Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 04 Aug 2012 08:29:12 -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/2012/Aug/04/t13440834466zxejwivbqufdza.htm/, Retrieved Sun, 28 Apr 2024 18:13:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=169014, Retrieved Sun, 28 Apr 2024 18:13:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsSelleslaghs Tessa
Estimated Impact194
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [Tijdreeks A stap 32] [2012-08-03 12:36:28] [da1dd7ba20267c8dec1286cd318791a0]
- R P     [Exponential Smoothing] [Tijdreeks A stap 32] [2012-08-04 12:29:12] [c55f1f83f487169d019dc495d8d2e134] [Current]
Feedback Forum

Post a new message
Dataseries X:
3028
3017
3007
2986
3193
3183
3028
2924
2935
2935
2945
2966
2955
3038
3069
3038
3152
3079
2914
2873
2873
2893
2811
2873
2821
2873
2955
2986
3059
3028
2842
2769
2738
2769
2718
2738
2676
2780
2831
2842
3038
3038
2780
2718
2718
2749
2614
2552
2480
2501
2594
2521
2718
2749
2552
2480
2439
2480
2366
2325
2160
2201
2211
2222
2418
2397
2160
2056
2015
2067
1870
1736
1488
1509
1509
1488
1664
1674
1467
1426
1343
1457
1250
1126
889
940
878
899
1054
1085
982
971
971
1106
868
713
444
661
630
641
889
858
744
796
796
982
765
641
444
703
682
692
909
889
816
827
878
992
816
672




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=169014&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=169014&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169014&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
alpha1
beta0
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169014&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[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169014&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169014&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
alpha1
beta0
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3300730061
429862996-10
531932975218
6318331821
730283172-144
829243017-93
92935291322
102935292411
112945292421
122966293432
13295529550
143038294494
153069302742
1630383058-20
1731523027125
1830793141-62
1929143068-154
2028732903-30
212873286211
222893286231
2328112882-71
242873280073
2528212862-41
262873281063
272955286293
282986294442
293059297584
3030283048-20
3128423017-175
3227692831-62
3327382758-20
342769272742
3527182758-40
362738270731
3726762727-51
3827802665115
392831276962
402842282022
4130382831207
423038302711
4327803027-247
4427182769-51
452718270711
462749270742
4726142738-124
4825522603-51
4924802541-61
502501246932
5125942490104
5225212583-62
5327182510208
542749270742
5525522738-186
5624802541-61
5724392469-30
582480242852
5923662469-103
6023252355-30
6121602314-154
622201214952
632211219021
642222220022
6524182211207
