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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 17 Aug 2011 13:09:45 -0400
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/Aug/17/t1313601046sfvvgnduhbuuat9.htm/, Retrieved Wed, 15 May 2024 00:04:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=123971, Retrieved Wed, 15 May 2024 00:04:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsVan Vlaenderen Lynn
Estimated Impact99
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [tijdreeksA- stap32] [2011-08-17 17:09:45] [d08a5fa9e4c562ec79e796d78c067f4f] [Current]
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Dataseries X:
465
455
444
424
630
620
465
362
372
372
382
403
434
424
362
372
661
723
558
465
486
496
548
599
610
506
517
382
765
878
620
537
589
651
744
858
858
785
754
568
878
1023
899
765
785
858
961
1085
1002
951
951
785
1023
1178
1054
920
961
1126
1199
1302
1219
1085
1054
806
971
1147
951
837
951
1064
1126
1292
1209
1002
1023
827
992
1137
971
858
961
1085
1064
1312
1271
1106
1116
899
1033
1240
1085
992
1147
1240
1168
1498
1416
1230
1178
940
1075
1199
1044
1044
1219
1312
1261
1622
1529
1354
1281
1023
1116
1281
1157
1126
1271
1395
1261
1581




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=123971&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=123971&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123971&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
alpha0.292250382435206
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.292250382435206 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123971&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]0.292250382435206[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123971&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123971&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
alpha0.292250382435206
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13434427.0988247863256.90117521367517
14424415.9790408701198.02095912988119
15362352.3115142316699.68848576833136
16372360.25632289102711.7436771089734
17661645.63509533899815.3649046610021
18723702.07217292393520.9278270760655
19558509.51001671213148.4899832878691
20465428.29457786063236.7054221393676
21486458.76009650665327.2399034933468
22496477.33431370842718.6656862915731
23548498.69437932056649.3056206794337
24599533.55064414201465.4493558579857
25610585.4258925282224.5741074717802
26506580.263556461646-74.2635564616464
27517493.72854001371923.2714599862811
28382507.097538968242-125.097538968242
29765755.0473360998129.9526639001881
30878813.83984046437364.160159535627
31620653.419455465607-33.4194554656074
32537539.925433167331-2.92543316733145
33589552.10960199196136.8903980080386
34651567.4357809608783.5642190391302
35744629.447869433185114.552130566815
36858694.79817412047163.20182587953
37858746.312177841255111.687822158745
38785696.65653935741888.3434606425817
39754726.67385643504627.3261435649539
40568636.219735947555-68.219735947555
41878996.373822196174-118.373822196174
4210231056.02819622763-33.0281962276345
43899798.142541889563100.857458110437
44765745.47313155572219.5268684442775
45785792.398633400288-7.3986334002883
46858827.81470498747130.185295012529
47961896.15846503188364.8415349681171
481085981.412632396584103.587367603416
491002979.0452714548922.9547285451096
50951886.93538949245164.064610507549
51951866.67222050650884.3277794934924
52785725.25429023369459.7457097663058
5310231087.30979156891-64.3097915689088
5411781223.16773336724-45.167733367238
5510541056.49181531271-2.49181531271324
56920916.0568465640133.94315343598703
57961939.37148810441321.6285118955871
5811261009.87076496607116.129235033928
5911991127.8596149245371.140385075473
