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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 23 Dec 2011 15:01:27 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/23/t1324670512kzh2y1rfsgias6i.htm/, Retrieved Mon, 29 Apr 2024 17:42:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160687, Retrieved Mon, 29 Apr 2024 17:42:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact65
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Spectral Analysis] [] [2011-12-23 18:50:40] [2ba7ee2cbaa966a49160c7cfb7436069]
- RMP     [Exponential Smoothing] [] [2011-12-23 20:01:27] [393d554610c677f923bed472882d0fdb] [Current]
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Dataseries X:
302
262
218
175
100
77
43
47
49
69
152
205
246
294
242
181
107
56
49
47
47
71
151
244
280
230
185
148
98
61
46
45
55
48
115
185
276
220
181
151
83
55
49
42
46
74
103
200
237
247
215
182
80
46
65
40
44
63
85
185
247
231
167
117
79
45
40
38
41
69
152
232
282
255
161
107
53
40
39
34
35
56
97
210
260
257
210
125
80
42
35
31
32
50
92
189
256
250
198
136
73
39
32
30
31
45




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160687&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160687&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160687&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999933893038648
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999933893038648 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160687&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]0.999933893038648[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160687&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160687&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
ParameterValue
alpha0.999933893038648
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2262302-40
3218262.002644278454-44.0026442784541
4175218.002908881105-43.0029088811047
5100175.002842791635-75.0028427916354
677100.00495821003-23.0049582100297
74377.0015207878833-34.0015207878833
84743.00224773722063.99775226277937
94946.99973572074572.00026427925433
106948.999867768606620.0001322313934
1115268.998677852031583.0013221479685
12205151.99451303480553.0054869651954
13246204.99649596832241.0035040316782
14294245.99728938294448.0027106170563
15242293.996826686664-51.9968266866645
16181242.003437352212-61.0034373522122
17107181.004032751875-74.0040327518754
1856107.004892181733-51.004892181733
194956.0033717784362-7.00337177843622
204749.0004629716275-2.00046297162749
214747.0001322445284-0.000132244528352032
227147.000000008742323.9999999912577
2315170.998413432928180.0015865670719
24244150.99471133820993.0052886617913
25280243.99385170297736.0061482970231
26230279.997619742946-49.9976197429461
27185230.003305190716-45.003305190716
28148185.002975031757-37.002975031757
2998148.00244615424-50.0024461542403
306198.0033055097754-37.0033055097754
314661.0024461760872-15.0024461760872
324546.0009917661295-1.00099176612954
335545.0000661725249.99993382747601
344854.9993389347609-6.99933893476094
3511548.000462705028466.9995372949716
36185114.99557086417770.0044291358225
37276184.99537221990991.0046277800913
38220275.993983960588-55.9939839605885
39181220.003701592134-39.0037015921336
40151181.002578416194-30.0025784161937
4183151.001983379292-68.0019833792918
425583.0044954044871-28.0044954044871
434955.0018512920954-6.00185129209538
444249.0003967641514-7.0003967641514
454642.00046277495833.99953722504166
467445.999735602747228.0002643972528
4710373.998148987603629.0018510123964
48200102.99808277575697.001917224244
