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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 computationThu, 27 Dec 2012 10:35:40 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/27/t1356622674ep4djz7av8oyzdw.htm/, Retrieved Tue, 07 Feb 2023 17:27:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=204778, Retrieved Tue, 07 Feb 2023 17:27:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact90
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential smoot...] [2012-12-27 15:35:40] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
132
133.7
127
128.7
127.3
136.7
133.8
137.2
147.4
137.6
123.6
117.4
113.7
106.8
103.3
96.3
96.2
94.7
94.6
95.7
106.7
100.2
94.2
97.6
94.3
98
93.6
86.3
90.7
81.8
87.6
73.8
63.3
59.1
52.9
54.6
52.4
67.5
90.4
126
144.3
167.8
166.2
156
137
129.3
118
114.7
112.8
115.7
103.9
96.9
88.8
93
86.3
82.3
82.4
76.6
72.7
67.5
77.3
73.7
73
78.2
90.7
91.5
86.3
86.8
86.1
77.1
75.7
78.7
71.5
69.6
73.6
78.1
78.3
71.5
68.7
61.2
64.7
64.6
56.3
54.5
49.5
54
59.2
52.4
52.8
47.8
45.2
47.1
42.6
42.1
39.4
39.6




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204778&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204778&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204778&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999926373388671
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999926373388671 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204778&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]0.999926373388671[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204778&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204778&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
alpha0.999926373388671
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2133.71321.69999999999999
3127133.699874834761-6.69987483476072
4128.7127.000493289081.69950671091958
5127.3128.69987487108-1.39987487107994
6136.7127.3001030680439.39989693195695
7133.8136.699307917442-2.89930791744203
8137.2133.8002134662173.39978653378282
9147.4137.19974968523810.2002503147617
10137.6147.399248990135-9.79924899013463
11123.6137.600721485497-14.0007214854967
12117.4123.601030825679-6.20103082567913
13113.7117.400456560886-3.70045656088644
14106.8113.700272452077-6.90027245207695
15103.3106.800508043678-3.5005080436779
1696.3103.300257730545-7.00025773054519
1796.296.3005154052551-0.100515405255123
1894.796.2000074006087-1.50000740060868
1994.694.7001104404619-0.10011044046189
2095.794.60000737079251.09999262920752
21106.795.699919011270211.0000809887298
22100.2106.699190101312-6.49919010131245
2394.2100.200478513344-6.00047851334354
2497.694.20044179489933.3995582051007
2594.397.5997497020493-3.29974970204934
269894.30024294938883.69975705061121
2793.697.9997275994256-4.39972759942563
2886.393.6003239370339-7.30032393703391
2990.786.30053749811314.39946250188692
3081.890.6996760824843-8.89967608248432
3187.681.80065525299195.79934474700812
3273.887.5995730138984-13.7995730138984
3363.373.8010160157988-10.5010160157988
3459.163.3007731542247-4.20077315422475
3552.959.1003092886923-6.20030928869231
3654.652.90045650776211.69954349223789
3752.454.5998748683719-2.19987486837186
3867.552.400161969331915.0998380306681
3990.467.498888250094222.9011117499058
4012690.398313868746235.6016861312538
41144.3125.99737876849318.3026212315074
42167.8144.2986524400223.5013475599797
43166.2167.798269675418-1.59826967541753
44156166.20011767518-10.2001176751802
45137156.0007510001-19.0007510000996
46129.3137.001398960909-7.70139896090882
47118129.300567027908-11.300567027908
48114.7118.000832022456-3.30083202245636
49112.8114.700243029076-1.90024302907638
50115.7112.8001399084552.89986009154508
51103.9115.699786493128-11.7997864931281
5296.9103.900868778294-7.00086877829389
5388.896.9005154502445-8.10051545024452
549388.80059641350264.19940358649738
5586.392.9996908121443-6.69969081214433
5682.386.3004932755315-4.00049327553145
5782.482.30029454276350.0997054572364817
5876.682.3999926590251-5.79999265902507
