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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 06 Jun 2010 19:17:39 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Jun/06/t1275852129h1codrpwmzrf8ts.htm/, Retrieved Sat, 27 Apr 2024 18:47:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=77772, Retrieved Sat, 27 Apr 2024 18:47:50 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact159
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [] [2010-06-02 07:27:00] [74be16979710d4c4e7c6647856088456]
-   PD    [Exponential Smoothing] [taak 10] [2010-06-06 19:17:39] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
41086
39690
43129
93.2
96
95.2
77.1
70.9
64.8
70.1
77.3
79.5
100.6
100.7
107.1
95.9
82.8
83.3
80
80.4
67.5
75.7
71.1
89.3
101.1
105.2
114.1
96.3
84.4
91.2
81.9
80.5
70.4
74.8
75.9
86.3
98.7
100.9
113.8
89.8
84.4
87.2
85.6
72
69.2
77.5
78.1
94.3
97.7
100.2
116.4
97.1
93
96
80.5
76.1
69.9
73.6
92.6
94.2
93.5
108.5
109.4
105.1
92.5
97.1




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77772&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77772&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77772&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.891950774998702
beta0.0308709918356764
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.891950774998702 \tabularnewline
beta & 0.0308709918356764 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77772&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]0.891950774998702[/C][/ROW]
[ROW][C]beta[/C][C]0.0308709918356764[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77772&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77772&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
alpha0.891950774998702
beta0.0308709918356764
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
343129382944835
493.241343.7156807425-41250.5156807425
5962151.5702742753-2055.5702742753
695.2-2137.214161060582232.41416106058
777.1-2539.857127856522616.95712785652
870.9-2527.447722772482598.34772277248
964.8-2460.090433856892524.89043385689
1070.1-2388.729549807652458.82954980765
1177.3-2308.586854775112385.88685477511
1279.5-2227.809092055492307.30909205549
13100.6-2153.586135167232254.18613516723
14100.7-2064.676312459252165.37631245925
15107.1-1995.355966001212102.45596600121
1695.9-1924.265494615972020.16549461597
1782.8-1870.947997709031953.74799770903
1883.3-1823.074396075531906.37439607553
1980-1764.962923879011844.96292387901
2080.4-1710.825660411761791.22566041176
2167.5-1655.297266568361722.79726656836
2275.7-1613.365711017751689.06571101775
2371.1-1555.011934001171626.11193400117
2489.3-1508.034176354651597.33417635465
25101.1-1442.741518329151543.84151832915
26105.2-1382.651376479941487.85137647994
27114.1-1331.533094676151445.63309467615
2896.3-1278.265349168891374.56534916889
2984.4-1250.537320628331334.93732062833
3091.2-1221.397502959181312.59750295919
3181.9-1176.040799005571257.94079900557
3280.5-1144.797275018871225.29727501887
3370.4-1108.931110724031179.33111072403
3474.8-1081.591142423351156.39114242335
3575.9-1042.870798074541118.77079807454
3686.3-1006.900141892381093.20014189238
3798.7-963.6355435546031062.33554355460
38100.9-918.6488080879631019.54880808796
39113.8-883.752045037863997.552045037863
4089.8-841.007312176484930.807312176484
4184.4-832.165439113764916.565439113764