6013021242.3769718718759.6230281281328
6112191170.0932964482548.9067035517455
6210851114.6633923435-29.6633923435033
6310541081.3494287799-27.349428779904
64806889.895841231527-83.8958412315269
659711122.17181072723-151.171810727232
6611471246.19207857908-99.1920785790826
679511093.9313896579-142.931389657901
68837917.007248268716-80.0072482687162
69951928.30415849160622.6958415083942
7010641065.99821350155-1.99821350154934
7111261117.623430096648.37656990336041
7212921205.64663308286.3533669179999
7312091133.5904347717175.4095652282895
7410021030.29804680567-28.2980468056653
751023999.02081282485223.9791871751482
76827782.54733113191144.4526688680887
779921004.71866010733-12.7186601073317
7811371205.99054972618-68.9905497261807
799711031.59978847381-60.5997884738063
80858923.271626020965-65.2716260209646
819611011.56309999365-50.5630999936529
8210851110.36999334341-25.3699933434132
8310641162.50754732867-98.5075473286697
8413121274.4818744427637.5181255572411
8512711180.4080867078790.5919132921256
8611061008.1537230141697.8462769858399
8711161050.7414082607165.2585917392898
88899860.82194717673638.1780528232639
8910331040.6965309954-7.69653099539755
9012401203.6097314104636.3902685895405
9110851065.9551126796419.044887320365
92992977.59664594924214.4033540507581
9311471099.5831169891847.4168830108197
9412401244.85510943997-4.85510943996906
9511681251.22507022893-83.2250702289311
9614981463.9378250839734.0621749160268
9714161406.41698742469.5830125754037
9812301215.6220146456714.3779853543335
9911781210.75213797113-32.7521379711279
100940973.022762585265-33.0227625852649
10110751099.62116171748-24.6211617174836
10211991288.79054787734-89.7905478773368
10310441101.98335031831-57.9833503183063
1041044987.82830828322356.1716917167771
10512191145.3869044756973.6130955243141
10613121261.319267385550.6807326144983
10712611228.4532894767932.5467105232128
10816221558.0103944284263.9896055715797
10915291491.9107420385537.0892579614506
11013541312.5481201435741.4518798564304
11112811282.2342727319-1.23427273190214
11210231053.52447104858-30.5244710485849
11311161186.79922663894-70.7992266389374
11412811316.34944753381-35.3494475338096
11511571167.96421427858-10.9642142785801
11611261148.3437200763-22.3437200763028
11712711295.30030401976-24.300304019758
11813951366.3870673880128.6129326119915
11912611314.23741928904-53.2374192890391
12015811640.97777644178-59.9777764417818

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 434 & 427.098824786325 & 6.90117521367517 \tabularnewline
14 & 424 & 415.979040870119 & 8.02095912988119 \tabularnewline
15 & 362 & 352.311514231669 & 9.68848576833136 \tabularnewline
16 & 372 & 360.256322891027 & 11.7436771089734 \tabularnewline
17 & 661 & 645.635095338998 & 15.3649046610021 \tabularnewline
18 & 723 & 702.072172923935 & 20.9278270760655 \tabularnewline
19 & 558 & 509.510016712131 & 48.4899832878691 \tabularnewline
20 & 465 & 428.294577860632 & 36.7054221393676 \tabularnewline
21 & 486 & 458.760096506653 & 27.2399034933468 \tabularnewline
22 & 496 & 477.334313708427 & 18.6656862915731 \tabularnewline
23 & 548 & 498.694379320566 & 49.3056206794337 \tabularnewline
24 & 599 & 533.550644142014 & 65.4493558579857 \tabularnewline
25 & 610 & 585.42589252822 & 24.5741074717802 \tabularnewline
26 & 506 & 580.263556461646 & -74.2635564616464 \tabularnewline
27 & 517 & 493.728540013719 & 23.2714599862811 \tabularnewline
28 & 382 & 507.097538968242 & -125.097538968242 \tabularnewline
29 & 765 & 755.047336099812 & 9.9526639001881 \tabularnewline
30 & 878 & 813.839840464373 & 64.160159535627 \tabularnewline
31 & 620 & 653.419455465607 & -33.4194554656074 \tabularnewline
32 & 537 & 539.925433167331 & -2.92543316733145 \tabularnewline
