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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 computationFri, 31 Jul 2015 12:34:27 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Jul/31/t14383426227vcqsulhzg8tqt6.htm/, Retrieved Fri, 17 May 2024 04:17:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=279786, Retrieved Fri, 17 May 2024 04:17:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact162
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2015-07-31 11:34:27] [517bf63cbd197750110a40d4d2cd39d6] [Current]
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Dataseries X:
152512
151944
151368
150176
161968
161344
152512
146640
147208
147208
147840
148976
150744
150744
149608
146640
161968
164304
160776
152512
156048
150744
153136
154280
155472
152512
153136
148976
161968
166072
162544
156048
163112
155472
162544
161968
163736
157240
164304
163736
174336
171944
162544
157808
164304
155472
161968
163112
165504
160208
163112
164880
171376
166072
159008
151368
158440
139000
148408
153704
159008
151368
151368
151368
155472
149608
141912
135472
140144
121904
133080
139576
140768
134272
134840
133080
139000
134840
126640
120712
130736
108968
123104
129544
129544
121904
114840
114272
120712
114840
103672
95976
104240
84808
102472
111872
114840
108344
100136
106008
108344
106576
88904
80704
86568
68904
87144
93640
98936
90104
81840
86568
88904
84232
66568
58872
65936
46504
67704
80704




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279786&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279786&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279786&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.659004759562522
beta0
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.659004759562522 \tabularnewline
beta & 0 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279786&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]0.659004759562522[/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=279786&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279786&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
alpha0.659004759562522
beta0
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3151368151376-8
4150176150802.727961924-626.72796192352
5161968149821.71125206512146.288747935
6161344157258.1733479754085.82665202513
7152512159382.752558407-6870.75255840685
8146640154286.89392064-7646.89392064034
9147208148679.554431069-1471.55443106865
10147208147141.79305703966.206942960911
11147840146617.4237475661222.57625243359
12148976146855.1073168482120.89268315173
13150744147684.7856895673059.21431043342
14150744149132.8224806641611.17751933602
15149608149626.596134407-18.5961344065727
16146640149046.341193323-2406.3411933232
17161968146892.55089379215075.4491062082
18164304156259.3436073268044.65639267443
19160776160992.810459143-216.810459143075
20152512160281.931334645-7769.93133464485
21156048154593.509603641454.49039636008
22150744154984.025697579-4240.0256975792
23153136151621.8285822071514.17141779288
24154280152051.6747533262228.32524667383
25155472152952.1516967382519.84830326244
26152512154044.743721963-1532.74372196305
27153136152466.658314669.341686000174
28148976152339.757670848-3363.75767084752
29161968149555.02535574412412.9746442559
30166072157167.2347266388904.76527336237
31162544162467.51742457176.482575429487
32156048161949.919805802-5901.91980580214
33163112157492.5265632225619.4734367778
34155472160627.786304294-5155.78630429393
35162544156662.0985904775881.90140952304
36161968159970.299614631997.70038536986
37163736160718.7936767693017.20632323122
38157240162139.14700436-4899.1470043603
39164304158342.585810695961.41418930961
40163736161703.1861351692032.81386483103
41174336162474.82014739711861.1798526027
42171944169723.394124292220.60587571043
43162544170618.783965495-8074.78396549524
44157808164729.462899795-6921.46289979474
45164304159600.1859056954703.81409430539
46155472162132.021781939-6660.02178193914
47161968157175.0357288514792.96427114881
48163112159765.6219959513346.37800404863
49165504161402.9010279154101.09897208525
50160208163537.544769956-3329.54476995589