6623972407-10
6721602386-226
6820562149-93
6920152045-30
702067200463
7118702056-186
7217361859-123
7314881725-237
741509147732
751509149811
7614881498-10
7716641477187
781674165321
7914671663-196
8014261456-30
8113431415-72
8214571332125
8312501446-196
8411261239-113
858891115-226
8694087862
87878929-51
8889986732
891054888166
901085104342
919821074-92
929719710
9397196011
941106960146
958681095-227
96713857-144
97444702-258
98661433228
99630650-20
10064161922
101889630259
102858878-20
103744847-103
10479673363
10579678511
106982785197
107765971-206
108641754-113
109444630-186
110703433270
111682692-10
11269267121
113909681228
114889898-9
115816878-62
11682780522
11787881662
118992867125
119816981-165
120672805-133

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 3007 & 3006 & 1 \tabularnewline
4 & 2986 & 2996 & -10 \tabularnewline
5 & 3193 & 2975 & 218 \tabularnewline
6 & 3183 & 3182 & 1 \tabularnewline
7 & 3028 & 3172 & -144 \tabularnewline
8 & 2924 & 3017 & -93 \tabularnewline
9 & 2935 & 2913 & 22 \tabularnewline
10 & 2935 & 2924 & 11 \tabularnewline
11 & 2945 & 2924 & 21 \tabularnewline
12 & 2966 & 2934 & 32 \tabularnewline
13 & 2955 & 2955 & 0 \tabularnewline
14 & 3038 & 2944 & 94 \tabularnewline
15 & 3069 & 3027 & 42 \tabularnewline
16 & 3038 & 3058 & -20 \tabularnewline
17 & 3152 & 3027 & 125 \tabularnewline
18 & 3079 & 3141 & -62 \tabularnewline
19 & 2914 & 3068 & -154 \tabularnewline
20 & 2873 & 2903 & -30 \tabularnewline
21 & 2873 & 2862 & 11 \tabularnewline
22 & 2893 & 2862 & 31 \tabularnewline
23 & 2811 & 2882 & -71 \tabularnewline
24 & 2873 & 2800 & 73 \tabularnewline
25 & 2821 & 2862 & -41 \tabularnewline
26 & 2873 & 2810 & 63 \tabularnewline
27 & 2955 & 2862 & 93 \tabularnewline
28 & 2986 & 2944 & 42 \tabularnewline
29 & 3059 & 2975 & 84 \tabularnewline
30 & 3028 & 3048 & -20 \tabularnewline
31 & 2842 & 3017 & -175 \tabularnewline
32 & 2769 & 2831 & -62 \tabularnewline
33 & 2738 & 2758 & -20 \tabularnewline
34 & 2769 & 2727 & 42 \tabularnewline
35 & 2718 & 2758 & -40 \tabularnewline
36 & 2738 & 2707 & 31 \tabularnewline
37 & 2676 & 2727 & -51 \tabularnewline
38 & 2780 & 2665 & 115 \tabularnewline
39 & 2831 & 2769 & 62 \tabularnewline
40 & 2842 & 2820 & 22 \tabularnewline
41 & 3038 & 2831 & 207 \tabularnewline
42 & 3038 & 3027 & 11 \tabularnewline
43 & 2780 & 3027 & -247 \tabularnewline
44 & 2718 & 2769 & -51 \tabularnewline
45 & 2718 & 2707 & 11 \tabularnewline
46 & 2749 & 2707 & 42 \tabularnewline
47 & 2614 & 2738 & -124 \tabularnewline
48 & 2552 & 2603 & -51 \tabularnewline
49 & 2480 & 2541 & -61 \tabularnewline
50 & 2501 & 2469 & 32 \tabularnewline
51 & 2594 & 2490 & 104 \tabularnewline
52 & 2521 & 2583 & -62 \tabularnewline
53 & 2718 & 2510 & 208 \tabularnewline