49237199.99358749800737.006412501993
50247236.99755361851910.002446381481
51215246.999338768664-31.9993387686636
52182215.002115379051-33.0021153790513
5380182.002181669566-102.002181669566
544680.0067430542814-34.0067430542814
556546.002248082448818.9977519175512
564064.9987441163482-24.9987441163482
574440.00165259101113.99834740898886
586343.999735681402419.0002643185976
598562.99874395026122.001256049739
6018584.9985455638166100.001454436183
61247184.99338920771662.0066107922835
62231246.995900931377-15.9959009313768
63167231.001057440405-64.0010574404047
64117167.004230915431-50.0042309154307
6579117.003305627761-38.0033056277606
664579.0025122830564-34.0025122830564
674045.0022478027654-5.00224780276536
683840.0003306834022-2.00033068340217
694138.00013223578322.99986776421682
706940.999801687857628.0001983121424
7115268.998148991972383.0018510080277
72232151.99451299984380.0054870001567
73282231.99471108036350.0052889196371
74255281.996694302298-26.996694302298
75161255.001784669427-94.0017846694269
76107161.006214172346-54.0062141723461
7753107.003570186713-54.003570186713
784053.0035700119272-13.0035700119272
793940.0008596265002-1.00085962650022
803439.0000661637886-5.00006616378865
813534.00033053918060.999669460819355
825634.999933914889621.0000660851104
839755.998611749442941.0013882505571
8421096.9972895228115113.002710477188
85260209.99252973418650.0074702658142
86257259.996694158096-2.99669415809581
87210257.000198102345-47.0001981023449
88125210.003107040279-85.0031070402795
8980125.005619297112-45.0056192971119
904280.0029751847355-38.0029751847355
913542.0025122612118-7.00251226121179
923135.0004629148074-4.00046291480742
933231.00026445844730.999735541552703
945031.999933910521218.0000660894788
959249.998810070326742.0011899296733
9618991.997223428960697.0027765710394
97256188.99358744119867.0064125588018
98250255.995570409675-5.99557040967466
99198250.000396348941-52.0003963489414
100136198.003437588192-62.0034375881917
10173136.004098858852-63.0040988588523
1023973.0041650095283-34.0041650095283
1033239.0022479120221-7.00224791202209
1043032.0004628973321-2.0004628973321
1053130.00013224452340.999867755476561
1064530.999933901780914.0000660982191

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 262 & 302 & -40 \tabularnewline
3 & 218 & 262.002644278454 & -44.0026442784541 \tabularnewline
4 & 175 & 218.002908881105 & -43.0029088811047 \tabularnewline
5 & 100 & 175.002842791635 & -75.0028427916354 \tabularnewline
6 & 77 & 100.00495821003 & -23.0049582100297 \tabularnewline
7 & 43 & 77.0015207878833 & -34.0015207878833 \tabularnewline
8 & 47 & 43.0022477372206 & 3.99775226277937 \tabularnewline
9 & 49 & 46.9997357207457 & 2.00026427925433 \tabularnewline
10 & 69 & 48.9998677686066 & 20.0001322313934 \tabularnewline
11 & 152 & 68.9986778520315 & 83.0013221479685 \tabularnewline
12 & 205 & 151.994513034805 & 53.0054869651954 \tabularnewline
13 & 246 & 204.996495968322 & 41.0035040316782 \tabularnewline
14 & 294 & 245.997289382944 & 48.0027106170563 \tabularnewline
15 & 242 & 293.996826686664 & -51.9968266866645 \tabularnewline
16 & 181 & 242.003437352212 & -61.0034373522122 \tabularnewline
17 & 107 & 181.004032751875 & -74.0040327518754 \tabularnewline
18 & 56 & 107.004892181733 & -51.004892181733 \tabularnewline
19 & 49 & 56.0033717784362 & -7.00337177843622 \tabularnewline
20 & 47 & 49.0004629716275 & -2.00046297162749 \tabularnewline
21 & 47 & 47.0001322445284 & -0.000132244528352032 \tabularnewline
22 & 71 & 47.0000000087423 & 23.9999999912577 \tabularnewline