51163112160775.3589193782336.64108062154
52164880161747.2165128973132.78348710263
53171376163243.7357415778132.26425842312
54166072168034.936593898-1962.9365938979
55159008166173.3520358-7165.35203579973
56151368160883.350940267-9515.35094026671
57158440154044.6893817234395.31061827677
58139000156373.219998923-17373.2199989233
59148408144356.1853307064051.81466929393
60153704146458.3504826367245.64951736399
61159008150665.2680007018342.73199929923
62151368155595.168095994-4227.16809599352
63151368152241.444201263-873.444201262959
64151368151097.840315418270.159684581624
65155472150707.87683344764.12316660042
66149608153279.456675331-3671.45667533134
67141912150291.94925176-8379.94925176041
68135472144201.522809958-8729.52280995791
69140144137880.7257294862263.27427051397
70121904138804.23424595-16900.2342459501
71133080127098.8994401475981.10055985255
72139576130472.4731765129103.52682348766
73140768135903.7406819964864.25931800419
74134272138541.310724307-4269.31072430691
75134840135159.814636937-319.814636937343
76133080134381.055269018-1301.05526901787
77139000132955.6536542816044.3463457188
78134840136370.906664554-1530.90666455423
79126640134794.031886167-8154.03188616701
80120712128852.486063558-8140.48606355838
81130736122919.8670025217816.13299747897
82108968127502.735849233-18534.7358492334
83123104114720.2567073548383.74329264552
84129544119677.1834401589866.81655984175
85129544125611.4625148243932.53748517574
86121904127635.023434713-5731.0234347131
87114840123290.251714073-8450.2517140728
88114272117153.495614997-2881.49561499746
89120712114686.5762900566025.4237099444
90114840118089.35919329-3249.35919328983
91103672115380.016019384-11708.0160193836
9295976107096.377737576-11120.3777375755
9310424099199.99588038025040.00411961984
9484808101953.382583424-17145.3825834244
9510247290086.493856427312385.5061435727
9611187297680.601354632614191.3986453674
97114840106464.8006067798375.19939322115
98108344111416.096869197-3072.09686919674
99100136108823.570410559-8687.57041055897
100106008102530.4201609663477.57983903393
101108344104254.1618266484089.83817335189
102106576106381.384648728194.6153512725
10388904105941.6370915-17037.6370915
1048070494145.7531565025-13441.7531565025
1058656884719.57384950281848.42615049719
1066890485369.6954803803-16465.6954803803
1078714473950.723789302613193.2762106974
1089364082077.155606375211562.8443936248
1099893689129.12509585489806.87490414524
1109010495023.9023341207-4919.90233412072
1118184091213.6632793524-9373.6632793524
1128656884468.37456372272099.62543627727
1138890485284.0377195283619.96228047201
1148423287101.6100917959-2869.61009179585
1156656884642.5233832137-18074.5233832137
1165887272163.3264468518-13291.3264468518
1176593662836.27905747723099.72094252278
1184650464311.0099119154-17807.0099119154
1196770452008.105626386115695.8943736139
1208070461783.774724188318920.2252758117

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 151368 & 151376 & -8 \tabularnewline
4 & 150176 & 150802.727961924 & -626.72796192352 \tabularnewline
5 & 161968 & 149821.711252065 & 12146.288747935 \tabularnewline
6 & 161344 & 157258.173347975 & 4085.82665202513 \tabularnewline
7 & 152512 & 159382.752558407 & -6870.75255840685 \tabularnewline
8 & 146640 & 154286.89392064 & -7646.89392064034 \tabularnewline
9 & 147208 & 148679.554431069 & -1471.55443106865 \tabularnewline
10 & 147208 & 147141.793057039 & 66.206942960911 \tabularnewline
11 & 147840 & 146617.423747566 & 1222.57625243359 \tabularnewline
12 & 148976 & 146855.107316848 & 2120.89268315173 \tabularnewline
13 & 150744 & 147684.785689567 & 3059.21431043342 \tabularnewline
14 & 150744 & 149132.822480664 & 1611.17751933602 \tabularnewline
15 & 149608 & 149626.596134407 & -18.5961344065727 \tabularnewline
16 & 146640 & 149046.341193323 & -2406.3411933232 \tabularnewline
17 & 161968 & 146892.550893792 & 15075.4491062082 \tabularnewline
18 & 164304 & 156259.343607326 & 8044.65639267443 \tabularnewline
19 & 160776 & 160992.810459143 & -216.810459143075 \tabularnewline
20 & 152512 & 160281.931334645 & -7769.93133464485 \tabularnewline
21 & 156048 & 154593.50960364 & 1454.49039636008 \tabularnewline