54 & 2749 & 2707 & 42 \tabularnewline
55 & 2552 & 2738 & -186 \tabularnewline
56 & 2480 & 2541 & -61 \tabularnewline
57 & 2439 & 2469 & -30 \tabularnewline
58 & 2480 & 2428 & 52 \tabularnewline
59 & 2366 & 2469 & -103 \tabularnewline
60 & 2325 & 2355 & -30 \tabularnewline
61 & 2160 & 2314 & -154 \tabularnewline
62 & 2201 & 2149 & 52 \tabularnewline
63 & 2211 & 2190 & 21 \tabularnewline
64 & 2222 & 2200 & 22 \tabularnewline
65 & 2418 & 2211 & 207 \tabularnewline
66 & 2397 & 2407 & -10 \tabularnewline
67 & 2160 & 2386 & -226 \tabularnewline
68 & 2056 & 2149 & -93 \tabularnewline
69 & 2015 & 2045 & -30 \tabularnewline
70 & 2067 & 2004 & 63 \tabularnewline
71 & 1870 & 2056 & -186 \tabularnewline
72 & 1736 & 1859 & -123 \tabularnewline
73 & 1488 & 1725 & -237 \tabularnewline
74 & 1509 & 1477 & 32 \tabularnewline
75 & 1509 & 1498 & 11 \tabularnewline
76 & 1488 & 1498 & -10 \tabularnewline
77 & 1664 & 1477 & 187 \tabularnewline
78 & 1674 & 1653 & 21 \tabularnewline
79 & 1467 & 1663 & -196 \tabularnewline
80 & 1426 & 1456 & -30 \tabularnewline
81 & 1343 & 1415 & -72 \tabularnewline
82 & 1457 & 1332 & 125 \tabularnewline
83 & 1250 & 1446 & -196 \tabularnewline
84 & 1126 & 1239 & -113 \tabularnewline
85 & 889 & 1115 & -226 \tabularnewline
86 & 940 & 878 & 62 \tabularnewline
87 & 878 & 929 & -51 \tabularnewline
88 & 899 & 867 & 32 \tabularnewline
89 & 1054 & 888 & 166 \tabularnewline
90 & 1085 & 1043 & 42 \tabularnewline
91 & 982 & 1074 & -92 \tabularnewline
92 & 971 & 971 & 0 \tabularnewline
93 & 971 & 960 & 11 \tabularnewline
94 & 1106 & 960 & 146 \tabularnewline
95 & 868 & 1095 & -227 \tabularnewline
96 & 713 & 857 & -144 \tabularnewline
97 & 444 & 702 & -258 \tabularnewline
98 & 661 & 433 & 228 \tabularnewline
99 & 630 & 650 & -20 \tabularnewline
100 & 641 & 619 & 22 \tabularnewline
101 & 889 & 630 & 259 \tabularnewline
102 & 858 & 878 & -20 \tabularnewline
103 & 744 & 847 & -103 \tabularnewline
104 & 796 & 733 & 63 \tabularnewline
105 & 796 & 785 & 11 \tabularnewline
106 & 982 & 785 & 197 \tabularnewline
107 & 765 & 971 & -206 \tabularnewline
108 & 641 & 754 & -113 \tabularnewline
109 & 444 & 630 & -186 \tabularnewline
110 & 703 & 433 & 270 \tabularnewline
111 & 682 & 692 & -10 \tabularnewline
112 & 692 & 671 & 21 \tabularnewline
113 & 909 & 681 & 228 \tabularnewline
114 & 889 & 898 & -9 \tabularnewline
115 & 816 & 878 & -62 \tabularnewline
116 & 827 & 805 & 22 \tabularnewline
117 & 878 & 816 & 62 \tabularnewline
118 & 992 & 867 & 125 \tabularnewline
119 & 816 & 981 & -165 \tabularnewline
120 & 672 & 805 & -133 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169014&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]3007[/C][C]3006[/C][C]1[/C][/ROW]
[ROW][C]4[/C][C]2986[/C][C]2996[/C][C]-10[/C][/ROW]
