.207411305693[/C][C]-1.31741130569335[/C][/ROW]
[ROW][C]82[/C][C]131.89[/C][C]133.290348498512[/C][C]-1.4003484985117[/C][/ROW]
[ROW][C]83[/C][C]131.96[/C][C]131.966223819071[/C][C]-0.0062238190713515[/C][/ROW]
[ROW][C]84[/C][C]131.99[/C][C]132.043662894101[/C][C]-0.0536628941005404[/C][/ROW]
[ROW][C]85[/C][C]132[/C][C]131.647720921313[/C][C]0.352279078687104[/C][/ROW]
[ROW][C]86[/C][C]132.06[/C][C]132.05200271488[/C][C]0.00799728511995568[/C][/ROW]
[ROW][C]87[/C][C]132.11[/C][C]132.122497666978[/C][C]-0.01249766697822[/C][/ROW]
[ROW][C]88[/C][C]132.88[/C][C]132.219458660638[/C][C]0.660541339362254[/C][/ROW]
[ROW][C]89[/C][C]135.48[/C][C]133.039674700432[/C][C]2.44032529956769[/C][/ROW]
[ROW][C]90[/C][C]136.56[/C][C]135.67397971376[/C][C]0.886020286240125[/C][/ROW]
[ROW][C]91[/C][C]136.96[/C][C]136.573069633845[/C][C]0.386930366155156[/C][/ROW]
[ROW][C]92[/C][C]137.4[/C][C]137.491857295564[/C][C]-0.091857295564381[/C][/ROW]
[ROW][C]93[/C][C]138.32[/C][C]138.905541437745[/C][C]-0.585541437744752[/C][/ROW]
[ROW][C]94[/C][C]138.82[/C][C]139.745642905391[/C][C]-0.925642905391271[/C][/ROW]
[ROW][C]95[/C][C]138.96[/C][C]138.92616511945[/C][C]0.0338348805499606[/C][/ROW]
[ROW][C]96[/C][C]138.94[/C][C]139.073996329128[/C][C]-0.133996329127626[/C][/ROW]
[ROW][C]97[/C][C]139[/C][C]138.627267972269[/C][C]0.372732027731331[/C][/ROW]
[ROW][C]98[/C][C]139.19[/C][C]139.081749979773[/C][C]0.108250020226677[/C][/ROW]
[ROW][C]99[/C][C]139.22[/C][C]139.28322630599[/C][C]-0.0632263059900993[/C][/ROW]
[ROW][C]100[/C][C]139.37[/C][C]139.359690716954[/C][C]0.010309283045558[/C][/ROW]
[ROW][C]101[/C][C]140.74[/C][C]139.553541634536[/C][C]1.18645836546406[/C][/ROW]
[ROW][C]102[/C][C]141.17[/C][C]140.945572543262[/C][C]0.224427456737942[/C][/ROW]
[ROW][C]103[/C][C]141.51[/C][C]141.188186130515[/C][C]0.321813869485482[/C][/ROW]
[ROW][C]104[/C][C]142.94[/C][C]142.046336366787[/C][C]0.893663633213293[/C][/ROW]
[ROW][C]105[/C][C]144.81[/C][C]144.459667774269[/C][C]0.350332225730909[/C][/ROW]
[ROW][C]106[/C][C]145.41[/C][C]146.258930510091[/C][C]-0.848930510090781[/C][/ROW]
[ROW][C]107[/C][C]146.11[/C][C]145.54020366186[/C][C]0.569796338140435[/C][/ROW]
[ROW][C]108[/C][C]146.23[/C][C]146.253281398751[/C][C]-0.0232813987514362[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261142&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261142&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
13	105.16	103.408632478633	1.75136752136748
14	105.16	105.180675606851	-0.0206756068512846
15	105.16	105.190889879983	-0.0308898799829365
16	105.16	105.237670832252	-0.0776708322519539
17	105.16	105.280660512402	-0.12066051240177
18	105.17	105.289896033199	-0.119896033198629
19	105.17	105.109139037483	0.0608609625168555
20	105.54	105.624734805503	-0.0847348055026629
21	106.9	106.968488669745	-0.0684886697449514
22	107.27	108.253651567425	-0.983651567425497
23	107.31	107.303605934637	0.00639406536315335
24	107.39	107.351168526149	0.0388314738513174
25	107.41	107.006131980816	0.403868019183776
26	107.46	107.420918778571	0.0390812214294414
27	113.14	107.481718011351	5.65828198864934
28	117	113.264190272412	3.73580972758818
29	119.28	117.204510117361	2.07548988263851
30	119.39	119.515243756448	-0.125243756448398
31	119.5	119.434434411865	0.0655655881350441
32	119.67	120.060076233469	-0.390076233469102
33	119.67	121.200841110185	-1.5308411101848
34	119.73	121.111689038446	-1.38168903844553
35	119.77	119.847747016477	-0.0777470164773746
36	119.77	119.89448595086	-0.124485950859651
37	119.78	119.467850691103	0.312149308897474