4287.2-810.788615106704897.988615106704
4385.6-781.25492338406866.85492338406
4472-755.621750649923827.621750649923
4569.2-742.19373657389811.39373657389
4677.5-720.898257003334798.398257003334
4778.1-689.209886075235767.309886075235
4894.3-664.122623145102758.422623145102
4997.7-626.078887113266723.778887113266
50100.2-599.00611342959699.20611342959
51116.4-574.598120700283690.998120700283
5297.1-538.484340275212635.584340275212
5393-534.295851965767627.295851965767
5496-520.227441830582616.227441830582
5580.5-499.063436453368579.563436453368
5676.1-494.643405087192570.743405087192
5769.9-482.374756670464552.274756670464
5873.6-471.37212437476544.97212437476
5992.6-451.877052405792544.477052405792
6094.2-417.831164061492512.031164061492
6193.5-398.626425448836492.126425448836
62108.5-383.624833386274492.124833386274
63109.4-355.073804721626464.473804721626
64105.1-338.396658135913443.496658135913
6592.5-328.218233565508420.718233565508
6697.1-326.772395452768423.872395452768

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 43129 & 38294 & 4835 \tabularnewline
4 & 93.2 & 41343.7156807425 & -41250.5156807425 \tabularnewline
5 & 96 & 2151.5702742753 & -2055.5702742753 \tabularnewline
6 & 95.2 & -2137.21416106058 & 2232.41416106058 \tabularnewline
7 & 77.1 & -2539.85712785652 & 2616.95712785652 \tabularnewline
8 & 70.9 & -2527.44772277248 & 2598.34772277248 \tabularnewline
9 & 64.8 & -2460.09043385689 & 2524.89043385689 \tabularnewline
10 & 70.1 & -2388.72954980765 & 2458.82954980765 \tabularnewline
11 & 77.3 & -2308.58685477511 & 2385.88685477511 \tabularnewline
12 & 79.5 & -2227.80909205549 & 2307.30909205549 \tabularnewline
13 & 100.6 & -2153.58613516723 & 2254.18613516723 \tabularnewline
14 & 100.7 & -2064.67631245925 & 2165.37631245925 \tabularnewline
15 & 107.1 & -1995.35596600121 & 2102.45596600121 \tabularnewline
16 & 95.9 & -1924.26549461597 & 2020.16549461597 \tabularnewline
17 & 82.8 & -1870.94799770903 & 1953.74799770903 \tabularnewline
18 & 83.3 & -1823.07439607553 & 1906.37439607553 \tabularnewline
19 & 80 & -1764.96292387901 & 1844.96292387901 \tabularnewline
20 & 80.4 & -1710.82566041176 & 1791.22566041176 \tabularnewline
21 & 67.5 & -1655.29726656836 & 1722.79726656836 \tabularnewline
22 & 75.7 & -1613.36571101775 & 1689.06571101775 \tabularnewline
23 & 71.1 & -1555.01193400117 & 1626.11193400117 \tabularnewline
24 & 89.3 & -1508.03417635465 & 1597.33417635465 \tabularnewline
25 & 101.1 & -1442.74151832915 & 1543.84151832915 \tabularnewline
26 & 105.2 & -1382.65137647994 & 1487.85137647994 \tabularnewline
27 & 114.1 & -1331.53309467615 & 1445.63309467615 \tabularnewline
28 & 96.3 & -1278.26534916889 & 1374.56534916889 \tabularnewline
29 & 84.4 & -1250.53732062833 & 1334.93732062833 \tabularnewline
30 & 91.2 & -1221.39750295918 & 1312.59750295919 \tabularnewline
31 & 81.9 & -1176.04079900557 & 1257.94079900557 \tabularnewline
32 & 80.5 & -1144.79727501887 & 1225.29727501887 \tabularnewline
33 & 70.4 & -1108.93111072403 & 1179.33111072403 \tabularnewline
34 & 74.8 & -1081.59114242335 & 1156.39114242335 \tabularnewline
35 & 75.9 & -1042.87079807454 & 1118.77079807454 \tabularnewline
36 & 86.3 & -1006.90014189238 & 1093.20014189238 \tabularnewline
37 & 98.7 & -963.635543554603 & 1062.33554355460 \tabularnewline
38 & 100.9 & -918.648808087963 & 1019.54880808796 \tabularnewline