33 & 589 & 552.109601991961 & 36.8903980080386 \tabularnewline
34 & 651 & 567.43578096087 & 83.5642190391302 \tabularnewline
35 & 744 & 629.447869433185 & 114.552130566815 \tabularnewline
36 & 858 & 694.79817412047 & 163.20182587953 \tabularnewline
37 & 858 & 746.312177841255 & 111.687822158745 \tabularnewline
38 & 785 & 696.656539357418 & 88.3434606425817 \tabularnewline
39 & 754 & 726.673856435046 & 27.3261435649539 \tabularnewline
40 & 568 & 636.219735947555 & -68.219735947555 \tabularnewline
41 & 878 & 996.373822196174 & -118.373822196174 \tabularnewline
42 & 1023 & 1056.02819622763 & -33.0281962276345 \tabularnewline
43 & 899 & 798.142541889563 & 100.857458110437 \tabularnewline
44 & 765 & 745.473131555722 & 19.5268684442775 \tabularnewline
45 & 785 & 792.398633400288 & -7.3986334002883 \tabularnewline
46 & 858 & 827.814704987471 & 30.185295012529 \tabularnewline
47 & 961 & 896.158465031883 & 64.8415349681171 \tabularnewline
48 & 1085 & 981.412632396584 & 103.587367603416 \tabularnewline
49 & 1002 & 979.04527145489 & 22.9547285451096 \tabularnewline
50 & 951 & 886.935389492451 & 64.064610507549 \tabularnewline
51 & 951 & 866.672220506508 & 84.3277794934924 \tabularnewline
52 & 785 & 725.254290233694 & 59.7457097663058 \tabularnewline
53 & 1023 & 1087.30979156891 & -64.3097915689088 \tabularnewline
54 & 1178 & 1223.16773336724 & -45.167733367238 \tabularnewline
55 & 1054 & 1056.49181531271 & -2.49181531271324 \tabularnewline
56 & 920 & 916.056846564013 & 3.94315343598703 \tabularnewline
57 & 961 & 939.371488104413 & 21.6285118955871 \tabularnewline
58 & 1126 & 1009.87076496607 & 116.129235033928 \tabularnewline
59 & 1199 & 1127.85961492453 & 71.140385075473 \tabularnewline
60 & 1302 & 1242.37697187187 & 59.6230281281328 \tabularnewline
61 & 1219 & 1170.09329644825 & 48.9067035517455 \tabularnewline
62 & 1085 & 1114.6633923435 & -29.6633923435033 \tabularnewline
63 & 1054 & 1081.3494287799 & -27.349428779904 \tabularnewline
64 & 806 & 889.895841231527 & -83.8958412315269 \tabularnewline
65 & 971 & 1122.17181072723 & -151.171810727232 \tabularnewline
66 & 1147 & 1246.19207857908 & -99.1920785790826 \tabularnewline
67 & 951 & 1093.9313896579 & -142.931389657901 \tabularnewline
68 & 837 & 917.007248268716 & -80.0072482687162 \tabularnewline
69 & 951 & 928.304158491606 & 22.6958415083942 \tabularnewline
70 & 1064 & 1065.99821350155 & -1.99821350154934 \tabularnewline
71 & 1126 & 1117.62343009664 & 8.37656990336041 \tabularnewline
72 & 1292 & 1205.646633082 & 86.3533669179999 \tabularnewline
73 & 1209 & 1133.59043477171 & 75.4095652282895 \tabularnewline
74 & 1002 & 1030.29804680567 & -28.2980468056653 \tabularnewline
75 & 1023 & 999.020812824852 & 23.9791871751482 \tabularnewline
76 & 827 & 782.547331131911 & 44.4526688680887 \tabularnewline
77 & 992 & 1004.71866010733 & -12.7186601073317 \tabularnewline
78 & 1137 & 1205.99054972618 & -68.9905497261807 \tabularnewline
79 & 971 & 1031.59978847381 & -60.5997884738063 \tabularnewline
80 & 858 & 923.271626020965 & -65.2716260209646 \tabularnewline
81 & 961 & 1011.56309999365 & -50.5630999936529 \tabularnewline
82 & 1085 & 1110.36999334341 & -25.3699933434132 \tabularnewline
83 & 1064 & 1162.50754732867 & -98.5075473286697 \tabularnewline
84 & 1312 & 1274.48187444276 & 37.5181255572411 \tabularnewline
85 & 1271 & 1180.40808670787 & 90.5919132921256 \tabularnewline
86 & 1106 & 1008.15372301416 & 97.8462769858399 \tabularnewline
87 & 1116 & 1050.74140826071 & 65.2585917392898 \tabularnewline
88 & 899 & 860.821947176736 & 38.1780528232639 \tabularnewline
89 & 1033 & 1040.6965309954 & -7.69653099539755 \tabularnewline
90 & 1240 & 1203.60973141046 & 36.3902685895405 \tabularnewline