23 & 151 & 70.9984134329281 & 80.0015865670719 \tabularnewline
24 & 244 & 150.994711338209 & 93.0052886617913 \tabularnewline
25 & 280 & 243.993851702977 & 36.0061482970231 \tabularnewline
26 & 230 & 279.997619742946 & -49.9976197429461 \tabularnewline
27 & 185 & 230.003305190716 & -45.003305190716 \tabularnewline
28 & 148 & 185.002975031757 & -37.002975031757 \tabularnewline
29 & 98 & 148.00244615424 & -50.0024461542403 \tabularnewline
30 & 61 & 98.0033055097754 & -37.0033055097754 \tabularnewline
31 & 46 & 61.0024461760872 & -15.0024461760872 \tabularnewline
32 & 45 & 46.0009917661295 & -1.00099176612954 \tabularnewline
33 & 55 & 45.000066172524 & 9.99993382747601 \tabularnewline
34 & 48 & 54.9993389347609 & -6.99933893476094 \tabularnewline
35 & 115 & 48.0004627050284 & 66.9995372949716 \tabularnewline
36 & 185 & 114.995570864177 & 70.0044291358225 \tabularnewline
37 & 276 & 184.995372219909 & 91.0046277800913 \tabularnewline
38 & 220 & 275.993983960588 & -55.9939839605885 \tabularnewline
39 & 181 & 220.003701592134 & -39.0037015921336 \tabularnewline
40 & 151 & 181.002578416194 & -30.0025784161937 \tabularnewline
41 & 83 & 151.001983379292 & -68.0019833792918 \tabularnewline
42 & 55 & 83.0044954044871 & -28.0044954044871 \tabularnewline
43 & 49 & 55.0018512920954 & -6.00185129209538 \tabularnewline
44 & 42 & 49.0003967641514 & -7.0003967641514 \tabularnewline
45 & 46 & 42.0004627749583 & 3.99953722504166 \tabularnewline
46 & 74 & 45.9997356027472 & 28.0002643972528 \tabularnewline
47 & 103 & 73.9981489876036 & 29.0018510123964 \tabularnewline
48 & 200 & 102.998082775756 & 97.001917224244 \tabularnewline
49 & 237 & 199.993587498007 & 37.006412501993 \tabularnewline
50 & 247 & 236.997553618519 & 10.002446381481 \tabularnewline
51 & 215 & 246.999338768664 & -31.9993387686636 \tabularnewline
52 & 182 & 215.002115379051 & -33.0021153790513 \tabularnewline
53 & 80 & 182.002181669566 & -102.002181669566 \tabularnewline
54 & 46 & 80.0067430542814 & -34.0067430542814 \tabularnewline
55 & 65 & 46.0022480824488 & 18.9977519175512 \tabularnewline
56 & 40 & 64.9987441163482 & -24.9987441163482 \tabularnewline
57 & 44 & 40.0016525910111 & 3.99834740898886 \tabularnewline
58 & 63 & 43.9997356814024 & 19.0002643185976 \tabularnewline
59 & 85 & 62.998743950261 & 22.001256049739 \tabularnewline
60 & 185 & 84.9985455638166 & 100.001454436183 \tabularnewline
61 & 247 & 184.993389207716 & 62.0066107922835 \tabularnewline
62 & 231 & 246.995900931377 & -15.9959009313768 \tabularnewline
63 & 167 & 231.001057440405 & -64.0010574404047 \tabularnewline
64 & 117 & 167.004230915431 & -50.0042309154307 \tabularnewline
65 & 79 & 117.003305627761 & -38.0033056277606 \tabularnewline
66 & 45 & 79.0025122830564 & -34.0025122830564 \tabularnewline
67 & 40 & 45.0022478027654 & -5.00224780276536 \tabularnewline
68 & 38 & 40.0003306834022 & -2.00033068340217 \tabularnewline
69 & 41 & 38.0001322357832 & 2.99986776421682 \tabularnewline
70 & 69 & 40.9998016878576 & 28.0001983121424 \tabularnewline
71 & 152 & 68.9981489919723 & 83.0018510080277 \tabularnewline
72 & 232 & 151.994512999843 & 80.0054870001567 \tabularnewline
73 & 282 & 231.994711080363 & 50.0052889196371 \tabularnewline
74 & 255 & 281.996694302298 & -26.996694302298 \tabularnewline
75 & 161 & 255.001784669427 & -94.0017846694269 \tabularnewline
76 & 107 & 161.006214172346 & -54.0062141723461 \tabularnewline
77 & 53 & 107.003570186713 & -54.003570186713 \tabularnewline
78 & 40 & 53.0035700119272 & -13.0035700119272 \tabularnewline
79 & 39 & 40.0008596265002 & -1.00085962650022 \tabularnewline