38	119.78	119.871739654315	-0.0917396543153046
39	119.78	119.881258281419	-0.101258281419263
40	121.28	119.92735039734	1.3526496026598
41	122.44	121.484341485577	0.955658514422538
42	122.72	122.664113094344	0.0558869056561377
43	122.75	122.755076837983	-0.00507683798274172
44	122.8	123.300027140811	-0.500027140810943
45	122.81	124.319715707991	-1.50971570799088
46	122.83	124.240770432834	-1.41077043283364
47	122.83	122.936543733068	-0.106543733068364
48	122.83	122.943000776365	-0.113000776364743
49	122.84	122.516477944992	0.323522055008411
50	122.85	122.920478236027	-0.0704782360268013
51	123.61	122.940204991174	0.66979500882556
52	124.74	123.753844948481	0.986155051518594
53	125.1	124.937248421212	0.162751578788416
54	125.29	125.309258263237	-0.0192582632366367
55	125.45	125.309486410746	0.1405135892537
56	125.51	125.985861898404	-0.475861898404133
57	125.55	127.015787019165	-1.46578701916482
58	125.57	126.967271761984	-1.39727176198394
59	125.81	125.66317720072	0.146822799279661
60	127.41	125.912114449241	1.49788555075894
61	127.75	127.101360585645	0.648639414355344
62	127.76	127.838543450817	-0.0785434508173779
63	127.8	127.85819125557	-0.0581912555698381
64	128.23	127.944704954647	0.285295045352512
65	130.01	128.421247708116	1.58875229188425
66	130.07	130.227216672467	-0.157216672467314
67	130.17	130.096094344979	0.0739056550212069
68	130.21	130.711817807506	-0.501817807505518
69	130.22	131.721488845848	-1.50148884584755
70	130.23	131.642624103452	-1.41262410345158
71	130.23	130.328379258103	-0.0983792581028808
72	130.23	130.334916223452	-0.104916223452392
73	130.23	129.908472531775	0.321527468224673
74	130.24	130.302453297799	-0.0624532977986405
75	130.13	130.322258609074	-0.192258609074145
76	130.14	130.257459922702	-0.117459922701812
77	130.79	130.310060107408	0.47993989259237
78	131.38	130.975174906136	0.404825093864105
79	131.61	131.379554406028	0.230445593971524
80	131.72	132.126810238165	-0.406810238165434
81	131.89	133.207411305693	-1.31741130569335
82	131.89	133.290348498512	-1.4003484985117
83	131.96	131.966223819071	-0.0062238190713515
84	131.99	132.043662894101	-0.0536628941005404
85	132	131.647720921313	0.352279078687104
86	132.06	132.05200271488	0.00799728511995568
87	132.11	132.122497666978	-0.01249766697822
88	132.88	132.219458660638	0.660541339362254
89	135.48	133.039674700432	2.44032529956769
90	136.56	135.67397971376	0.886020286240125
91	136.96	136.573069633845	0.386930366155156
92	137.4	137.491857295564	-0.091857295564381
93	138.32	138.905541437745	-0.585541437744752
94	138.82	139.745642905391	-0.925642905391271
95	138.96	138.92616511945	0.0338348805499606
96	138.94	139.073996329128	-0.133996329127626
97	139	138.627267972269	0.372732027731331
98	139.19	139.081749979773	0.108250020226677
99	139.22	139.28322630599	-0.0632263059900993
100	139.37	139.359690716954	0.010309283045558
101	140.74	139.553541634536	1.18645836546406
102	141.17	140.945572543262	0.224427456737942
103	141.51	141.188186130515	0.321813869485482
104	142.94	142.046336366787	0.893663633213293
105	144.81	144.459667774269	0.350332225730909
106	145.41	146.258930510091	-0.848930510090781
107	146.11	145.54020366186	0.569796338140435
108	146.23	146.253281398751	-0.0232813987514362

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
109	145.94763683045	143.959220500804	147.936053160096
110	146.056106994234	143.230264577344	148.881949411124
111	146.174993824685	142.697133083178	149.652854566191
112	146.340963988468	142.305502780788	150.376425196148
113	146.550684152252	142.016983834493	151.084384470012