39 & 113.8 & -883.752045037863 & 997.552045037863 \tabularnewline
40 & 89.8 & -841.007312176484 & 930.807312176484 \tabularnewline
41 & 84.4 & -832.165439113764 & 916.565439113764 \tabularnewline
42 & 87.2 & -810.788615106704 & 897.988615106704 \tabularnewline
43 & 85.6 & -781.25492338406 & 866.85492338406 \tabularnewline
44 & 72 & -755.621750649923 & 827.621750649923 \tabularnewline
45 & 69.2 & -742.19373657389 & 811.39373657389 \tabularnewline
46 & 77.5 & -720.898257003334 & 798.398257003334 \tabularnewline
47 & 78.1 & -689.209886075235 & 767.309886075235 \tabularnewline
48 & 94.3 & -664.122623145102 & 758.422623145102 \tabularnewline
49 & 97.7 & -626.078887113266 & 723.778887113266 \tabularnewline
50 & 100.2 & -599.00611342959 & 699.20611342959 \tabularnewline
51 & 116.4 & -574.598120700283 & 690.998120700283 \tabularnewline
52 & 97.1 & -538.484340275212 & 635.584340275212 \tabularnewline
53 & 93 & -534.295851965767 & 627.295851965767 \tabularnewline
54 & 96 & -520.227441830582 & 616.227441830582 \tabularnewline
55 & 80.5 & -499.063436453368 & 579.563436453368 \tabularnewline
56 & 76.1 & -494.643405087192 & 570.743405087192 \tabularnewline
57 & 69.9 & -482.374756670464 & 552.274756670464 \tabularnewline
58 & 73.6 & -471.37212437476 & 544.97212437476 \tabularnewline
59 & 92.6 & -451.877052405792 & 544.477052405792 \tabularnewline
60 & 94.2 & -417.831164061492 & 512.031164061492 \tabularnewline
61 & 93.5 & -398.626425448836 & 492.126425448836 \tabularnewline
62 & 108.5 & -383.624833386274 & 492.124833386274 \tabularnewline
63 & 109.4 & -355.073804721626 & 464.473804721626 \tabularnewline
64 & 105.1 & -338.396658135913 & 443.496658135913 \tabularnewline
65 & 92.5 & -328.218233565508 & 420.718233565508 \tabularnewline
66 & 97.1 & -326.772395452768 & 423.872395452768 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77772&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]43129[/C][C]38294[/C][C]4835[/C][/ROW]
[ROW][C]4[/C][C]93.2[/C][C]41343.7156807425[/C][C]-41250.5156807425[/C][/ROW]
[ROW][C]5[/C][C]96[/C][C]2151.5702742753[/C][C]-2055.5702742753[/C][/ROW]
[ROW][C]6[/C][C]95.2[/C][C]-2137.21416106058[/C][C]2232.41416106058[/C][/ROW]
[ROW][C]7[/C][C]77.1[/C][C]-2539.85712785652[/C][C]2616.95712785652[/C][/ROW]
[ROW][C]8[/C][C]70.9[/C][C]-2527.44772277248[/C][C]2598.34772277248[/C][/ROW]
[ROW][C]9[/C][C]64.8[/C][C]-2460.09043385689[/C][C]2524.89043385689[/C][/ROW]
[ROW][C]10[/C][C]70.1[/C][C]-2388.72954980765[/C][C]2458.82954980765[/C][/ROW]
[ROW][C]11[/C][C]77.3[/C][C]-2308.58685477511[/C][C]2385.88685477511[/C][/ROW]
[ROW][C]12[/C][C]79.5[/C][C]-2227.80909205549[/C][C]2307.30909205549[/C][/ROW]
[ROW][C]13[/C][C]100.6[/C][C]-2153.58613516723[/C][C]2254.18613516723[/C][/ROW]
[ROW][C]14[/C][C]100.7[/C][C]-2064.67631245925[/C][C]2165.37631245925[/C][/ROW]
[ROW][C]15[/C][C]107.1[/C][C]-1995.35596600121[/C][C]2102.45596600121[/C][/ROW]
[ROW][C]16[/C][C]95.9[/C][C]-1924.26549461597[/C][C]2020.16549461597[/C][/ROW]
[ROW][C]17[/C][C]82.8[/C][C]-1870.94799770903[/C][C]1953.74799770903[/C][/ROW]
[ROW][C]18[/C][C]83.3[/C][C]-1823.07439607553[/C][C]1906.37439607553[/C][/ROW]
[ROW][C]19[/C][C]80[/C][C]-1764.96292387901[/C][C]1844.96292387901[/C][/ROW]
[ROW][C]20[/C][C]80.4[/C][C]-1710.82566041176[/C][C]1791.22566041176[/C][/ROW]