22 & 150744 & 154984.025697579 & -4240.0256975792 \tabularnewline
23 & 153136 & 151621.828582207 & 1514.17141779288 \tabularnewline
24 & 154280 & 152051.674753326 & 2228.32524667383 \tabularnewline
25 & 155472 & 152952.151696738 & 2519.84830326244 \tabularnewline
26 & 152512 & 154044.743721963 & -1532.74372196305 \tabularnewline
27 & 153136 & 152466.658314 & 669.341686000174 \tabularnewline
28 & 148976 & 152339.757670848 & -3363.75767084752 \tabularnewline
29 & 161968 & 149555.025355744 & 12412.9746442559 \tabularnewline
30 & 166072 & 157167.234726638 & 8904.76527336237 \tabularnewline
31 & 162544 & 162467.517424571 & 76.482575429487 \tabularnewline
32 & 156048 & 161949.919805802 & -5901.91980580214 \tabularnewline
33 & 163112 & 157492.526563222 & 5619.4734367778 \tabularnewline
34 & 155472 & 160627.786304294 & -5155.78630429393 \tabularnewline
35 & 162544 & 156662.098590477 & 5881.90140952304 \tabularnewline
36 & 161968 & 159970.29961463 & 1997.70038536986 \tabularnewline
37 & 163736 & 160718.793676769 & 3017.20632323122 \tabularnewline
38 & 157240 & 162139.14700436 & -4899.1470043603 \tabularnewline
39 & 164304 & 158342.58581069 & 5961.41418930961 \tabularnewline
40 & 163736 & 161703.186135169 & 2032.81386483103 \tabularnewline
41 & 174336 & 162474.820147397 & 11861.1798526027 \tabularnewline
42 & 171944 & 169723.39412429 & 2220.60587571043 \tabularnewline
43 & 162544 & 170618.783965495 & -8074.78396549524 \tabularnewline
44 & 157808 & 164729.462899795 & -6921.46289979474 \tabularnewline
45 & 164304 & 159600.185905695 & 4703.81409430539 \tabularnewline
46 & 155472 & 162132.021781939 & -6660.02178193914 \tabularnewline
47 & 161968 & 157175.035728851 & 4792.96427114881 \tabularnewline
48 & 163112 & 159765.621995951 & 3346.37800404863 \tabularnewline
49 & 165504 & 161402.901027915 & 4101.09897208525 \tabularnewline
50 & 160208 & 163537.544769956 & -3329.54476995589 \tabularnewline
51 & 163112 & 160775.358919378 & 2336.64108062154 \tabularnewline
52 & 164880 & 161747.216512897 & 3132.78348710263 \tabularnewline
53 & 171376 & 163243.735741577 & 8132.26425842312 \tabularnewline
54 & 166072 & 168034.936593898 & -1962.9365938979 \tabularnewline
55 & 159008 & 166173.3520358 & -7165.35203579973 \tabularnewline
56 & 151368 & 160883.350940267 & -9515.35094026671 \tabularnewline
57 & 158440 & 154044.689381723 & 4395.31061827677 \tabularnewline
58 & 139000 & 156373.219998923 & -17373.2199989233 \tabularnewline
59 & 148408 & 144356.185330706 & 4051.81466929393 \tabularnewline
60 & 153704 & 146458.350482636 & 7245.64951736399 \tabularnewline
61 & 159008 & 150665.268000701 & 8342.73199929923 \tabularnewline
62 & 151368 & 155595.168095994 & -4227.16809599352 \tabularnewline
63 & 151368 & 152241.444201263 & -873.444201262959 \tabularnewline
64 & 151368 & 151097.840315418 & 270.159684581624 \tabularnewline
65 & 155472 & 150707.8768334 & 4764.12316660042 \tabularnewline
66 & 149608 & 153279.456675331 & -3671.45667533134 \tabularnewline
67 & 141912 & 150291.94925176 & -8379.94925176041 \tabularnewline
68 & 135472 & 144201.522809958 & -8729.52280995791 \tabularnewline
69 & 140144 & 137880.725729486 & 2263.27427051397 \tabularnewline
70 & 121904 & 138804.23424595 & -16900.2342459501 \tabularnewline
71 & 133080 & 127098.899440147 & 5981.10055985255 \tabularnewline
72 & 139576 & 130472.473176512 & 9103.52682348766 \tabularnewline
73 & 140768 & 135903.740681996 & 4864.25931800419 \tabularnewline
74 & 134272 & 138541.310724307 & -4269.31072430691 \tabularnewline
75 & 134840 & 135159.814636937 & -319.814636937343 \tabularnewline
76 & 133080 & 134381.055269018 & -1301.05526901787 \tabularnewline
77 & 139000 & 132955.653654281 & 6044.3463457188 \tabularnewline
78 & 134840 & 136370.906664554 & -1530.90666455423 \tabularnewline
79 & 126640 & 134794.031886167 & -8154.03188616701 \tabularnewline
80 & 120712 & 128852.486063558 & -8140.48606355838 \tabularnewline
81 & 130736 & 122919.867002521 & 7816.13299747897 \tabularnewline
82 & 108968 & 127502.735849233 & -18534.7358492334 \tabularnewline
83 & 123104 & 114720.256707354 & 8383.74329264552 \tabularnewline