[ROW][C]5[/C][C]3193[/C][C]2975[/C][C]218[/C][/ROW]
[ROW][C]6[/C][C]3183[/C][C]3182[/C][C]1[/C][/ROW]
[ROW][C]7[/C][C]3028[/C][C]3172[/C][C]-144[/C][/ROW]
[ROW][C]8[/C][C]2924[/C][C]3017[/C][C]-93[/C][/ROW]
[ROW][C]9[/C][C]2935[/C][C]2913[/C][C]22[/C][/ROW]
[ROW][C]10[/C][C]2935[/C][C]2924[/C][C]11[/C][/ROW]
[ROW][C]11[/C][C]2945[/C][C]2924[/C][C]21[/C][/ROW]
[ROW][C]12[/C][C]2966[/C][C]2934[/C][C]32[/C][/ROW]
[ROW][C]13[/C][C]2955[/C][C]2955[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]3038[/C][C]2944[/C][C]94[/C][/ROW]
[ROW][C]15[/C][C]3069[/C][C]3027[/C][C]42[/C][/ROW]
[ROW][C]16[/C][C]3038[/C][C]3058[/C][C]-20[/C][/ROW]
[ROW][C]17[/C][C]3152[/C][C]3027[/C][C]125[/C][/ROW]
[ROW][C]18[/C][C]3079[/C][C]3141[/C][C]-62[/C][/ROW]
[ROW][C]19[/C][C]2914[/C][C]3068[/C][C]-154[/C][/ROW]
[ROW][C]20[/C][C]2873[/C][C]2903[/C][C]-30[/C][/ROW]
[ROW][C]21[/C][C]2873[/C][C]2862[/C][C]11[/C][/ROW]
[ROW][C]22[/C][C]2893[/C][C]2862[/C][C]31[/C][/ROW]
[ROW][C]23[/C][C]2811[/C][C]2882[/C][C]-71[/C][/ROW]
[ROW][C]24[/C][C]2873[/C][C]2800[/C][C]73[/C][/ROW]
[ROW][C]25[/C][C]2821[/C][C]2862[/C][C]-41[/C][/ROW]
[ROW][C]26[/C][C]2873[/C][C]2810[/C][C]63[/C][/ROW]
[ROW][C]27[/C][C]2955[/C][C]2862[/C][C]93[/C][/ROW]
[ROW][C]28[/C][C]2986[/C][C]2944[/C][C]42[/C][/ROW]
[ROW][C]29[/C][C]3059[/C][C]2975[/C][C]84[/C][/ROW]
[ROW][C]30[/C][C]3028[/C][C]3048[/C][C]-20[/C][/ROW]
[ROW][C]31[/C][C]2842[/C][C]3017[/C][C]-175[/C][/ROW]
[ROW][C]32[/C][C]2769[/C][C]2831[/C][C]-62[/C][/ROW]
[ROW][C]33[/C][C]2738[/C][C]2758[/C][C]-20[/C][/ROW]
[ROW][C]34[/C][C]2769[/C][C]2727[/C][C]42[/C][/ROW]
[ROW][C]35[/C][C]2718[/C][C]2758[/C][C]-40[/C][/ROW]
[ROW][C]36[/C][C]2738[/C][C]2707[/C][C]31[/C][/ROW]
[ROW][C]37[/C][C]2676[/C][C]2727[/C][C]-51[/C][/ROW]
[ROW][C]38[/C][C]2780[/C][C]2665[/C][C]115[/C][/ROW]
[ROW][C]39[/C][C]2831[/C][C]2769[/C][C]62[/C][/ROW]
[ROW][C]40[/C][C]2842[/C][C]2820[/C][C]22[/C][/ROW]
[ROW][C]41[/C][C]3038[/C][C]2831[/C][C]207[/C][/ROW]
[ROW][C]42[/C][C]3038[/C][C]3027[/C][C]11[/C][/ROW]
[ROW][C]43[/C][C]2780[/C][C]3027[/C][C]-247[/C][/ROW]
[ROW][C]44[/C][C]2718[/C][C]2769[/C][C]-51[/C][/ROW]
[ROW][C]45[/C][C]2718[/C][C]2707[/C][C]11[/C][/ROW]
[ROW][C]46[/C][C]2749[/C][C]2707[/C][C]42[/C][/ROW]
[ROW][C]47[/C][C]2614[/C][C]2738[/C][C]-124[/C][/ROW]
[ROW][C]48[/C][C]2552[/C][C]2603[/C][C]-51[/C][/ROW]
[ROW][C]49[/C][C]2480[/C][C]2541[/C][C]-61[/C][/ROW]
[ROW][C]50[/C][C]2501[/C][C]2469[/C][C]32[/C][/ROW]
[ROW][C]51[/C][C]2594[/C][C]2490[/C][C]104[/C][/ROW]
[ROW][C]52[/C][C]2521[/C][C]2583[/C][C]-62[/C][/ROW]
[ROW][C]53[/C][C]2718[/C][C]2510[/C][C]208[/C][/ROW]
[ROW][C]54[/C][C]2749[/C][C]2707[/C][C]42[/C][/ROW]
[ROW][C]55[/C][C]2552[/C][C]2738[/C][C]-186[/C][/ROW]