114	146.770820982702	141.780355341398	151.761286624007
115	146.80137447982	141.385044436508	152.217704523131
116	147.346927976937	141.528779837158	153.165076116715
117	148.867064807387	142.666407183066	155.067722431708
118	150.313034971171	143.745744017281	156.880325925061
119	150.448588468288	143.527961905943	157.369215030632
120	150.591641965405	143.328984232644	157.854299698166

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 145.94763683045 & 143.959220500804 & 147.936053160096 \tabularnewline
110 & 146.056106994234 & 143.230264577344 & 148.881949411124 \tabularnewline
111 & 146.174993824685 & 142.697133083178 & 149.652854566191 \tabularnewline
112 & 146.340963988468 & 142.305502780788 & 150.376425196148 \tabularnewline
113 & 146.550684152252 & 142.016983834493 & 151.084384470012 \tabularnewline
114 & 146.770820982702 & 141.780355341398 & 151.761286624007 \tabularnewline
115 & 146.80137447982 & 141.385044436508 & 152.217704523131 \tabularnewline
116 & 147.346927976937 & 141.528779837158 & 153.165076116715 \tabularnewline
117 & 148.867064807387 & 142.666407183066 & 155.067722431708 \tabularnewline
118 & 150.313034971171 & 143.745744017281 & 156.880325925061 \tabularnewline
119 & 150.448588468288 & 143.527961905943 & 157.369215030632 \tabularnewline
120 & 150.591641965405 & 143.328984232644 & 157.854299698166 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261142&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]109[/C][C]145.94763683045[/C][C]143.959220500804[/C][C]147.936053160096[/C][/ROW]
[ROW][C]110[/C][C]146.056106994234[/C][C]143.230264577344[/C][C]148.881949411124[/C][/ROW]
[ROW][C]111[/C][C]146.174993824685[/C][C]142.697133083178[/C][C]149.652854566191[/C][/ROW]
[ROW][C]112[/C][C]146.340963988468[/C][C]142.305502780788[/C][C]150.376425196148[/C][/ROW]
[ROW][C]113[/C][C]146.550684152252[/C][C]142.016983834493[/C][C]151.084384470012[/C][/ROW]
[ROW][C]114[/C][C]146.770820982702[/C][C]141.780355341398[/C][C]151.761286624007[/C][/ROW]
[ROW][C]115[/C][C]146.80137447982[/C][C]141.385044436508[/C][C]152.217704523131[/C][/ROW]
[ROW][C]116[/C][C]147.346927976937[/C][C]141.528779837158[/C][C]153.165076116715[/C][/ROW]
[ROW][C]117[/C][C]148.867064807387[/C][C]142.666407183066[/C][C]155.067722431708[/C][/ROW]
[ROW][C]118[/C][C]150.313034971171[/C][C]143.745744017281[/C][C]156.880325925061[/C][/ROW]
[ROW][C]119[/C][C]150.448588468288[/C][C]143.527961905943[/C][C]157.369215030632[/C][/ROW]
[ROW][C]120[/C][C]150.591641965405[/C][C]143.328984232644[/C][C]157.854299698166[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261142&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261142&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
109	145.94763683045	143.959220500804	147.936053160096
110	146.056106994234	143.230264577344	148.881949411124
111	146.174993824685	142.697133083178	149.652854566191
112	146.340963988468	142.305502780788	150.376425196148
113	146.550684152252	142.016983834493	151.084384470012
114	146.770820982702	141.780355341398	151.761286624007
115	146.80137447982	141.385044436508	152.217704523131
116	147.346927976937	141.528779837158	153.165076116715
117	148.867064807387	142.666407183066	155.067722431708
118	150.313034971171	143.745744017281	156.880325925061
119	150.448588468288	143.527961905943	157.369215030632
120	150.591641965405	143.328984232644	157.854299698166

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 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = additive ;

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