84 & 129544 & 119677.183440158 & 9866.81655984175 \tabularnewline
85 & 129544 & 125611.462514824 & 3932.53748517574 \tabularnewline
86 & 121904 & 127635.023434713 & -5731.0234347131 \tabularnewline
87 & 114840 & 123290.251714073 & -8450.2517140728 \tabularnewline
88 & 114272 & 117153.495614997 & -2881.49561499746 \tabularnewline
89 & 120712 & 114686.576290056 & 6025.4237099444 \tabularnewline
90 & 114840 & 118089.35919329 & -3249.35919328983 \tabularnewline
91 & 103672 & 115380.016019384 & -11708.0160193836 \tabularnewline
92 & 95976 & 107096.377737576 & -11120.3777375755 \tabularnewline
93 & 104240 & 99199.9958803802 & 5040.00411961984 \tabularnewline
94 & 84808 & 101953.382583424 & -17145.3825834244 \tabularnewline
95 & 102472 & 90086.4938564273 & 12385.5061435727 \tabularnewline
96 & 111872 & 97680.6013546326 & 14191.3986453674 \tabularnewline
97 & 114840 & 106464.800606779 & 8375.19939322115 \tabularnewline
98 & 108344 & 111416.096869197 & -3072.09686919674 \tabularnewline
99 & 100136 & 108823.570410559 & -8687.57041055897 \tabularnewline
100 & 106008 & 102530.420160966 & 3477.57983903393 \tabularnewline
101 & 108344 & 104254.161826648 & 4089.83817335189 \tabularnewline
102 & 106576 & 106381.384648728 & 194.6153512725 \tabularnewline
103 & 88904 & 105941.6370915 & -17037.6370915 \tabularnewline
104 & 80704 & 94145.7531565025 & -13441.7531565025 \tabularnewline
105 & 86568 & 84719.5738495028 & 1848.42615049719 \tabularnewline
106 & 68904 & 85369.6954803803 & -16465.6954803803 \tabularnewline
107 & 87144 & 73950.7237893026 & 13193.2762106974 \tabularnewline
108 & 93640 & 82077.1556063752 & 11562.8443936248 \tabularnewline
109 & 98936 & 89129.1250958548 & 9806.87490414524 \tabularnewline
110 & 90104 & 95023.9023341207 & -4919.90233412072 \tabularnewline
111 & 81840 & 91213.6632793524 & -9373.6632793524 \tabularnewline
112 & 86568 & 84468.3745637227 & 2099.62543627727 \tabularnewline
113 & 88904 & 85284.037719528 & 3619.96228047201 \tabularnewline
114 & 84232 & 87101.6100917959 & -2869.61009179585 \tabularnewline
115 & 66568 & 84642.5233832137 & -18074.5233832137 \tabularnewline
116 & 58872 & 72163.3264468518 & -13291.3264468518 \tabularnewline
117 & 65936 & 62836.2790574772 & 3099.72094252278 \tabularnewline
118 & 46504 & 64311.0099119154 & -17807.0099119154 \tabularnewline
119 & 67704 & 52008.1056263861 & 15695.8943736139 \tabularnewline
120 & 80704 & 61783.7747241883 & 18920.2252758117 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279786&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]151368[/C][C]151376[/C][C]-8[/C][/ROW]
[ROW][C]4[/C][C]150176[/C][C]150802.727961924[/C][C]-626.72796192352[/C][/ROW]
[ROW][C]5[/C][C]161968[/C][C]149821.711252065[/C][C]12146.288747935[/C][/ROW]
[ROW][C]6[/C][C]161344[/C][C]157258.173347975[/C][C]4085.82665202513[/C][/ROW]
[ROW][C]7[/C][C]152512[/C][C]159382.752558407[/C][C]-6870.75255840685[/C][/ROW]
[ROW][C]8[/C][C]146640[/C][C]154286.89392064[/C][C]-7646.89392064034[/C][/ROW]
[ROW][C]9[/C][C]147208[/C][C]148679.554431069[/C][C]-1471.55443106865[/C][/ROW]
[ROW][C]10[/C][C]147208[/C][C]147141.793057039[/C][C]66.206942960911[/C][/ROW]
[ROW][C]11[/C][C]147840[/C][C]146617.423747566[/C][C]1222.57625243359[/C][/ROW]
[ROW][C]12[/C][C]148976[/C][C]146855.107316848[/C][C]2120.89268315173[/C][/ROW]
[ROW][C]13[/C][C]150744[/C][C]147684.785689567[/C][C]3059.21431043342[/C][/ROW]
[ROW][C]14[/C][C]150744[/C][C]149132.822480664[/C][C]1611.17751933602[/C][/ROW]
[ROW][C]15[/C][C]149608[/C][C]149626.596134407[/C][C]-18.5961344065727[/C][/ROW]
[ROW][C]16[/C][C]146640[/C][C]149046.341193323[/C][C]-2406.3411933232[/C][/ROW]
[ROW][C]17[/C][C]161968[/C][C]146892.550893792[/C][C]15075.4491062082[/C][/ROW]
[ROW][C]18[/C][C]164304[/C][C]156259.343607326[/C][C]8044.65639267443[/C][/ROW]
[ROW][C]19[/C][C]160776[/C][C]160992.810459143[/C][C]-216.810459143075[/C][/ROW]
[ROW][C]20[/C][C]152512[/C][C]160281.931334645[/C][C]-7769.93133464485[/C][/ROW]
[ROW][C]21[/C][C]156048[/C][C]154593.50960364[/C][C]1454.49039636008[/C][/ROW]
[ROW][C]22[/C][C]150744[/C][C]154984.025697579[/C][C]-4240.0256975792[/C][/ROW]