91 & 1085 & 1065.95511267964 & 19.044887320365 \tabularnewline
92 & 992 & 977.596645949242 & 14.4033540507581 \tabularnewline
93 & 1147 & 1099.58311698918 & 47.4168830108197 \tabularnewline
94 & 1240 & 1244.85510943997 & -4.85510943996906 \tabularnewline
95 & 1168 & 1251.22507022893 & -83.2250702289311 \tabularnewline
96 & 1498 & 1463.93782508397 & 34.0621749160268 \tabularnewline
97 & 1416 & 1406.4169874246 & 9.5830125754037 \tabularnewline
98 & 1230 & 1215.62201464567 & 14.3779853543335 \tabularnewline
99 & 1178 & 1210.75213797113 & -32.7521379711279 \tabularnewline
100 & 940 & 973.022762585265 & -33.0227625852649 \tabularnewline
101 & 1075 & 1099.62116171748 & -24.6211617174836 \tabularnewline
102 & 1199 & 1288.79054787734 & -89.7905478773368 \tabularnewline
103 & 1044 & 1101.98335031831 & -57.9833503183063 \tabularnewline
104 & 1044 & 987.828308283223 & 56.1716917167771 \tabularnewline
105 & 1219 & 1145.38690447569 & 73.6130955243141 \tabularnewline
106 & 1312 & 1261.3192673855 & 50.6807326144983 \tabularnewline
107 & 1261 & 1228.45328947679 & 32.5467105232128 \tabularnewline
108 & 1622 & 1558.01039442842 & 63.9896055715797 \tabularnewline
109 & 1529 & 1491.91074203855 & 37.0892579614506 \tabularnewline
110 & 1354 & 1312.54812014357 & 41.4518798564304 \tabularnewline
111 & 1281 & 1282.2342727319 & -1.23427273190214 \tabularnewline
112 & 1023 & 1053.52447104858 & -30.5244710485849 \tabularnewline
113 & 1116 & 1186.79922663894 & -70.7992266389374 \tabularnewline
114 & 1281 & 1316.34944753381 & -35.3494475338096 \tabularnewline
115 & 1157 & 1167.96421427858 & -10.9642142785801 \tabularnewline
116 & 1126 & 1148.3437200763 & -22.3437200763028 \tabularnewline
117 & 1271 & 1295.30030401976 & -24.300304019758 \tabularnewline
118 & 1395 & 1366.38706738801 & 28.6129326119915 \tabularnewline
119 & 1261 & 1314.23741928904 & -53.2374192890391 \tabularnewline
120 & 1581 & 1640.97777644178 & -59.9777764417818 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123971&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]434[/C][C]427.098824786325[/C][C]6.90117521367517[/C][/ROW]
[ROW][C]14[/C][C]424[/C][C]415.979040870119[/C][C]8.02095912988119[/C][/ROW]
[ROW][C]15[/C][C]362[/C][C]352.311514231669[/C][C]9.68848576833136[/C][/ROW]
[ROW][C]16[/C][C]372[/C][C]360.256322891027[/C][C]11.7436771089734[/C][/ROW]
[ROW][C]17[/C][C]661[/C][C]645.635095338998[/C][C]15.3649046610021[/C][/ROW]
[ROW][C]18[/C][C]723[/C][C]702.072172923935[/C][C]20.9278270760655[/C][/ROW]
[ROW][C]19[/C][C]558[/C][C]509.510016712131[/C][C]48.4899832878691[/C][/ROW]
[ROW][C]20[/C][C]465[/C][C]428.294577860632[/C][C]36.7054221393676[/C][/ROW]
[ROW][C]21[/C][C]486[/C][C]458.760096506653[/C][C]27.2399034933468[/C][/ROW]
[ROW][C]22[/C][C]496[/C][C]477.334313708427[/C][C]18.6656862915731[/C][/ROW]
[ROW][C]23[/C][C]548[/C][C]498.694379320566[/C][C]49.3056206794337[/C][/ROW]
[ROW][C]24[/C][C]599[/C][C]533.550644142014[/C][C]65.4493558579857[/C][/ROW]
[ROW][C]25[/C][C]610[/C][C]585.42589252822[/C][C]24.5741074717802[/C][/ROW]
[ROW][C]26[/C][C]506[/C][C]580.263556461646[/C][C]-74.2635564616464[/C][/ROW]
[ROW][C]27[/C][C]517[/C][C]493.728540013719[/C][C]23.2714599862811[/C][/ROW]
[ROW][C]28[/C][C]382[/C][C]507.097538968242[/C][C]-125.097538968242[/C][/ROW]
[ROW][C]29[/C][C]765[/C][C]755.047336099812[/C][C]9.9526639001881[/C][/ROW]
[ROW][C]30[/C][C]878[/C][C]813.839840464373[/C][C]64.160159535627[/C][/ROW]
[ROW][C]31[/C][C]620[/C][C]653.419455465607[/C][C]-33.4194554656074[/C][/ROW]
[ROW][C]32[/C][C]537[/C][C]539.925433167331[/C][C]-2.92543316733145[/C][/ROW]
[ROW][C]33[/C][C]589[/C][C]552.109601991961[/C][C]36.8903980080386[/C][/ROW]
[ROW][C]34[/C][C]651[/C][C]567.43578096087[/C][C]83.5642190391302[/C][/ROW]