[ROW][C]56[/C][C]2480[/C][C]2541[/C][C]-61[/C][/ROW]
[ROW][C]57[/C][C]2439[/C][C]2469[/C][C]-30[/C][/ROW]
[ROW][C]58[/C][C]2480[/C][C]2428[/C][C]52[/C][/ROW]
[ROW][C]59[/C][C]2366[/C][C]2469[/C][C]-103[/C][/ROW]
[ROW][C]60[/C][C]2325[/C][C]2355[/C][C]-30[/C][/ROW]
[ROW][C]61[/C][C]2160[/C][C]2314[/C][C]-154[/C][/ROW]
[ROW][C]62[/C][C]2201[/C][C]2149[/C][C]52[/C][/ROW]
[ROW][C]63[/C][C]2211[/C][C]2190[/C][C]21[/C][/ROW]
[ROW][C]64[/C][C]2222[/C][C]2200[/C][C]22[/C][/ROW]
[ROW][C]65[/C][C]2418[/C][C]2211[/C][C]207[/C][/ROW]
[ROW][C]66[/C][C]2397[/C][C]2407[/C][C]-10[/C][/ROW]
[ROW][C]67[/C][C]2160[/C][C]2386[/C][C]-226[/C][/ROW]
[ROW][C]68[/C][C]2056[/C][C]2149[/C][C]-93[/C][/ROW]
[ROW][C]69[/C][C]2015[/C][C]2045[/C][C]-30[/C][/ROW]
[ROW][C]70[/C][C]2067[/C][C]2004[/C][C]63[/C][/ROW]
[ROW][C]71[/C][C]1870[/C][C]2056[/C][C]-186[/C][/ROW]
[ROW][C]72[/C][C]1736[/C][C]1859[/C][C]-123[/C][/ROW]
[ROW][C]73[/C][C]1488[/C][C]1725[/C][C]-237[/C][/ROW]
[ROW][C]74[/C][C]1509[/C][C]1477[/C][C]32[/C][/ROW]
[ROW][C]75[/C][C]1509[/C][C]1498[/C][C]11[/C][/ROW]
[ROW][C]76[/C][C]1488[/C][C]1498[/C][C]-10[/C][/ROW]
[ROW][C]77[/C][C]1664[/C][C]1477[/C][C]187[/C][/ROW]
[ROW][C]78[/C][C]1674[/C][C]1653[/C][C]21[/C][/ROW]
[ROW][C]79[/C][C]1467[/C][C]1663[/C][C]-196[/C][/ROW]
[ROW][C]80[/C][C]1426[/C][C]1456[/C][C]-30[/C][/ROW]
[ROW][C]81[/C][C]1343[/C][C]1415[/C][C]-72[/C][/ROW]
[ROW][C]82[/C][C]1457[/C][C]1332[/C][C]125[/C][/ROW]
[ROW][C]83[/C][C]1250[/C][C]1446[/C][C]-196[/C][/ROW]
[ROW][C]84[/C][C]1126[/C][C]1239[/C][C]-113[/C][/ROW]
[ROW][C]85[/C][C]889[/C][C]1115[/C][C]-226[/C][/ROW]
[ROW][C]86[/C][C]940[/C][C]878[/C][C]62[/C][/ROW]
[ROW][C]87[/C][C]878[/C][C]929[/C][C]-51[/C][/ROW]
[ROW][C]88[/C][C]899[/C][C]867[/C][C]32[/C][/ROW]
[ROW][C]89[/C][C]1054[/C][C]888[/C][C]166[/C][/ROW]
[ROW][C]90[/C][C]1085[/C][C]1043[/C][C]42[/C][/ROW]
[ROW][C]91[/C][C]982[/C][C]1074[/C][C]-92[/C][/ROW]
[ROW][C]92[/C][C]971[/C][C]971[/C][C]0[/C][/ROW]
[ROW][C]93[/C][C]971[/C][C]960[/C][C]11[/C][/ROW]
[ROW][C]94[/C][C]1106[/C][C]960[/C][C]146[/C][/ROW]
[ROW][C]95[/C][C]868[/C][C]1095[/C][C]-227[/C][/ROW]
[ROW][C]96[/C][C]713[/C][C]857[/C][C]-144[/C][/ROW]
[ROW][C]97[/C][C]444[/C][C]702[/C][C]-258[/C][/ROW]
[ROW][C]98[/C][C]661[/C][C]433[/C][C]228[/C][/ROW]
[ROW][C]99[/C][C]630[/C][C]650[/C][C]-20[/C][/ROW]
[ROW][C]100[/C][C]641[/C][C]619[/C][C]22[/C][/ROW]
[ROW][C]101[/C][C]889[/C][C]630[/C][C]259[/C][/ROW]
[ROW][C]102[/C][C]858[/C][C]878[/C][C]-20[/C][/ROW]
[ROW][C]103[/C][C]744[/C][C]847[/C][C]-103[/C][/ROW]
[ROW][C]104[/C][C]796[/C][C]733[/C][C]63[/C][/ROW]
[ROW][C]105[/C][C]796[/C][C]785[/C][C]11[/C][/ROW]
[ROW][C]106[/C][C]982[/C][C]785[/C][C]197[/C][/ROW]
[ROW][C]107[/C][C]765[/C][C]971[/C][C]-206[/C][/ROW]