80 & 34 & 39.0000661637886 & -5.00006616378865 \tabularnewline
81 & 35 & 34.0003305391806 & 0.999669460819355 \tabularnewline
82 & 56 & 34.9999339148896 & 21.0000660851104 \tabularnewline
83 & 97 & 55.9986117494429 & 41.0013882505571 \tabularnewline
84 & 210 & 96.9972895228115 & 113.002710477188 \tabularnewline
85 & 260 & 209.992529734186 & 50.0074702658142 \tabularnewline
86 & 257 & 259.996694158096 & -2.99669415809581 \tabularnewline
87 & 210 & 257.000198102345 & -47.0001981023449 \tabularnewline
88 & 125 & 210.003107040279 & -85.0031070402795 \tabularnewline
89 & 80 & 125.005619297112 & -45.0056192971119 \tabularnewline
90 & 42 & 80.0029751847355 & -38.0029751847355 \tabularnewline
91 & 35 & 42.0025122612118 & -7.00251226121179 \tabularnewline
92 & 31 & 35.0004629148074 & -4.00046291480742 \tabularnewline
93 & 32 & 31.0002644584473 & 0.999735541552703 \tabularnewline
94 & 50 & 31.9999339105212 & 18.0000660894788 \tabularnewline
95 & 92 & 49.9988100703267 & 42.0011899296733 \tabularnewline
96 & 189 & 91.9972234289606 & 97.0027765710394 \tabularnewline
97 & 256 & 188.993587441198 & 67.0064125588018 \tabularnewline
98 & 250 & 255.995570409675 & -5.99557040967466 \tabularnewline
99 & 198 & 250.000396348941 & -52.0003963489414 \tabularnewline
100 & 136 & 198.003437588192 & -62.0034375881917 \tabularnewline
101 & 73 & 136.004098858852 & -63.0040988588523 \tabularnewline
102 & 39 & 73.0041650095283 & -34.0041650095283 \tabularnewline
103 & 32 & 39.0022479120221 & -7.00224791202209 \tabularnewline
104 & 30 & 32.0004628973321 & -2.0004628973321 \tabularnewline
105 & 31 & 30.0001322445234 & 0.999867755476561 \tabularnewline
106 & 45 & 30.9999339017809 & 14.0000660982191 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160687&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]2[/C][C]262[/C][C]302[/C][C]-40[/C][/ROW]
[ROW][C]3[/C][C]218[/C][C]262.002644278454[/C][C]-44.0026442784541[/C][/ROW]
[ROW][C]4[/C][C]175[/C][C]218.002908881105[/C][C]-43.0029088811047[/C][/ROW]
[ROW][C]5[/C][C]100[/C][C]175.002842791635[/C][C]-75.0028427916354[/C][/ROW]
[ROW][C]6[/C][C]77[/C][C]100.00495821003[/C][C]-23.0049582100297[/C][/ROW]
[ROW][C]7[/C][C]43[/C][C]77.0015207878833[/C][C]-34.0015207878833[/C][/ROW]
[ROW][C]8[/C][C]47[/C][C]43.0022477372206[/C][C]3.99775226277937[/C][/ROW]
[ROW][C]9[/C][C]49[/C][C]46.9997357207457[/C][C]2.00026427925433[/C][/ROW]
[ROW][C]10[/C][C]69[/C][C]48.9998677686066[/C][C]20.0001322313934[/C][/ROW]
[ROW][C]11[/C][C]152[/C][C]68.9986778520315[/C][C]83.0013221479685[/C][/ROW]
[ROW][C]12[/C][C]205[/C][C]151.994513034805[/C][C]53.0054869651954[/C][/ROW]
[ROW][C]13[/C][C]246[/C][C]204.996495968322[/C][C]41.0035040316782[/C][/ROW]
[ROW][C]14[/C][C]294[/C][C]245.997289382944[/C][C]48.0027106170563[/C][/ROW]
[ROW][C]15[/C][C]242[/C][C]293.996826686664[/C][C]-51.9968266866645[/C][/ROW]
[ROW][C]16[/C][C]181[/C][C]242.003437352212[/C][C]-61.0034373522122[/C][/ROW]
[ROW][C]17[/C][C]107[/C][C]181.004032751875[/C][C]-74.0040327518754[/C][/ROW]
[ROW][C]18[/C][C]56[/C][C]107.004892181733[/C][C]-51.004892181733[/C][/ROW]
[ROW][C]19[/C][C]49[/C][C]56.0033717784362[/C][C]-7.00337177843622[/C][/ROW]
[ROW][C]20[/C][C]47[/C][C]49.0004629716275[/C][C]-2.00046297162749[/C][/ROW]
[ROW][C]21[/C][C]47[/C][C]47.0001322445284[/C][C]-0.000132244528352032[/C][/ROW]
[ROW][C]22[/C][C]71[/C][C]47.0000000087423[/C][C]23.9999999912577[/C][/ROW]
[ROW][C]23[/C][C]151[/C][C]70.9984134329281[/C][C]80.0015865670719[/C][/ROW]
[ROW][C]24[/C][C]244[/C][C]150.994711338209[/C][C]93.0052886617913[/C][/ROW]