[ROW][C]21[/C][C]67.5[/C][C]-1655.29726656836[/C][C]1722.79726656836[/C][/ROW]
[ROW][C]22[/C][C]75.7[/C][C]-1613.36571101775[/C][C]1689.06571101775[/C][/ROW]
[ROW][C]23[/C][C]71.1[/C][C]-1555.01193400117[/C][C]1626.11193400117[/C][/ROW]
[ROW][C]24[/C][C]89.3[/C][C]-1508.03417635465[/C][C]1597.33417635465[/C][/ROW]
[ROW][C]25[/C][C]101.1[/C][C]-1442.74151832915[/C][C]1543.84151832915[/C][/ROW]
[ROW][C]26[/C][C]105.2[/C][C]-1382.65137647994[/C][C]1487.85137647994[/C][/ROW]
[ROW][C]27[/C][C]114.1[/C][C]-1331.53309467615[/C][C]1445.63309467615[/C][/ROW]
[ROW][C]28[/C][C]96.3[/C][C]-1278.26534916889[/C][C]1374.56534916889[/C][/ROW]
[ROW][C]29[/C][C]84.4[/C][C]-1250.53732062833[/C][C]1334.93732062833[/C][/ROW]
[ROW][C]30[/C][C]91.2[/C][C]-1221.39750295918[/C][C]1312.59750295919[/C][/ROW]
[ROW][C]31[/C][C]81.9[/C][C]-1176.04079900557[/C][C]1257.94079900557[/C][/ROW]
[ROW][C]32[/C][C]80.5[/C][C]-1144.79727501887[/C][C]1225.29727501887[/C][/ROW]
[ROW][C]33[/C][C]70.4[/C][C]-1108.93111072403[/C][C]1179.33111072403[/C][/ROW]
[ROW][C]34[/C][C]74.8[/C][C]-1081.59114242335[/C][C]1156.39114242335[/C][/ROW]
[ROW][C]35[/C][C]75.9[/C][C]-1042.87079807454[/C][C]1118.77079807454[/C][/ROW]
[ROW][C]36[/C][C]86.3[/C][C]-1006.90014189238[/C][C]1093.20014189238[/C][/ROW]
[ROW][C]37[/C][C]98.7[/C][C]-963.635543554603[/C][C]1062.33554355460[/C][/ROW]
[ROW][C]38[/C][C]100.9[/C][C]-918.648808087963[/C][C]1019.54880808796[/C][/ROW]
[ROW][C]39[/C][C]113.8[/C][C]-883.752045037863[/C][C]997.552045037863[/C][/ROW]
[ROW][C]40[/C][C]89.8[/C][C]-841.007312176484[/C][C]930.807312176484[/C][/ROW]
[ROW][C]41[/C][C]84.4[/C][C]-832.165439113764[/C][C]916.565439113764[/C][/ROW]
[ROW][C]42[/C][C]87.2[/C][C]-810.788615106704[/C][C]897.988615106704[/C][/ROW]
[ROW][C]43[/C][C]85.6[/C][C]-781.25492338406[/C][C]866.85492338406[/C][/ROW]
[ROW][C]44[/C][C]72[/C][C]-755.621750649923[/C][C]827.621750649923[/C][/ROW]
[ROW][C]45[/C][C]69.2[/C][C]-742.19373657389[/C][C]811.39373657389[/C][/ROW]
[ROW][C]46[/C][C]77.5[/C][C]-720.898257003334[/C][C]798.398257003334[/C][/ROW]
[ROW][C]47[/C][C]78.1[/C][C]-689.209886075235[/C][C]767.309886075235[/C][/ROW]
[ROW][C]48[/C][C]94.3[/C][C]-664.122623145102[/C][C]758.422623145102[/C][/ROW]
[ROW][C]49[/C][C]97.7[/C][C]-626.078887113266[/C][C]723.778887113266[/C][/ROW]
[ROW][C]50[/C][C]100.2[/C][C]-599.00611342959[/C][C]699.20611342959[/C][/ROW]
[ROW][C]51[/C][C]116.4[/C][C]-574.598120700283[/C][C]690.998120700283[/C][/ROW]
[ROW][C]52[/C][C]97.1[/C][C]-538.484340275212[/C][C]635.584340275212[/C][/ROW]
[ROW][C]53[/C][C]93[/C][C]-534.295851965767[/C][C]627.295851965767[/C][/ROW]
[ROW][C]54[/C][C]96[/C][C]-520.227441830582[/C][C]616.227441830582[/C][/ROW]
[ROW][C]55[/C][C]80.5[/C][C]-499.063436453368[/C][C]579.563436453368[/C][/ROW]
[ROW][C]56[/C][C]76.1[/C][C]-494.643405087192[/C][C]570.743405087192[/C][/ROW]
[ROW][C]57[/C][C]69.9[/C][C]-482.374756670464[/C][C]552.274756670464[/C][/ROW]
[ROW][C]58[/C][C]73.6[/C][C]-471.37212437476[/C][C]544.97212437476[/C][/ROW]
[ROW][C]59[/C][C]92.6[/C][C]-451.877052405792[/C][C]544.477052405792[/C][/ROW]
[ROW][C]60[/C][C]94.2[/C][C]-417.831164061492[/C][C]512.031164061492[/C][/ROW]
[ROW][C]61[/C][C]93.5[/C][C]-398.626425448836[/C][C]492.126425448836[/C][/ROW]
[ROW][C]62[/C][C]108.5[/C][C]-383.624833386274[/C][C]492.124833386274[/C][/ROW]
[ROW][C]63[/C][C]109.4[/C][C]-355.073804721626[/C][C]464.473804721626[/C][/ROW]