[ROW][C]35[/C][C]744[/C][C]629.447869433185[/C][C]114.552130566815[/C][/ROW]
[ROW][C]36[/C][C]858[/C][C]694.79817412047[/C][C]163.20182587953[/C][/ROW]
[ROW][C]37[/C][C]858[/C][C]746.312177841255[/C][C]111.687822158745[/C][/ROW]
[ROW][C]38[/C][C]785[/C][C]696.656539357418[/C][C]88.3434606425817[/C][/ROW]
[ROW][C]39[/C][C]754[/C][C]726.673856435046[/C][C]27.3261435649539[/C][/ROW]
[ROW][C]40[/C][C]568[/C][C]636.219735947555[/C][C]-68.219735947555[/C][/ROW]
[ROW][C]41[/C][C]878[/C][C]996.373822196174[/C][C]-118.373822196174[/C][/ROW]
[ROW][C]42[/C][C]1023[/C][C]1056.02819622763[/C][C]-33.0281962276345[/C][/ROW]
[ROW][C]43[/C][C]899[/C][C]798.142541889563[/C][C]100.857458110437[/C][/ROW]
[ROW][C]44[/C][C]765[/C][C]745.473131555722[/C][C]19.5268684442775[/C][/ROW]
[ROW][C]45[/C][C]785[/C][C]792.398633400288[/C][C]-7.3986334002883[/C][/ROW]
[ROW][C]46[/C][C]858[/C][C]827.814704987471[/C][C]30.185295012529[/C][/ROW]
[ROW][C]47[/C][C]961[/C][C]896.158465031883[/C][C]64.8415349681171[/C][/ROW]
[ROW][C]48[/C][C]1085[/C][C]981.412632396584[/C][C]103.587367603416[/C][/ROW]
[ROW][C]49[/C][C]1002[/C][C]979.04527145489[/C][C]22.9547285451096[/C][/ROW]
[ROW][C]50[/C][C]951[/C][C]886.935389492451[/C][C]64.064610507549[/C][/ROW]
[ROW][C]51[/C][C]951[/C][C]866.672220506508[/C][C]84.3277794934924[/C][/ROW]
[ROW][C]52[/C][C]785[/C][C]725.254290233694[/C][C]59.7457097663058[/C][/ROW]
[ROW][C]53[/C][C]1023[/C][C]1087.30979156891[/C][C]-64.3097915689088[/C][/ROW]
[ROW][C]54[/C][C]1178[/C][C]1223.16773336724[/C][C]-45.167733367238[/C][/ROW]
[ROW][C]55[/C][C]1054[/C][C]1056.49181531271[/C][C]-2.49181531271324[/C][/ROW]
[ROW][C]56[/C][C]920[/C][C]916.056846564013[/C][C]3.94315343598703[/C][/ROW]
[ROW][C]57[/C][C]961[/C][C]939.371488104413[/C][C]21.6285118955871[/C][/ROW]
[ROW][C]58[/C][C]1126[/C][C]1009.87076496607[/C][C]116.129235033928[/C][/ROW]
[ROW][C]59[/C][C]1199[/C][C]1127.85961492453[/C][C]71.140385075473[/C][/ROW]
[ROW][C]60[/C][C]1302[/C][C]1242.37697187187[/C][C]59.6230281281328[/C][/ROW]
[ROW][C]61[/C][C]1219[/C][C]1170.09329644825[/C][C]48.9067035517455[/C][/ROW]
[ROW][C]62[/C][C]1085[/C][C]1114.6633923435[/C][C]-29.6633923435033[/C][/ROW]
[ROW][C]63[/C][C]1054[/C][C]1081.3494287799[/C][C]-27.349428779904[/C][/ROW]
[ROW][C]64[/C][C]806[/C][C]889.895841231527[/C][C]-83.8958412315269[/C][/ROW]
[ROW][C]65[/C][C]971[/C][C]1122.17181072723[/C][C]-151.171810727232[/C][/ROW]
[ROW][C]66[/C][C]1147[/C][C]1246.19207857908[/C][C]-99.1920785790826[/C][/ROW]
[ROW][C]67[/C][C]951[/C][C]1093.9313896579[/C][C]-142.931389657901[/C][/ROW]
[ROW][C]68[/C][C]837[/C][C]917.007248268716[/C][C]-80.0072482687162[/C][/ROW]
[ROW][C]69[/C][C]951[/C][C]928.304158491606[/C][C]22.6958415083942[/C][/ROW]
[ROW][C]70[/C][C]1064[/C][C]1065.99821350155[/C][C]-1.99821350154934[/C][/ROW]
[ROW][C]71[/C][C]1126[/C][C]1117.62343009664[/C][C]8.37656990336041[/C][/ROW]
[ROW][C]72[/C][C]1292[/C][C]1205.646633082[/C][C]86.3533669179999[/C][/ROW]
[ROW][C]73[/C][C]1209[/C][C]1133.59043477171[/C][C]75.4095652282895[/C][/ROW]
[ROW][C]74[/C][C]1002[/C][C]1030.29804680567[/C][C]-28.2980468056653[/C][/ROW]
[ROW][C]75[/C][C]1023[/C][C]999.020812824852[/C][C]23.9791871751482[/C][/ROW]
[ROW][C]76[/C][C]827[/C][C]782.547331131911[/C][C]44.4526688680887[/C][/ROW]
[ROW][C]77[/C][C]992[/C][C]1004.71866010733[/C][C]-12.7186601073317[/C][/ROW]
[ROW][C]78[/C][C]1137[/C][C]1205.99054972618[/C][C]-68.9905497261807[/C][/ROW]
[ROW][C]79[/C][C]971[/C][C]1031.59978847381[/C][C]-60.5997884738063[/C][/ROW]
[ROW][C]80[/C][C]858[/C][C]923.271626020965[/C][C]-65.2716260209646[/C][/ROW]
[ROW][C]81[/C][C]961[/C][C]1011.56309999365[/C][C]-50.5630999936529[/C][/ROW]