[ROW][C]23[/C][C]153136[/C][C]151621.828582207[/C][C]1514.17141779288[/C][/ROW]
[ROW][C]24[/C][C]154280[/C][C]152051.674753326[/C][C]2228.32524667383[/C][/ROW]
[ROW][C]25[/C][C]155472[/C][C]152952.151696738[/C][C]2519.84830326244[/C][/ROW]
[ROW][C]26[/C][C]152512[/C][C]154044.743721963[/C][C]-1532.74372196305[/C][/ROW]
[ROW][C]27[/C][C]153136[/C][C]152466.658314[/C][C]669.341686000174[/C][/ROW]
[ROW][C]28[/C][C]148976[/C][C]152339.757670848[/C][C]-3363.75767084752[/C][/ROW]
[ROW][C]29[/C][C]161968[/C][C]149555.025355744[/C][C]12412.9746442559[/C][/ROW]
[ROW][C]30[/C][C]166072[/C][C]157167.234726638[/C][C]8904.76527336237[/C][/ROW]
[ROW][C]31[/C][C]162544[/C][C]162467.517424571[/C][C]76.482575429487[/C][/ROW]
[ROW][C]32[/C][C]156048[/C][C]161949.919805802[/C][C]-5901.91980580214[/C][/ROW]
[ROW][C]33[/C][C]163112[/C][C]157492.526563222[/C][C]5619.4734367778[/C][/ROW]
[ROW][C]34[/C][C]155472[/C][C]160627.786304294[/C][C]-5155.78630429393[/C][/ROW]
[ROW][C]35[/C][C]162544[/C][C]156662.098590477[/C][C]5881.90140952304[/C][/ROW]
[ROW][C]36[/C][C]161968[/C][C]159970.29961463[/C][C]1997.70038536986[/C][/ROW]
[ROW][C]37[/C][C]163736[/C][C]160718.793676769[/C][C]3017.20632323122[/C][/ROW]
[ROW][C]38[/C][C]157240[/C][C]162139.14700436[/C][C]-4899.1470043603[/C][/ROW]
[ROW][C]39[/C][C]164304[/C][C]158342.58581069[/C][C]5961.41418930961[/C][/ROW]
[ROW][C]40[/C][C]163736[/C][C]161703.186135169[/C][C]2032.81386483103[/C][/ROW]
[ROW][C]41[/C][C]174336[/C][C]162474.820147397[/C][C]11861.1798526027[/C][/ROW]
[ROW][C]42[/C][C]171944[/C][C]169723.39412429[/C][C]2220.60587571043[/C][/ROW]
[ROW][C]43[/C][C]162544[/C][C]170618.783965495[/C][C]-8074.78396549524[/C][/ROW]
[ROW][C]44[/C][C]157808[/C][C]164729.462899795[/C][C]-6921.46289979474[/C][/ROW]
[ROW][C]45[/C][C]164304[/C][C]159600.185905695[/C][C]4703.81409430539[/C][/ROW]
[ROW][C]46[/C][C]155472[/C][C]162132.021781939[/C][C]-6660.02178193914[/C][/ROW]
[ROW][C]47[/C][C]161968[/C][C]157175.035728851[/C][C]4792.96427114881[/C][/ROW]
[ROW][C]48[/C][C]163112[/C][C]159765.621995951[/C][C]3346.37800404863[/C][/ROW]
[ROW][C]49[/C][C]165504[/C][C]161402.901027915[/C][C]4101.09897208525[/C][/ROW]
[ROW][C]50[/C][C]160208[/C][C]163537.544769956[/C][C]-3329.54476995589[/C][/ROW]
[ROW][C]51[/C][C]163112[/C][C]160775.358919378[/C][C]2336.64108062154[/C][/ROW]
[ROW][C]52[/C][C]164880[/C][C]161747.216512897[/C][C]3132.78348710263[/C][/ROW]
[ROW][C]53[/C][C]171376[/C][C]163243.735741577[/C][C]8132.26425842312[/C][/ROW]
[ROW][C]54[/C][C]166072[/C][C]168034.936593898[/C][C]-1962.9365938979[/C][/ROW]
[ROW][C]55[/C][C]159008[/C][C]166173.3520358[/C][C]-7165.35203579973[/C][/ROW]
[ROW][C]56[/C][C]151368[/C][C]160883.350940267[/C][C]-9515.35094026671[/C][/ROW]
[ROW][C]57[/C][C]158440[/C][C]154044.689381723[/C][C]4395.31061827677[/C][/ROW]
[ROW][C]58[/C][C]139000[/C][C]156373.219998923[/C][C]-17373.2199989233[/C][/ROW]
[ROW][C]59[/C][C]148408[/C][C]144356.185330706[/C][C]4051.81466929393[/C][/ROW]
[ROW][C]60[/C][C]153704[/C][C]146458.350482636[/C][C]7245.64951736399[/C][/ROW]
[ROW][C]61[/C][C]159008[/C][C]150665.268000701[/C][C]8342.73199929923[/C][/ROW]
[ROW][C]62[/C][C]151368[/C][C]155595.168095994[/C][C]-4227.16809599352[/C][/ROW]
[ROW][C]63[/C][C]151368[/C][C]152241.444201263[/C][C]-873.444201262959[/C][/ROW]
[ROW][C]64[/C][C]151368[/C][C]151097.840315418[/C][C]270.159684581624[/C][/ROW]
[ROW][C]65[/C][C]155472[/C][C]150707.8768334[/C][C]4764.12316660042[/C][/ROW]
[ROW][C]66[/C][C]149608[/C][C]153279.456675331[/C][C]-3671.45667533134[/C][/ROW]
[ROW][C]67[/C][C]141912[/C][C]150291.94925176[/C][C]-8379.94925176041[/C][/ROW]
[ROW][C]68[/C][C]135472[/C][C]144201.522809958[/C][C]-8729.52280995791[/C][/ROW]
[ROW][C]69[/C][C]140144[/C][C]137880.725729486[/C][C]2263.27427051397[/C][/ROW]
[ROW][C]70[/C][C]121904[/C][C]138804.23424595[/C][C]-16900.2342459501[/C][/ROW]
[ROW][C]71[/C][C]133080[/C][C]127098.899440147[/C][C]5981.10055985255[/C][/ROW]
[ROW][C]72[/C][C]139576[/C][C]130472.473176512[/C][C]9103.52682348766[/C][/ROW]
[ROW][C]73[/C][C]140768[/C][C]135903.740681996[/C][C]4864.25931800419[/C][/ROW]
[ROW][C]74[/C][C]134272[/C][C]138541.310724307[/C][C]-4269.31072430691[/C][/ROW]