5972.776.6004270338052-3.9004270338052
6067.572.7002871752252-5.20028717522524
6177.367.50038287952269.79961712047735
6273.777.2992784873991-3.59927848739909
637373.7002650026783-0.700265002678265
6478.273.00005155813925.19994844186083
6590.778.199617145417212.5003828545829
6691.590.69907963917010.800920360829892
6786.391.4999410309479-5.1999410309479
6886.886.30038285403720.499617145962787
6986.186.7999632148826-0.699963214882587
7077.186.1000515359196-9.00005153591957
7175.777.1006626432964-1.40066264329637
7278.775.7001031260442.99989687395596
7371.578.6997791277588-7.19977912775883
7469.671.5005300953395-1.90053009533951
7573.669.60013992959063.99986007040935
7678.173.59970550385724.50029449614277
7778.378.09966865856630.200331341433738
7871.578.2999852502822-6.79998525028219
7968.771.5005006598711-2.80050065987106
8061.268.7002061913736-7.50020619137361
8164.761.20055221476613.49944778523386
8264.664.6997423475181-0.0997423475180597
8356.364.600007343691-8.30000734369105
8454.556.3006111014147-1.80061110141472
8549.554.5001325728937-5.00013257289372
865449.50036814281754.49963185718246
8759.253.99966870735415.20033129264588
8852.459.1996171172291-6.79961711722914
8952.852.40050063276670.399499367233325
9047.852.7999705862154-4.99997058621536
9145.247.800368130891-2.600368130891
9247.145.20019145629371.89980854370631
9342.647.0998601235348-4.49986012353475
9442.142.6003313094524-0.500331309452349
9539.442.1000368376989-2.70003683769886
9639.639.40019879456280.199801205437183

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 133.7 & 132 & 1.69999999999999 \tabularnewline
3 & 127 & 133.699874834761 & -6.69987483476072 \tabularnewline
4 & 128.7 & 127.00049328908 & 1.69950671091958 \tabularnewline
5 & 127.3 & 128.69987487108 & -1.39987487107994 \tabularnewline
6 & 136.7 & 127.300103068043 & 9.39989693195695 \tabularnewline
7 & 133.8 & 136.699307917442 & -2.89930791744203 \tabularnewline
8 & 137.2 & 133.800213466217 & 3.39978653378282 \tabularnewline
9 & 147.4 & 137.199749685238 & 10.2002503147617 \tabularnewline
10 & 137.6 & 147.399248990135 & -9.79924899013463 \tabularnewline
11 & 123.6 & 137.600721485497 & -14.0007214854967 \tabularnewline
12 & 117.4 & 123.601030825679 & -6.20103082567913 \tabularnewline
13 & 113.7 & 117.400456560886 & -3.70045656088644 \tabularnewline
14 & 106.8 & 113.700272452077 & -6.90027245207695 \tabularnewline
15 & 103.3 & 106.800508043678 & -3.5005080436779 \tabularnewline
16 & 96.3 & 103.300257730545 & -7.00025773054519 \tabularnewline
17 & 96.2 & 96.3005154052551 & -0.100515405255123 \tabularnewline
18 & 94.7 & 96.2000074006087 & -1.50000740060868 \tabularnewline
19 & 94.6 & 94.7001104404619 & -0.10011044046189 \tabularnewline
20 & 95.7 & 94.6000073707925 & 1.09999262920752 \tabularnewline
21 & 106.7 & 95.6999190112702 & 11.0000809887298 \tabularnewline
22 & 100.2 & 106.699190101312 & -6.49919010131245 \tabularnewline
23 & 94.2 & 100.200478513344 & -6.00047851334354 \tabularnewline
24 & 97.6 & 94.2004417948993 & 3.3995582051007 \tabularnewline
25 & 94.3 & 97.5997497020493 & -3.29974970204934 \tabularnewline
26 & 98 & 94.3002429493888 & 3.69975705061121 \tabularnewline
27 & 93.6 & 97.9997275994256 & -4.39972759942563 \tabularnewline
28 & 86.3 & 93.6003239370339 & -7.30032393703391 \tabularnewline
29 & 90.7 & 86.3005374981131 & 4.39946250188692 \tabularnewline
30 & 81.8 & 90.6996760824843 & -8.89967608248432 \tabularnewline
31 & 87.6 & 81.8006552529919 & 5.79934474700812 \tabularnewline
32 & 73.8 & 87.5995730138984 & -13.7995730138984 \tabularnewline
33 & 63.3 & 73.8010160157988 & -10.5010160157988 \tabularnewline
34 & 59.1 & 63.3007731542247 & -4.20077315422475 \tabularnewline
35 & 52.9 & 59.1003092886923 & -6.20030928869231 \tabularnewline
36 & 54.6 & 52.9004565077621 & 1.69954349223789 \tabularnewline
37 & 52.4 & 54.5998748683719 & -2.19987486837186 \tabularnewline
38 & 67.5 & 52.4001619693319 & 15.0998380306681 \tabularnewline
39 & 90.4 & 67.4988882500942 & 22.9011117499058 \tabularnewline
40 & 126 & 90.3983138687462 & 35.6016861312538 \tabularnewline