[ROW][C]82[/C][C]1085[/C][C]1110.36999334341[/C][C]-25.3699933434132[/C][/ROW]
[ROW][C]83[/C][C]1064[/C][C]1162.50754732867[/C][C]-98.5075473286697[/C][/ROW]
[ROW][C]84[/C][C]1312[/C][C]1274.48187444276[/C][C]37.5181255572411[/C][/ROW]
[ROW][C]85[/C][C]1271[/C][C]1180.40808670787[/C][C]90.5919132921256[/C][/ROW]
[ROW][C]86[/C][C]1106[/C][C]1008.15372301416[/C][C]97.8462769858399[/C][/ROW]
[ROW][C]87[/C][C]1116[/C][C]1050.74140826071[/C][C]65.2585917392898[/C][/ROW]
[ROW][C]88[/C][C]899[/C][C]860.821947176736[/C][C]38.1780528232639[/C][/ROW]
[ROW][C]89[/C][C]1033[/C][C]1040.6965309954[/C][C]-7.69653099539755[/C][/ROW]
[ROW][C]90[/C][C]1240[/C][C]1203.60973141046[/C][C]36.3902685895405[/C][/ROW]
[ROW][C]91[/C][C]1085[/C][C]1065.95511267964[/C][C]19.044887320365[/C][/ROW]
[ROW][C]92[/C][C]992[/C][C]977.596645949242[/C][C]14.4033540507581[/C][/ROW]
[ROW][C]93[/C][C]1147[/C][C]1099.58311698918[/C][C]47.4168830108197[/C][/ROW]
[ROW][C]94[/C][C]1240[/C][C]1244.85510943997[/C][C]-4.85510943996906[/C][/ROW]
[ROW][C]95[/C][C]1168[/C][C]1251.22507022893[/C][C]-83.2250702289311[/C][/ROW]
[ROW][C]96[/C][C]1498[/C][C]1463.93782508397[/C][C]34.0621749160268[/C][/ROW]
[ROW][C]97[/C][C]1416[/C][C]1406.4169874246[/C][C]9.5830125754037[/C][/ROW]
[ROW][C]98[/C][C]1230[/C][C]1215.62201464567[/C][C]14.3779853543335[/C][/ROW]
[ROW][C]99[/C][C]1178[/C][C]1210.75213797113[/C][C]-32.7521379711279[/C][/ROW]
[ROW][C]100[/C][C]940[/C][C]973.022762585265[/C][C]-33.0227625852649[/C][/ROW]
[ROW][C]101[/C][C]1075[/C][C]1099.62116171748[/C][C]-24.6211617174836[/C][/ROW]
[ROW][C]102[/C][C]1199[/C][C]1288.79054787734[/C][C]-89.7905478773368[/C][/ROW]
[ROW][C]103[/C][C]1044[/C][C]1101.98335031831[/C][C]-57.9833503183063[/C][/ROW]
[ROW][C]104[/C][C]1044[/C][C]987.828308283223[/C][C]56.1716917167771[/C][/ROW]
[ROW][C]105[/C][C]1219[/C][C]1145.38690447569[/C][C]73.6130955243141[/C][/ROW]
[ROW][C]106[/C][C]1312[/C][C]1261.3192673855[/C][C]50.6807326144983[/C][/ROW]
[ROW][C]107[/C][C]1261[/C][C]1228.45328947679[/C][C]32.5467105232128[/C][/ROW]
[ROW][C]108[/C][C]1622[/C][C]1558.01039442842[/C][C]63.9896055715797[/C][/ROW]
[ROW][C]109[/C][C]1529[/C][C]1491.91074203855[/C][C]37.0892579614506[/C][/ROW]
[ROW][C]110[/C][C]1354[/C][C]1312.54812014357[/C][C]41.4518798564304[/C][/ROW]
[ROW][C]111[/C][C]1281[/C][C]1282.2342727319[/C][C]-1.23427273190214[/C][/ROW]
[ROW][C]112[/C][C]1023[/C][C]1053.52447104858[/C][C]-30.5244710485849[/C][/ROW]
[ROW][C]113[/C][C]1116[/C][C]1186.79922663894[/C][C]-70.7992266389374[/C][/ROW]
[ROW][C]114[/C][C]1281[/C][C]1316.34944753381[/C][C]-35.3494475338096[/C][/ROW]
[ROW][C]115[/C][C]1157[/C][C]1167.96421427858[/C][C]-10.9642142785801[/C][/ROW]
[ROW][C]116[/C][C]1126[/C][C]1148.3437200763[/C][C]-22.3437200763028[/C][/ROW]
[ROW][C]117[/C][C]1271[/C][C]1295.30030401976[/C][C]-24.300304019758[/C][/ROW]
[ROW][C]118[/C][C]1395[/C][C]1366.38706738801[/C][C]28.6129326119915[/C][/ROW]
[ROW][C]119[/C][C]1261[/C][C]1314.23741928904[/C][C]-53.2374192890391[/C][/ROW]
[ROW][C]120[/C][C]1581[/C][C]1640.97777644178[/C][C]-59.9777764417818[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123971&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123971&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
13434427.0988247863256.90117521367517
14424415.9790408701198.02095912988119
15362352.3115142316699.68848576833136
16372360.25632289102711.7436771089734
17661645.63509533899815.3649046610021
18723702.07217292393520.9278270760655
19558509.51001671213148.4899832878691
20465428.29457786063236.7054221393676
21486458.76009650665327.2399034933468
22496477.33431370842718.6656862915731
23548498.69437932056649.3056206794337
24599533.55064414201465.4493558579857
25610585.4258925282224.5741074717802