[ROW][C]75[/C][C]134840[/C][C]135159.814636937[/C][C]-319.814636937343[/C][/ROW]
[ROW][C]76[/C][C]133080[/C][C]134381.055269018[/C][C]-1301.05526901787[/C][/ROW]
[ROW][C]77[/C][C]139000[/C][C]132955.653654281[/C][C]6044.3463457188[/C][/ROW]
[ROW][C]78[/C][C]134840[/C][C]136370.906664554[/C][C]-1530.90666455423[/C][/ROW]
[ROW][C]79[/C][C]126640[/C][C]134794.031886167[/C][C]-8154.03188616701[/C][/ROW]
[ROW][C]80[/C][C]120712[/C][C]128852.486063558[/C][C]-8140.48606355838[/C][/ROW]
[ROW][C]81[/C][C]130736[/C][C]122919.867002521[/C][C]7816.13299747897[/C][/ROW]
[ROW][C]82[/C][C]108968[/C][C]127502.735849233[/C][C]-18534.7358492334[/C][/ROW]
[ROW][C]83[/C][C]123104[/C][C]114720.256707354[/C][C]8383.74329264552[/C][/ROW]
[ROW][C]84[/C][C]129544[/C][C]119677.183440158[/C][C]9866.81655984175[/C][/ROW]
[ROW][C]85[/C][C]129544[/C][C]125611.462514824[/C][C]3932.53748517574[/C][/ROW]
[ROW][C]86[/C][C]121904[/C][C]127635.023434713[/C][C]-5731.0234347131[/C][/ROW]
[ROW][C]87[/C][C]114840[/C][C]123290.251714073[/C][C]-8450.2517140728[/C][/ROW]
[ROW][C]88[/C][C]114272[/C][C]117153.495614997[/C][C]-2881.49561499746[/C][/ROW]
[ROW][C]89[/C][C]120712[/C][C]114686.576290056[/C][C]6025.4237099444[/C][/ROW]
[ROW][C]90[/C][C]114840[/C][C]118089.35919329[/C][C]-3249.35919328983[/C][/ROW]
[ROW][C]91[/C][C]103672[/C][C]115380.016019384[/C][C]-11708.0160193836[/C][/ROW]
[ROW][C]92[/C][C]95976[/C][C]107096.377737576[/C][C]-11120.3777375755[/C][/ROW]
[ROW][C]93[/C][C]104240[/C][C]99199.9958803802[/C][C]5040.00411961984[/C][/ROW]
[ROW][C]94[/C][C]84808[/C][C]101953.382583424[/C][C]-17145.3825834244[/C][/ROW]
[ROW][C]95[/C][C]102472[/C][C]90086.4938564273[/C][C]12385.5061435727[/C][/ROW]
[ROW][C]96[/C][C]111872[/C][C]97680.6013546326[/C][C]14191.3986453674[/C][/ROW]
[ROW][C]97[/C][C]114840[/C][C]106464.800606779[/C][C]8375.19939322115[/C][/ROW]
[ROW][C]98[/C][C]108344[/C][C]111416.096869197[/C][C]-3072.09686919674[/C][/ROW]
[ROW][C]99[/C][C]100136[/C][C]108823.570410559[/C][C]-8687.57041055897[/C][/ROW]
[ROW][C]100[/C][C]106008[/C][C]102530.420160966[/C][C]3477.57983903393[/C][/ROW]
[ROW][C]101[/C][C]108344[/C][C]104254.161826648[/C][C]4089.83817335189[/C][/ROW]
[ROW][C]102[/C][C]106576[/C][C]106381.384648728[/C][C]194.6153512725[/C][/ROW]
[ROW][C]103[/C][C]88904[/C][C]105941.6370915[/C][C]-17037.6370915[/C][/ROW]
[ROW][C]104[/C][C]80704[/C][C]94145.7531565025[/C][C]-13441.7531565025[/C][/ROW]
[ROW][C]105[/C][C]86568[/C][C]84719.5738495028[/C][C]1848.42615049719[/C][/ROW]
[ROW][C]106[/C][C]68904[/C][C]85369.6954803803[/C][C]-16465.6954803803[/C][/ROW]
[ROW][C]107[/C][C]87144[/C][C]73950.7237893026[/C][C]13193.2762106974[/C][/ROW]
[ROW][C]108[/C][C]93640[/C][C]82077.1556063752[/C][C]11562.8443936248[/C][/ROW]
[ROW][C]109[/C][C]98936[/C][C]89129.1250958548[/C][C]9806.87490414524[/C][/ROW]
[ROW][C]110[/C][C]90104[/C][C]95023.9023341207[/C][C]-4919.90233412072[/C][/ROW]
[ROW][C]111[/C][C]81840[/C][C]91213.6632793524[/C][C]-9373.6632793524[/C][/ROW]
[ROW][C]112[/C][C]86568[/C][C]84468.3745637227[/C][C]2099.62543627727[/C][/ROW]
[ROW][C]113[/C][C]88904[/C][C]85284.037719528[/C][C]3619.96228047201[/C][/ROW]
[ROW][C]114[/C][C]84232[/C][C]87101.6100917959[/C][C]-2869.61009179585[/C][/ROW]
[ROW][C]115[/C][C]66568[/C][C]84642.5233832137[/C][C]-18074.5233832137[/C][/ROW]
[ROW][C]116[/C][C]58872[/C][C]72163.3264468518[/C][C]-13291.3264468518[/C][/ROW]
[ROW][C]117[/C][C]65936[/C][C]62836.2790574772[/C][C]3099.72094252278[/C][/ROW]
[ROW][C]118[/C][C]46504[/C][C]64311.0099119154[/C][C]-17807.0099119154[/C][/ROW]
[ROW][C]119[/C][C]67704[/C][C]52008.1056263861[/C][C]15695.8943736139[/C][/ROW]
[ROW][C]120[/C][C]80704[/C][C]61783.7747241883[/C][C]18920.2252758117[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279786&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279786&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
3151368151376-8
4150176150802.727961924-626.72796192352
5161968149821.71125206512146.288747935
6161344157258.1733479754085.82665202513
7152512159382.752558407-6870.75255840685
8146640154286.89392064-7646.89392064034
9147208148679.554431069-1471.55443106865