[ROW][C]25[/C][C]280[/C][C]243.993851702977[/C][C]36.0061482970231[/C][/ROW]
[ROW][C]26[/C][C]230[/C][C]279.997619742946[/C][C]-49.9976197429461[/C][/ROW]
[ROW][C]27[/C][C]185[/C][C]230.003305190716[/C][C]-45.003305190716[/C][/ROW]
[ROW][C]28[/C][C]148[/C][C]185.002975031757[/C][C]-37.002975031757[/C][/ROW]
[ROW][C]29[/C][C]98[/C][C]148.00244615424[/C][C]-50.0024461542403[/C][/ROW]
[ROW][C]30[/C][C]61[/C][C]98.0033055097754[/C][C]-37.0033055097754[/C][/ROW]
[ROW][C]31[/C][C]46[/C][C]61.0024461760872[/C][C]-15.0024461760872[/C][/ROW]
[ROW][C]32[/C][C]45[/C][C]46.0009917661295[/C][C]-1.00099176612954[/C][/ROW]
[ROW][C]33[/C][C]55[/C][C]45.000066172524[/C][C]9.99993382747601[/C][/ROW]
[ROW][C]34[/C][C]48[/C][C]54.9993389347609[/C][C]-6.99933893476094[/C][/ROW]
[ROW][C]35[/C][C]115[/C][C]48.0004627050284[/C][C]66.9995372949716[/C][/ROW]
[ROW][C]36[/C][C]185[/C][C]114.995570864177[/C][C]70.0044291358225[/C][/ROW]
[ROW][C]37[/C][C]276[/C][C]184.995372219909[/C][C]91.0046277800913[/C][/ROW]
[ROW][C]38[/C][C]220[/C][C]275.993983960588[/C][C]-55.9939839605885[/C][/ROW]
[ROW][C]39[/C][C]181[/C][C]220.003701592134[/C][C]-39.0037015921336[/C][/ROW]
[ROW][C]40[/C][C]151[/C][C]181.002578416194[/C][C]-30.0025784161937[/C][/ROW]
[ROW][C]41[/C][C]83[/C][C]151.001983379292[/C][C]-68.0019833792918[/C][/ROW]
[ROW][C]42[/C][C]55[/C][C]83.0044954044871[/C][C]-28.0044954044871[/C][/ROW]
[ROW][C]43[/C][C]49[/C][C]55.0018512920954[/C][C]-6.00185129209538[/C][/ROW]
[ROW][C]44[/C][C]42[/C][C]49.0003967641514[/C][C]-7.0003967641514[/C][/ROW]
[ROW][C]45[/C][C]46[/C][C]42.0004627749583[/C][C]3.99953722504166[/C][/ROW]
[ROW][C]46[/C][C]74[/C][C]45.9997356027472[/C][C]28.0002643972528[/C][/ROW]
[ROW][C]47[/C][C]103[/C][C]73.9981489876036[/C][C]29.0018510123964[/C][/ROW]
[ROW][C]48[/C][C]200[/C][C]102.998082775756[/C][C]97.001917224244[/C][/ROW]
[ROW][C]49[/C][C]237[/C][C]199.993587498007[/C][C]37.006412501993[/C][/ROW]
[ROW][C]50[/C][C]247[/C][C]236.997553618519[/C][C]10.002446381481[/C][/ROW]
[ROW][C]51[/C][C]215[/C][C]246.999338768664[/C][C]-31.9993387686636[/C][/ROW]
[ROW][C]52[/C][C]182[/C][C]215.002115379051[/C][C]-33.0021153790513[/C][/ROW]
[ROW][C]53[/C][C]80[/C][C]182.002181669566[/C][C]-102.002181669566[/C][/ROW]
[ROW][C]54[/C][C]46[/C][C]80.0067430542814[/C][C]-34.0067430542814[/C][/ROW]
[ROW][C]55[/C][C]65[/C][C]46.0022480824488[/C][C]18.9977519175512[/C][/ROW]
[ROW][C]56[/C][C]40[/C][C]64.9987441163482[/C][C]-24.9987441163482[/C][/ROW]
[ROW][C]57[/C][C]44[/C][C]40.0016525910111[/C][C]3.99834740898886[/C][/ROW]
[ROW][C]58[/C][C]63[/C][C]43.9997356814024[/C][C]19.0002643185976[/C][/ROW]
[ROW][C]59[/C][C]85[/C][C]62.998743950261[/C][C]22.001256049739[/C][/ROW]
[ROW][C]60[/C][C]185[/C][C]84.9985455638166[/C][C]100.001454436183[/C][/ROW]
[ROW][C]61[/C][C]247[/C][C]184.993389207716[/C][C]62.0066107922835[/C][/ROW]
[ROW][C]62[/C][C]231[/C][C]246.995900931377[/C][C]-15.9959009313768[/C][/ROW]
[ROW][C]63[/C][C]167[/C][C]231.001057440405[/C][C]-64.0010574404047[/C][/ROW]
[ROW][C]64[/C][C]117[/C][C]167.004230915431[/C][C]-50.0042309154307[/C][/ROW]
[ROW][C]65[/C][C]79[/C][C]117.003305627761[/C][C]-38.0033056277606[/C][/ROW]
[ROW][C]66[/C][C]45[/C][C]79.0025122830564[/C][C]-34.0025122830564[/C][/ROW]
[ROW][C]67[/C][C]40[/C][C]45.0022478027654[/C][C]-5.00224780276536[/C][/ROW]
[ROW][C]68[/C][C]38[/C][C]40.0003306834022[/C][C]-2.00033068340217[/C][/ROW]
[ROW][C]69[/C][C]41[/C][C]38.0001322357832[/C][C]2.99986776421682[/C][/ROW]
[ROW][C]70[/C][C]69[/C][C]40.9998016878576[/C][C]28.0001983121424[/C][/ROW]
[ROW][C]71[/C][C]152[/C][C]68.9981489919723[/C][C]83.0018510080277[/C][/ROW]