[ROW][C]108[/C][C]641[/C][C]754[/C][C]-113[/C][/ROW]
[ROW][C]109[/C][C]444[/C][C]630[/C][C]-186[/C][/ROW]
[ROW][C]110[/C][C]703[/C][C]433[/C][C]270[/C][/ROW]
[ROW][C]111[/C][C]682[/C][C]692[/C][C]-10[/C][/ROW]
[ROW][C]112[/C][C]692[/C][C]671[/C][C]21[/C][/ROW]
[ROW][C]113[/C][C]909[/C][C]681[/C][C]228[/C][/ROW]
[ROW][C]114[/C][C]889[/C][C]898[/C][C]-9[/C][/ROW]
[ROW][C]115[/C][C]816[/C][C]878[/C][C]-62[/C][/ROW]
[ROW][C]116[/C][C]827[/C][C]805[/C][C]22[/C][/ROW]
[ROW][C]117[/C][C]878[/C][C]816[/C][C]62[/C][/ROW]
[ROW][C]118[/C][C]992[/C][C]867[/C][C]125[/C][/ROW]
[ROW][C]119[/C][C]816[/C][C]981[/C][C]-165[/C][/ROW]
[ROW][C]120[/C][C]672[/C][C]805[/C][C]-133[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169014&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169014&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
3300730061
429862996-10
531932975218
6318331821
730283172-144
829243017-93
92935291322
102935292411
112945292421
122966293432
13295529550
143038294494
153069302742
1630383058-20
1731523027125
1830793141-62
1929143068-154
2028732903-30
212873286211
222893286231
2328112882-71
242873280073
2528212862-41
262873281063
272955286293
282986294442
293059297584
3030283048-20
3128423017-175
3227692831-62
3327382758-20
342769272742
3527182758-40
362738270731
3726762727-51
3827802665115
392831276962
402842282022
4130382831207
423038302711
4327803027-247
4427182769-51
452718270711
462749270742
4726142738-124
4825522603-51
4924802541-61
502501246932
5125942490104
5225212583-62
5327182510208
542749270742
5525522738-186
5624802541-61
5724392469-30
582480242852
5923662469-103
6023252355-30
6121602314-154
622201214952
632211219021
642222220022
6524182211207
6623972407-10
6721602386-226
6820562149-93
6920152045-30
702067200463
7118702056-186
7217361859-123
7314881725-237
741509147732
751509149811
7614881498-10
7716641477187
781674165321
7914671663-196
8014261456-30
8113431415-72
8214571332125
8312501446-196
8411261239-113
858891115-226
8694087862
87878929-51
8889986732
891054888166
901085104342
919821074-92
929719710
9397196011
941106960146
958681095-227
96713857-144
97444702-258
98661433228
99630650-20
10064161922
101889630259
102858878-20
103744847-103
10479673363
10579678511
106982785197
107765971-206
108641754-113
109444630-186
110703433270
111682692-10
11269267121
113909681228
114889898-9
115816878-62
11682780522
11787881662
118992867125
119816981-165
120672805-133







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121661434.196135087659887.803864912341
122650329.250898242332970.749101757668
123639246.1641826188371031.83581738116
124628174.3922701753181081.60772982468
125617109.8511404963261124.14885950367
12660650.4462592736391161.55374072636
127595-5.06662294634271195.06662294634