26506580.263556461646-74.2635564616464
27517493.72854001371923.2714599862811
28382507.097538968242-125.097538968242
29765755.0473360998129.9526639001881
30878813.83984046437364.160159535627
31620653.419455465607-33.4194554656074
32537539.925433167331-2.92543316733145
33589552.10960199196136.8903980080386
34651567.4357809608783.5642190391302
35744629.447869433185114.552130566815
36858694.79817412047163.20182587953
37858746.312177841255111.687822158745
38785696.65653935741888.3434606425817
39754726.67385643504627.3261435649539
40568636.219735947555-68.219735947555
41878996.373822196174-118.373822196174
4210231056.02819622763-33.0281962276345
43899798.142541889563100.857458110437
44765745.47313155572219.5268684442775
45785792.398633400288-7.3986334002883
46858827.81470498747130.185295012529
47961896.15846503188364.8415349681171
481085981.412632396584103.587367603416
491002979.0452714548922.9547285451096
50951886.93538949245164.064610507549
51951866.67222050650884.3277794934924
52785725.25429023369459.7457097663058
5310231087.30979156891-64.3097915689088
5411781223.16773336724-45.167733367238
5510541056.49181531271-2.49181531271324
56920916.0568465640133.94315343598703
57961939.37148810441321.6285118955871
5811261009.87076496607116.129235033928
5911991127.8596149245371.140385075473
6013021242.3769718718759.6230281281328
6112191170.0932964482548.9067035517455
6210851114.6633923435-29.6633923435033
6310541081.3494287799-27.349428779904
64806889.895841231527-83.8958412315269
659711122.17181072723-151.171810727232
6611471246.19207857908-99.1920785790826
679511093.9313896579-142.931389657901
68837917.007248268716-80.0072482687162
69951928.30415849160622.6958415083942
7010641065.99821350155-1.99821350154934
7111261117.623430096648.37656990336041
7212921205.64663308286.3533669179999
7312091133.5904347717175.4095652282895
7410021030.29804680567-28.2980468056653
751023999.02081282485223.9791871751482
76827782.54733113191144.4526688680887
779921004.71866010733-12.7186601073317
7811371205.99054972618-68.9905497261807
799711031.59978847381-60.5997884738063
80858923.271626020965-65.2716260209646
819611011.56309999365-50.5630999936529
8210851110.36999334341-25.3699933434132
8310641162.50754732867-98.5075473286697
8413121274.4818744427637.5181255572411
8512711180.4080867078790.5919132921256
8611061008.1537230141697.8462769858399
8711161050.7414082607165.2585917392898
88899860.82194717673638.1780528232639
8910331040.6965309954-7.69653099539755
9012401203.6097314104636.3902685895405
9110851065.9551126796419.044887320365
92992977.59664594924214.4033540507581
9311471099.5831169891847.4168830108197
9412401244.85510943997-4.85510943996906
9511681251.22507022893-83.2250702289311
9614981463.9378250839734.0621749160268
9714161406.41698742469.5830125754037
9812301215.6220146456714.3779853543335
9911781210.75213797113-32.7521379711279
100940973.022762585265-33.0227625852649
10110751099.62116171748-24.6211617174836
10211991288.79054787734-89.7905478773368
10310441101.98335031831-57.9833503183063
1041044987.82830828322356.1716917167771
10512191145.3869044756973.6130955243141
10613121261.319267385550.6807326144983
10712611228.4532894767932.5467105232128
10816221558.0103944284263.9896055715797
10915291491.9107420385537.0892579614506
11013541312.5481201435741.4518798564304
11112811282.2342727319-1.23427273190214
11210231053.52447104858-30.5244710485849
11311161186.79922663894-70.7992266389374
11412811316.34944753381-35.3494475338096
11511571167.96421427858-10.9642142785801
11611261148.3437200763-22.3437200763028
11712711295.30030401976-24.300304019758
11813951366.3870673880128.6129326119915
11912611314.23741928904-53.2374192890391