[ROW][C]72[/C][C]232[/C][C]151.994512999843[/C][C]80.0054870001567[/C][/ROW]
[ROW][C]73[/C][C]282[/C][C]231.994711080363[/C][C]50.0052889196371[/C][/ROW]
[ROW][C]74[/C][C]255[/C][C]281.996694302298[/C][C]-26.996694302298[/C][/ROW]
[ROW][C]75[/C][C]161[/C][C]255.001784669427[/C][C]-94.0017846694269[/C][/ROW]
[ROW][C]76[/C][C]107[/C][C]161.006214172346[/C][C]-54.0062141723461[/C][/ROW]
[ROW][C]77[/C][C]53[/C][C]107.003570186713[/C][C]-54.003570186713[/C][/ROW]
[ROW][C]78[/C][C]40[/C][C]53.0035700119272[/C][C]-13.0035700119272[/C][/ROW]
[ROW][C]79[/C][C]39[/C][C]40.0008596265002[/C][C]-1.00085962650022[/C][/ROW]
[ROW][C]80[/C][C]34[/C][C]39.0000661637886[/C][C]-5.00006616378865[/C][/ROW]
[ROW][C]81[/C][C]35[/C][C]34.0003305391806[/C][C]0.999669460819355[/C][/ROW]
[ROW][C]82[/C][C]56[/C][C]34.9999339148896[/C][C]21.0000660851104[/C][/ROW]
[ROW][C]83[/C][C]97[/C][C]55.9986117494429[/C][C]41.0013882505571[/C][/ROW]
[ROW][C]84[/C][C]210[/C][C]96.9972895228115[/C][C]113.002710477188[/C][/ROW]
[ROW][C]85[/C][C]260[/C][C]209.992529734186[/C][C]50.0074702658142[/C][/ROW]
[ROW][C]86[/C][C]257[/C][C]259.996694158096[/C][C]-2.99669415809581[/C][/ROW]
[ROW][C]87[/C][C]210[/C][C]257.000198102345[/C][C]-47.0001981023449[/C][/ROW]
[ROW][C]88[/C][C]125[/C][C]210.003107040279[/C][C]-85.0031070402795[/C][/ROW]
[ROW][C]89[/C][C]80[/C][C]125.005619297112[/C][C]-45.0056192971119[/C][/ROW]
[ROW][C]90[/C][C]42[/C][C]80.0029751847355[/C][C]-38.0029751847355[/C][/ROW]
[ROW][C]91[/C][C]35[/C][C]42.0025122612118[/C][C]-7.00251226121179[/C][/ROW]
[ROW][C]92[/C][C]31[/C][C]35.0004629148074[/C][C]-4.00046291480742[/C][/ROW]
[ROW][C]93[/C][C]32[/C][C]31.0002644584473[/C][C]0.999735541552703[/C][/ROW]
[ROW][C]94[/C][C]50[/C][C]31.9999339105212[/C][C]18.0000660894788[/C][/ROW]
[ROW][C]95[/C][C]92[/C][C]49.9988100703267[/C][C]42.0011899296733[/C][/ROW]
[ROW][C]96[/C][C]189[/C][C]91.9972234289606[/C][C]97.0027765710394[/C][/ROW]
[ROW][C]97[/C][C]256[/C][C]188.993587441198[/C][C]67.0064125588018[/C][/ROW]
[ROW][C]98[/C][C]250[/C][C]255.995570409675[/C][C]-5.99557040967466[/C][/ROW]
[ROW][C]99[/C][C]198[/C][C]250.000396348941[/C][C]-52.0003963489414[/C][/ROW]
[ROW][C]100[/C][C]136[/C][C]198.003437588192[/C][C]-62.0034375881917[/C][/ROW]
[ROW][C]101[/C][C]73[/C][C]136.004098858852[/C][C]-63.0040988588523[/C][/ROW]
[ROW][C]102[/C][C]39[/C][C]73.0041650095283[/C][C]-34.0041650095283[/C][/ROW]
[ROW][C]103[/C][C]32[/C][C]39.0022479120221[/C][C]-7.00224791202209[/C][/ROW]
[ROW][C]104[/C][C]30[/C][C]32.0004628973321[/C][C]-2.0004628973321[/C][/ROW]
[ROW][C]105[/C][C]31[/C][C]30.0001322445234[/C][C]0.999867755476561[/C][/ROW]
[ROW][C]106[/C][C]45[/C][C]30.9999339017809[/C][C]14.0000660982191[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160687&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160687&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
tObservedFittedResiduals
2262302-40
3218262.002644278454-44.0026442784541
4175218.002908881105-43.0029088811047
5100175.002842791635-75.0028427916354
677100.00495821003-23.0049582100297
74377.0015207878833-34.0015207878833
84743.00224773722063.99775226277937
94946.99973572074572.00026427925433
106948.999867768606620.0001322313934
1115268.998677852031583.0013221479685
12205151.99451303480553.0054869651954
13246204.99649596832241.0035040316782
14294245.99728938294448.0027106170563
15242293.996826686664-51.9968266866645
16181242.003437352212-61.0034373522122
17107181.004032751875-74.0040327518754
1856107.004892181733-51.004892181733
194956.0033717784362-7.00337177843622