10147208147141.79305703966.206942960911
11147840146617.4237475661222.57625243359
12148976146855.1073168482120.89268315173
13150744147684.7856895673059.21431043342
14150744149132.8224806641611.17751933602
15149608149626.596134407-18.5961344065727
16146640149046.341193323-2406.3411933232
17161968146892.55089379215075.4491062082
18164304156259.3436073268044.65639267443
19160776160992.810459143-216.810459143075
20152512160281.931334645-7769.93133464485
21156048154593.509603641454.49039636008
22150744154984.025697579-4240.0256975792
23153136151621.8285822071514.17141779288
24154280152051.6747533262228.32524667383
25155472152952.1516967382519.84830326244
26152512154044.743721963-1532.74372196305
27153136152466.658314669.341686000174
28148976152339.757670848-3363.75767084752
29161968149555.02535574412412.9746442559
30166072157167.2347266388904.76527336237
31162544162467.51742457176.482575429487
32156048161949.919805802-5901.91980580214
33163112157492.5265632225619.4734367778
34155472160627.786304294-5155.78630429393
35162544156662.0985904775881.90140952304
36161968159970.299614631997.70038536986
37163736160718.7936767693017.20632323122
38157240162139.14700436-4899.1470043603
39164304158342.585810695961.41418930961
40163736161703.1861351692032.81386483103
41174336162474.82014739711861.1798526027
42171944169723.394124292220.60587571043
43162544170618.783965495-8074.78396549524
44157808164729.462899795-6921.46289979474
45164304159600.1859056954703.81409430539
46155472162132.021781939-6660.02178193914
47161968157175.0357288514792.96427114881
48163112159765.6219959513346.37800404863
49165504161402.9010279154101.09897208525
50160208163537.544769956-3329.54476995589
51163112160775.3589193782336.64108062154
52164880161747.2165128973132.78348710263
53171376163243.7357415778132.26425842312
54166072168034.936593898-1962.9365938979
55159008166173.3520358-7165.35203579973
56151368160883.350940267-9515.35094026671
57158440154044.6893817234395.31061827677
58139000156373.219998923-17373.2199989233
59148408144356.1853307064051.81466929393
60153704146458.3504826367245.64951736399
61159008150665.2680007018342.73199929923
62151368155595.168095994-4227.16809599352
63151368152241.444201263-873.444201262959
64151368151097.840315418270.159684581624
65155472150707.87683344764.12316660042
66149608153279.456675331-3671.45667533134
67141912150291.94925176-8379.94925176041
68135472144201.522809958-8729.52280995791
69140144137880.7257294862263.27427051397
70121904138804.23424595-16900.2342459501
71133080127098.8994401475981.10055985255
72139576130472.4731765129103.52682348766
73140768135903.7406819964864.25931800419
74134272138541.310724307-4269.31072430691
75134840135159.814636937-319.814636937343
76133080134381.055269018-1301.05526901787
77139000132955.6536542816044.3463457188
78134840136370.906664554-1530.90666455423
79126640134794.031886167-8154.03188616701
80120712128852.486063558-8140.48606355838
81130736122919.8670025217816.13299747897
82108968127502.735849233-18534.7358492334
83123104114720.2567073548383.74329264552
84129544119677.1834401589866.81655984175
85129544125611.4625148243932.53748517574
86121904127635.023434713-5731.0234347131
87114840123290.251714073-8450.2517140728
88114272117153.495614997-2881.49561499746
89120712114686.5762900566025.4237099444
90114840118089.35919329-3249.35919328983
91103672115380.016019384-11708.0160193836
9295976107096.377737576-11120.3777375755
9310424099199.99588038025040.00411961984
9484808101953.382583424-17145.3825834244
9510247290086.493856427312385.5061435727
9611187297680.601354632614191.3986453674
97114840106464.8006067798375.19939322115
98108344111416.096869197-3072.09686919674
99100136108823.570410559-8687.57041055897
100106008102530.4201609663477.57983903393
101108344104254.1618266484089.83817335189
102106576106381.384648728194.6153512725
10388904105941.6370915-17037.6370915
1048070494145.7531565025-13441.7531565025
1058656884719.57384950281848.42615049719
1066890485369.6954803803-16465.6954803803
1078714473950.723789302613193.2762106974
1089364082077.155606375211562.8443936248
1099893689129.12509585489806.87490414524