12015811640.97777644178-59.9777764417818







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1211519.609898515591400.800577299691638.41921973148
1221332.495570774891208.716425025431456.27471652434
1231259.856287452811131.299299944751388.41327496088
1241010.7770757904877.6135629506121143.94058863018
1251124.46817685174986.8522502061891262.08410349729
1261299.799066412371157.870332953651441.72779987109
1271179.003362228391032.889066227341325.11765822943
1281154.533322965711004.350069536561304.71657639486
1291306.635096108781152.490256022431460.77993619513
1301422.272955610331264.265823366471580.28008785419
1311303.831611757421142.054369987711465.60885352712
1321641.360139860141475.898669815611806.82160990467

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 1519.60989851559 & 1400.80057729969 & 1638.41921973148 \tabularnewline
122 & 1332.49557077489 & 1208.71642502543 & 1456.27471652434 \tabularnewline
123 & 1259.85628745281 & 1131.29929994475 & 1388.41327496088 \tabularnewline
124 & 1010.7770757904 & 877.613562950612 & 1143.94058863018 \tabularnewline
125 & 1124.46817685174 & 986.852250206189 & 1262.08410349729 \tabularnewline
126 & 1299.79906641237 & 1157.87033295365 & 1441.72779987109 \tabularnewline
127 & 1179.00336222839 & 1032.88906622734 & 1325.11765822943 \tabularnewline
128 & 1154.53332296571 & 1004.35006953656 & 1304.71657639486 \tabularnewline
129 & 1306.63509610878 & 1152.49025602243 & 1460.77993619513 \tabularnewline
130 & 1422.27295561033 & 1264.26582336647 & 1580.28008785419 \tabularnewline
131 & 1303.83161175742 & 1142.05436998771 & 1465.60885352712 \tabularnewline
132 & 1641.36013986014 & 1475.89866981561 & 1806.82160990467 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123971&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]121[/C][C]1519.60989851559[/C][C]1400.80057729969[/C][C]1638.41921973148[/C][/ROW]
[ROW][C]122[/C][C]1332.49557077489[/C][C]1208.71642502543[/C][C]1456.27471652434[/C][/ROW]
[ROW][C]123[/C][C]1259.85628745281[/C][C]1131.29929994475[/C][C]1388.41327496088[/C][/ROW]
[ROW][C]124[/C][C]1010.7770757904[/C][C]877.613562950612[/C][C]1143.94058863018[/C][/ROW]
[ROW][C]125[/C][C]1124.46817685174[/C][C]986.852250206189[/C][C]1262.08410349729[/C][/ROW]
[ROW][C]126[/C][C]1299.79906641237[/C][C]1157.87033295365[/C][C]1441.72779987109[/C][/ROW]
[ROW][C]127[/C][C]1179.00336222839[/C][C]1032.88906622734[/C][C]1325.11765822943[/C][/ROW]
[ROW][C]128[/C][C]1154.53332296571[/C][C]1004.35006953656[/C][C]1304.71657639486[/C][/ROW]
[ROW][C]129[/C][C]1306.63509610878[/C][C]1152.49025602243[/C][C]1460.77993619513[/C][/ROW]
[ROW][C]130[/C][C]1422.27295561033[/C][C]1264.26582336647[/C][C]1580.28008785419[/C][/ROW]
[ROW][C]131[/C][C]1303.83161175742[/C][C]1142.05436998771[/C][C]1465.60885352712[/C][/ROW]
[ROW][C]132[/C][C]1641.36013986014[/C][C]1475.89866981561[/C][C]1806.82160990467[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123971&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123971&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
1211519.609898515591400.800577299691638.41921973148
1221332.495570774891208.716425025431456.27471652434
1231259.856287452811131.299299944751388.41327496088
1241010.7770757904877.6135629506121143.94058863018
1251124.46817685174986.8522502061891262.08410349729
1261299.799066412371157.870332953651441.72779987109
1271179.003362228391032.889066227341325.11765822943
1281154.533322965711004.350069536561304.71657639486
1291306.635096108781152.490256022431460.77993619513
1301422.272955610331264.265823366471580.28008785419
1311303.831611757421142.054369987711465.60885352712
1321641.360139860141475.898669815611806.82160990467



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')