128584-57.49820351533621225.49820351534
129573-107.4115947370231253.41159473702
130562-155.2167952521431279.21679525214
131551-201.2233209166881303.22332091669
132540-245.6716347623261325.67163476233

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 661 & 434.196135087659 & 887.803864912341 \tabularnewline
122 & 650 & 329.250898242332 & 970.749101757668 \tabularnewline
123 & 639 & 246.164182618837 & 1031.83581738116 \tabularnewline
124 & 628 & 174.392270175318 & 1081.60772982468 \tabularnewline
125 & 617 & 109.851140496326 & 1124.14885950367 \tabularnewline
126 & 606 & 50.446259273639 & 1161.55374072636 \tabularnewline
127 & 595 & -5.0666229463427 & 1195.06662294634 \tabularnewline
128 & 584 & -57.4982035153362 & 1225.49820351534 \tabularnewline
129 & 573 & -107.411594737023 & 1253.41159473702 \tabularnewline
130 & 562 & -155.216795252143 & 1279.21679525214 \tabularnewline
131 & 551 & -201.223320916688 & 1303.22332091669 \tabularnewline
132 & 540 & -245.671634762326 & 1325.67163476233 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169014&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]661[/C][C]434.196135087659[/C][C]887.803864912341[/C][/ROW]
[ROW][C]122[/C][C]650[/C][C]329.250898242332[/C][C]970.749101757668[/C][/ROW]
[ROW][C]123[/C][C]639[/C][C]246.164182618837[/C][C]1031.83581738116[/C][/ROW]
[ROW][C]124[/C][C]628[/C][C]174.392270175318[/C][C]1081.60772982468[/C][/ROW]
[ROW][C]125[/C][C]617[/C][C]109.851140496326[/C][C]1124.14885950367[/C][/ROW]
[ROW][C]126[/C][C]606[/C][C]50.446259273639[/C][C]1161.55374072636[/C][/ROW]
[ROW][C]127[/C][C]595[/C][C]-5.0666229463427[/C][C]1195.06662294634[/C][/ROW]
[ROW][C]128[/C][C]584[/C][C]-57.4982035153362[/C][C]1225.49820351534[/C][/ROW]
[ROW][C]129[/C][C]573[/C][C]-107.411594737023[/C][C]1253.41159473702[/C][/ROW]
[ROW][C]130[/C][C]562[/C][C]-155.216795252143[/C][C]1279.21679525214[/C][/ROW]
[ROW][C]131[/C][C]551[/C][C]-201.223320916688[/C][C]1303.22332091669[/C][/ROW]
[ROW][C]132[/C][C]540[/C][C]-245.671634762326[/C][C]1325.67163476233[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169014&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169014&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
121661434.196135087659887.803864912341
122650329.250898242332970.749101757668
123639246.1641826188371031.83581738116
124628174.3922701753181081.60772982468
125617109.8511404963261124.14885950367
12660650.4462592736391161.55374072636
127595-5.06662294634271195.06662294634
128584-57.49820351533621225.49820351534
129573-107.4115947370231253.41159473702
130562-155.2167952521431279.21679525214
131551-201.2233209166881303.22332091669
132540-245.6716347623261325.67163476233



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')