1109010495023.9023341207-4919.90233412072
1118184091213.6632793524-9373.6632793524
1128656884468.37456372272099.62543627727
1138890485284.0377195283619.96228047201
1148423287101.6100917959-2869.61009179585
1156656884642.5233832137-18074.5233832137
1165887272163.3264468518-13291.3264468518
1176593662836.27905747723099.72094252278
1184650464311.0099119154-17807.0099119154
1196770452008.105626386115695.8943736139
1208070461783.774724188318920.2252758117







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12173684.293232943357867.335912089789501.250553797
12273116.293232943354173.631011140492058.9554547463
12372548.293232943350927.174732529594169.4117333572
12471980.293232943347977.770899476995982.8155664097
12571412.293232943345244.194495584497580.3919703023
12670844.293232943342676.621964487699011.964501399
12770276.293232943340241.8793407529100310.707125134
12869708.293232943337916.5595430828101500.026922804
12969140.293232943335683.4158507573102597.170615129
13068572.293232943333529.3059555115103615.280510375
13168004.293232943331443.9421612446104564.644304642
13267436.293232943329419.0920781308105453.494387756

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 73684.2932329433 & 57867.3359120897 & 89501.250553797 \tabularnewline
122 & 73116.2932329433 & 54173.6310111404 & 92058.9554547463 \tabularnewline
123 & 72548.2932329433 & 50927.1747325295 & 94169.4117333572 \tabularnewline
124 & 71980.2932329433 & 47977.7708994769 & 95982.8155664097 \tabularnewline
125 & 71412.2932329433 & 45244.1944955844 & 97580.3919703023 \tabularnewline
126 & 70844.2932329433 & 42676.6219644876 & 99011.964501399 \tabularnewline
127 & 70276.2932329433 & 40241.8793407529 & 100310.707125134 \tabularnewline
128 & 69708.2932329433 & 37916.5595430828 & 101500.026922804 \tabularnewline
129 & 69140.2932329433 & 35683.4158507573 & 102597.170615129 \tabularnewline
130 & 68572.2932329433 & 33529.3059555115 & 103615.280510375 \tabularnewline
131 & 68004.2932329433 & 31443.9421612446 & 104564.644304642 \tabularnewline
132 & 67436.2932329433 & 29419.0920781308 & 105453.494387756 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279786&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]73684.2932329433[/C][C]57867.3359120897[/C][C]89501.250553797[/C][/ROW]
[ROW][C]122[/C][C]73116.2932329433[/C][C]54173.6310111404[/C][C]92058.9554547463[/C][/ROW]
[ROW][C]123[/C][C]72548.2932329433[/C][C]50927.1747325295[/C][C]94169.4117333572[/C][/ROW]
[ROW][C]124[/C][C]71980.2932329433[/C][C]47977.7708994769[/C][C]95982.8155664097[/C][/ROW]
[ROW][C]125[/C][C]71412.2932329433[/C][C]45244.1944955844[/C][C]97580.3919703023[/C][/ROW]
[ROW][C]126[/C][C]70844.2932329433[/C][C]42676.6219644876[/C][C]99011.964501399[/C][/ROW]
[ROW][C]127[/C][C]70276.2932329433[/C][C]40241.8793407529[/C][C]100310.707125134[/C][/ROW]
[ROW][C]128[/C][C]69708.2932329433[/C][C]37916.5595430828[/C][C]101500.026922804[/C][/ROW]
[ROW][C]129[/C][C]69140.2932329433[/C][C]35683.4158507573[/C][C]102597.170615129[/C][/ROW]
[ROW][C]130[/C][C]68572.2932329433[/C][C]33529.3059555115[/C][C]103615.280510375[/C][/ROW]
[ROW][C]131[/C][C]68004.2932329433[/C][C]31443.9421612446[/C][C]104564.644304642[/C][/ROW]
[ROW][C]132[/C][C]67436.2932329433[/C][C]29419.0920781308[/C][C]105453.494387756[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279786&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279786&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
12173684.293232943357867.335912089789501.250553797
12273116.293232943354173.631011140492058.9554547463
12372548.293232943350927.174732529594169.4117333572
12471980.293232943347977.770899476995982.8155664097
12571412.293232943345244.194495584497580.3919703023
12670844.293232943342676.621964487699011.964501399
12770276.293232943340241.8793407529100310.707125134
12869708.293232943337916.5595430828101500.026922804
12969140.293232943335683.4158507573102597.170615129
13068572.293232943333529.3059555115103615.280510375
13168004.293232943331443.9421612446104564.644304642
13267436.293232943329419.0920781308105453.494387756



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