204749.0004629716275-2.00046297162749
214747.0001322445284-0.000132244528352032
227147.000000008742323.9999999912577
2315170.998413432928180.0015865670719
24244150.99471133820993.0052886617913
25280243.99385170297736.0061482970231
26230279.997619742946-49.9976197429461
27185230.003305190716-45.003305190716
28148185.002975031757-37.002975031757
2998148.00244615424-50.0024461542403
306198.0033055097754-37.0033055097754
314661.0024461760872-15.0024461760872
324546.0009917661295-1.00099176612954
335545.0000661725249.99993382747601
344854.9993389347609-6.99933893476094
3511548.000462705028466.9995372949716
36185114.99557086417770.0044291358225
37276184.99537221990991.0046277800913
38220275.993983960588-55.9939839605885
39181220.003701592134-39.0037015921336
40151181.002578416194-30.0025784161937
4183151.001983379292-68.0019833792918
425583.0044954044871-28.0044954044871
434955.0018512920954-6.00185129209538
444249.0003967641514-7.0003967641514
454642.00046277495833.99953722504166
467445.999735602747228.0002643972528
4710373.998148987603629.0018510123964
48200102.99808277575697.001917224244
49237199.99358749800737.006412501993
50247236.99755361851910.002446381481
51215246.999338768664-31.9993387686636
52182215.002115379051-33.0021153790513
5380182.002181669566-102.002181669566
544680.0067430542814-34.0067430542814
556546.002248082448818.9977519175512
564064.9987441163482-24.9987441163482
574440.00165259101113.99834740898886
586343.999735681402419.0002643185976
598562.99874395026122.001256049739
6018584.9985455638166100.001454436183
61247184.99338920771662.0066107922835
62231246.995900931377-15.9959009313768
63167231.001057440405-64.0010574404047
64117167.004230915431-50.0042309154307
6579117.003305627761-38.0033056277606
664579.0025122830564-34.0025122830564
674045.0022478027654-5.00224780276536
683840.0003306834022-2.00033068340217
694138.00013223578322.99986776421682
706940.999801687857628.0001983121424
7115268.998148991972383.0018510080277
72232151.99451299984380.0054870001567
73282231.99471108036350.0052889196371
74255281.996694302298-26.996694302298
75161255.001784669427-94.0017846694269
76107161.006214172346-54.0062141723461
7753107.003570186713-54.003570186713
784053.0035700119272-13.0035700119272
793940.0008596265002-1.00085962650022
803439.0000661637886-5.00006616378865
813534.00033053918060.999669460819355
825634.999933914889621.0000660851104
839755.998611749442941.0013882505571
8421096.9972895228115113.002710477188
85260209.99252973418650.0074702658142
86257259.996694158096-2.99669415809581
87210257.000198102345-47.0001981023449
88125210.003107040279-85.0031070402795
8980125.005619297112-45.0056192971119
904280.0029751847355-38.0029751847355
913542.0025122612118-7.00251226121179
923135.0004629148074-4.00046291480742
933231.00026445844730.999735541552703
945031.999933910521218.0000660894788
959249.998810070326742.0011899296733
9618991.997223428960697.0027765710394
97256188.99358744119867.0064125588018
98250255.995570409675-5.99557040967466
99198250.000396348941-52.0003963489414
100136198.003437588192-62.0034375881917
10173136.004098858852-63.0040988588523
1023973.0041650095283-34.0041650095283
1033239.0022479120221-7.00224791202209
1043032.0004628973321-2.0004628973321
1053130.00013224452340.999867755476561
1064530.999933901780914.0000660982191







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
10744.9990744981715-48.8355303783435138.833679374687
10844.9990744981715-87.6987101419704177.696859138313
10944.9990744981715-117.52006598833207.518214984673
11044.9990744981715-142.660830650853232.658979647196