[ROW][C]64[/C][C]105.1[/C][C]-338.396658135913[/C][C]443.496658135913[/C][/ROW]
[ROW][C]65[/C][C]92.5[/C][C]-328.218233565508[/C][C]420.718233565508[/C][/ROW]
[ROW][C]66[/C][C]97.1[/C][C]-326.772395452768[/C][C]423.872395452768[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77772&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77772&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
343129382944835
493.241343.7156807425-41250.5156807425
5962151.5702742753-2055.5702742753
695.2-2137.214161060582232.41416106058
777.1-2539.857127856522616.95712785652
870.9-2527.447722772482598.34772277248
964.8-2460.090433856892524.89043385689
1070.1-2388.729549807652458.82954980765
1177.3-2308.586854775112385.88685477511
1279.5-2227.809092055492307.30909205549
13100.6-2153.586135167232254.18613516723
14100.7-2064.676312459252165.37631245925
15107.1-1995.355966001212102.45596600121
1695.9-1924.265494615972020.16549461597
1782.8-1870.947997709031953.74799770903
1883.3-1823.074396075531906.37439607553
1980-1764.962923879011844.96292387901
2080.4-1710.825660411761791.22566041176
2167.5-1655.297266568361722.79726656836
2275.7-1613.365711017751689.06571101775
2371.1-1555.011934001171626.11193400117
2489.3-1508.034176354651597.33417635465
25101.1-1442.741518329151543.84151832915
26105.2-1382.651376479941487.85137647994
27114.1-1331.533094676151445.63309467615
2896.3-1278.265349168891374.56534916889
2984.4-1250.537320628331334.93732062833
3091.2-1221.397502959181312.59750295919
3181.9-1176.040799005571257.94079900557
3280.5-1144.797275018871225.29727501887
3370.4-1108.931110724031179.33111072403
3474.8-1081.591142423351156.39114242335
3575.9-1042.870798074541118.77079807454
3686.3-1006.900141892381093.20014189238
3798.7-963.6355435546031062.33554355460
38100.9-918.6488080879631019.54880808796
39113.8-883.752045037863997.552045037863
4089.8-841.007312176484930.807312176484
4184.4-832.165439113764916.565439113764
4287.2-810.788615106704897.988615106704
4385.6-781.25492338406866.85492338406
4472-755.621750649923827.621750649923
4569.2-742.19373657389811.39373657389
4677.5-720.898257003334798.398257003334
4778.1-689.209886075235767.309886075235
4894.3-664.122623145102758.422623145102
4997.7-626.078887113266723.778887113266
50100.2-599.00611342959699.20611342959
51116.4-574.598120700283690.998120700283
5297.1-538.484340275212635.584340275212
5393-534.295851965767627.295851965767
5496-520.227441830582616.227441830582
5580.5-499.063436453368579.563436453368
5676.1-494.643405087192570.743405087192
5769.9-482.374756670464552.274756670464
5873.6-471.37212437476544.97212437476
5992.6-451.877052405792544.477052405792
6094.2-417.831164061492512.031164061492
6193.5-398.626425448836492.126425448836
62108.5-383.624833386274492.124833386274
63109.4-355.073804721626464.473804721626
64105.1-338.396658135913443.496658135913
6592.5-328.218233565508420.718233565508
6697.1-326.772395452768423.872395452768







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
67-310.841702083763-10869.060922989410247.3775188219
68-672.984320339411-15016.063157392713670.0945167139
69-1035.12693859506-18519.438245827416449.1843686373
70-1397.26955685071-21684.623476783118890.0843630817
71-1759.41217510635-24639.965357844521121.1410076318
72-2121.55479336200-27453.335985843923210.2263991199