11144.9990744981715-164.810384241445254.808533237788
11244.9990744981715-184.835165667824274.833314664167
11344.9990744981715-203.249887088278293.248036084621
11444.9990744981715-220.3899152976310.388064293943
11544.9990744981715-236.4881985372326.486347533543
11644.9990744981715-251.714345921195341.712494917538
11744.9990744981715-266.196399172365356.194548168708
11844.9990744981715-280.033834311228370.031983307571

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
107 & 44.9990744981715 & -48.8355303783435 & 138.833679374687 \tabularnewline
108 & 44.9990744981715 & -87.6987101419704 & 177.696859138313 \tabularnewline
109 & 44.9990744981715 & -117.52006598833 & 207.518214984673 \tabularnewline
110 & 44.9990744981715 & -142.660830650853 & 232.658979647196 \tabularnewline
111 & 44.9990744981715 & -164.810384241445 & 254.808533237788 \tabularnewline
112 & 44.9990744981715 & -184.835165667824 & 274.833314664167 \tabularnewline
113 & 44.9990744981715 & -203.249887088278 & 293.248036084621 \tabularnewline
114 & 44.9990744981715 & -220.3899152976 & 310.388064293943 \tabularnewline
115 & 44.9990744981715 & -236.4881985372 & 326.486347533543 \tabularnewline
116 & 44.9990744981715 & -251.714345921195 & 341.712494917538 \tabularnewline
117 & 44.9990744981715 & -266.196399172365 & 356.194548168708 \tabularnewline
118 & 44.9990744981715 & -280.033834311228 & 370.031983307571 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160687&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]107[/C][C]44.9990744981715[/C][C]-48.8355303783435[/C][C]138.833679374687[/C][/ROW]
[ROW][C]108[/C][C]44.9990744981715[/C][C]-87.6987101419704[/C][C]177.696859138313[/C][/ROW]
[ROW][C]109[/C][C]44.9990744981715[/C][C]-117.52006598833[/C][C]207.518214984673[/C][/ROW]
[ROW][C]110[/C][C]44.9990744981715[/C][C]-142.660830650853[/C][C]232.658979647196[/C][/ROW]
[ROW][C]111[/C][C]44.9990744981715[/C][C]-164.810384241445[/C][C]254.808533237788[/C][/ROW]
[ROW][C]112[/C][C]44.9990744981715[/C][C]-184.835165667824[/C][C]274.833314664167[/C][/ROW]
[ROW][C]113[/C][C]44.9990744981715[/C][C]-203.249887088278[/C][C]293.248036084621[/C][/ROW]
[ROW][C]114[/C][C]44.9990744981715[/C][C]-220.3899152976[/C][C]310.388064293943[/C][/ROW]
[ROW][C]115[/C][C]44.9990744981715[/C][C]-236.4881985372[/C][C]326.486347533543[/C][/ROW]
[ROW][C]116[/C][C]44.9990744981715[/C][C]-251.714345921195[/C][C]341.712494917538[/C][/ROW]
[ROW][C]117[/C][C]44.9990744981715[/C][C]-266.196399172365[/C][C]356.194548168708[/C][/ROW]
[ROW][C]118[/C][C]44.9990744981715[/C][C]-280.033834311228[/C][C]370.031983307571[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160687&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160687&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
tForecast95% Lower Bound95% Upper Bound
10744.9990744981715-48.8355303783435138.833679374687
10844.9990744981715-87.6987101419704177.696859138313
10944.9990744981715-117.52006598833207.518214984673
11044.9990744981715-142.660830650853232.658979647196
11144.9990744981715-164.810384241445254.808533237788
11244.9990744981715-184.835165667824274.833314664167
11344.9990744981715-203.249887088278293.248036084621
11444.9990744981715-220.3899152976310.388064293943
11544.9990744981715-236.4881985372326.486347533543
11644.9990744981715-251.714345921195341.712494917538
11744.9990744981715-266.196399172365356.194548168708
11844.9990744981715-280.033834311228370.031983307571



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; 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')