73-2483.69741161765-30165.533410131825198.1385868965
74-2845.84002987330-32803.200951885727111.5208921391
75-3207.98264812895-35384.782795782628968.8174995247
76-3570.12526638459-37923.612267104830783.3617343356
77-3932.26788464024-40429.655727889832565.1199586093
78-4294.41050289589-42910.56334632234321.7423405302

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
67 & -310.841702083763 & -10869.0609229894 & 10247.3775188219 \tabularnewline
68 & -672.984320339411 & -15016.0631573927 & 13670.0945167139 \tabularnewline
69 & -1035.12693859506 & -18519.4382458274 & 16449.1843686373 \tabularnewline
70 & -1397.26955685071 & -21684.6234767831 & 18890.0843630817 \tabularnewline
71 & -1759.41217510635 & -24639.9653578445 & 21121.1410076318 \tabularnewline
72 & -2121.55479336200 & -27453.3359858439 & 23210.2263991199 \tabularnewline
73 & -2483.69741161765 & -30165.5334101318 & 25198.1385868965 \tabularnewline
74 & -2845.84002987330 & -32803.2009518857 & 27111.5208921391 \tabularnewline
75 & -3207.98264812895 & -35384.7827957826 & 28968.8174995247 \tabularnewline
76 & -3570.12526638459 & -37923.6122671048 & 30783.3617343356 \tabularnewline
77 & -3932.26788464024 & -40429.6557278898 & 32565.1199586093 \tabularnewline
78 & -4294.41050289589 & -42910.563346322 & 34321.7423405302 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77772&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]67[/C][C]-310.841702083763[/C][C]-10869.0609229894[/C][C]10247.3775188219[/C][/ROW]
[ROW][C]68[/C][C]-672.984320339411[/C][C]-15016.0631573927[/C][C]13670.0945167139[/C][/ROW]
[ROW][C]69[/C][C]-1035.12693859506[/C][C]-18519.4382458274[/C][C]16449.1843686373[/C][/ROW]
[ROW][C]70[/C][C]-1397.26955685071[/C][C]-21684.6234767831[/C][C]18890.0843630817[/C][/ROW]
[ROW][C]71[/C][C]-1759.41217510635[/C][C]-24639.9653578445[/C][C]21121.1410076318[/C][/ROW]
[ROW][C]72[/C][C]-2121.55479336200[/C][C]-27453.3359858439[/C][C]23210.2263991199[/C][/ROW]
[ROW][C]73[/C][C]-2483.69741161765[/C][C]-30165.5334101318[/C][C]25198.1385868965[/C][/ROW]
[ROW][C]74[/C][C]-2845.84002987330[/C][C]-32803.2009518857[/C][C]27111.5208921391[/C][/ROW]
[ROW][C]75[/C][C]-3207.98264812895[/C][C]-35384.7827957826[/C][C]28968.8174995247[/C][/ROW]
[ROW][C]76[/C][C]-3570.12526638459[/C][C]-37923.6122671048[/C][C]30783.3617343356[/C][/ROW]
[ROW][C]77[/C][C]-3932.26788464024[/C][C]-40429.6557278898[/C][C]32565.1199586093[/C][/ROW]
[ROW][C]78[/C][C]-4294.41050289589[/C][C]-42910.563346322[/C][C]34321.7423405302[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77772&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77772&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
67-310.841702083763-10869.060922989410247.3775188219
68-672.984320339411-15016.063157392713670.0945167139
69-1035.12693859506-18519.438245827416449.1843686373
70-1397.26955685071-21684.623476783118890.0843630817
71-1759.41217510635-24639.965357844521121.1410076318
72-2121.55479336200-27453.335985843923210.2263991199
73-2483.69741161765-30165.533410131825198.1385868965
74-2845.84002987330-32803.200951885727111.5208921391
75-3207.98264812895-35384.782795782628968.8174995247
76-3570.12526638459-37923.612267104830783.3617343356
77-3932.26788464024-40429.655727889832565.1199586093
78-4294.41050289589-42910.56334632234321.7423405302



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')