41 & 144.3 & 125.997378768493 & 18.3026212315074 \tabularnewline
42 & 167.8 & 144.29865244002 & 23.5013475599797 \tabularnewline
43 & 166.2 & 167.798269675418 & -1.59826967541753 \tabularnewline
44 & 156 & 166.20011767518 & -10.2001176751802 \tabularnewline
45 & 137 & 156.0007510001 & -19.0007510000996 \tabularnewline
46 & 129.3 & 137.001398960909 & -7.70139896090882 \tabularnewline
47 & 118 & 129.300567027908 & -11.300567027908 \tabularnewline
48 & 114.7 & 118.000832022456 & -3.30083202245636 \tabularnewline
49 & 112.8 & 114.700243029076 & -1.90024302907638 \tabularnewline
50 & 115.7 & 112.800139908455 & 2.89986009154508 \tabularnewline
51 & 103.9 & 115.699786493128 & -11.7997864931281 \tabularnewline
52 & 96.9 & 103.900868778294 & -7.00086877829389 \tabularnewline
53 & 88.8 & 96.9005154502445 & -8.10051545024452 \tabularnewline
54 & 93 & 88.8005964135026 & 4.19940358649738 \tabularnewline
55 & 86.3 & 92.9996908121443 & -6.69969081214433 \tabularnewline
56 & 82.3 & 86.3004932755315 & -4.00049327553145 \tabularnewline
57 & 82.4 & 82.3002945427635 & 0.0997054572364817 \tabularnewline
58 & 76.6 & 82.3999926590251 & -5.79999265902507 \tabularnewline
59 & 72.7 & 76.6004270338052 & -3.9004270338052 \tabularnewline
60 & 67.5 & 72.7002871752252 & -5.20028717522524 \tabularnewline
61 & 77.3 & 67.5003828795226 & 9.79961712047735 \tabularnewline
62 & 73.7 & 77.2992784873991 & -3.59927848739909 \tabularnewline
63 & 73 & 73.7002650026783 & -0.700265002678265 \tabularnewline
64 & 78.2 & 73.0000515581392 & 5.19994844186083 \tabularnewline
65 & 90.7 & 78.1996171454172 & 12.5003828545829 \tabularnewline
66 & 91.5 & 90.6990796391701 & 0.800920360829892 \tabularnewline
67 & 86.3 & 91.4999410309479 & -5.1999410309479 \tabularnewline
68 & 86.8 & 86.3003828540372 & 0.499617145962787 \tabularnewline
69 & 86.1 & 86.7999632148826 & -0.699963214882587 \tabularnewline
70 & 77.1 & 86.1000515359196 & -9.00005153591957 \tabularnewline
71 & 75.7 & 77.1006626432964 & -1.40066264329637 \tabularnewline
72 & 78.7 & 75.700103126044 & 2.99989687395596 \tabularnewline
73 & 71.5 & 78.6997791277588 & -7.19977912775883 \tabularnewline
74 & 69.6 & 71.5005300953395 & -1.90053009533951 \tabularnewline
75 & 73.6 & 69.6001399295906 & 3.99986007040935 \tabularnewline
76 & 78.1 & 73.5997055038572 & 4.50029449614277 \tabularnewline
77 & 78.3 & 78.0996686585663 & 0.200331341433738 \tabularnewline
78 & 71.5 & 78.2999852502822 & -6.79998525028219 \tabularnewline
79 & 68.7 & 71.5005006598711 & -2.80050065987106 \tabularnewline
80 & 61.2 & 68.7002061913736 & -7.50020619137361 \tabularnewline
81 & 64.7 & 61.2005522147661 & 3.49944778523386 \tabularnewline
82 & 64.6 & 64.6997423475181 & -0.0997423475180597 \tabularnewline
83 & 56.3 & 64.600007343691 & -8.30000734369105 \tabularnewline
84 & 54.5 & 56.3006111014147 & -1.80061110141472 \tabularnewline
85 & 49.5 & 54.5001325728937 & -5.00013257289372 \tabularnewline
86 & 54 & 49.5003681428175 & 4.49963185718246 \tabularnewline
87 & 59.2 & 53.9996687073541 & 5.20033129264588 \tabularnewline
88 & 52.4 & 59.1996171172291 & -6.79961711722914 \tabularnewline
89 & 52.8 & 52.4005006327667 & 0.399499367233325 \tabularnewline
90 & 47.8 & 52.7999705862154 & -4.99997058621536 \tabularnewline
91 & 45.2 & 47.800368130891 & -2.600368130891 \tabularnewline
92 & 47.1 & 45.2001914562937 & 1.89980854370631 \tabularnewline
93 & 42.6 & 47.0998601235348 & -4.49986012353475 \tabularnewline
94 & 42.1 & 42.6003313094524 & -0.500331309452349 \tabularnewline
95 & 39.4 & 42.1000368376989 & -2.70003683769886 \tabularnewline
96 & 39.6 & 39.4001987945628 & 0.199801205437183 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204778&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]2[/C][C]133.7[/C][C]132[/C][C]1.69999999999999[/C][/ROW]
[ROW][C]3[/C][C]127[/C][C]133.699874834761[/C][C]-6.69987483476072[/C][/ROW]
[ROW][C]4[/C][C]128.7[/C][C]127.00049328908[/C][C]1.69950671091958[/C][/ROW]
[ROW][C]5[/C][C]127.3[/C][C]128.69987487108[/C][C]-1.39987487107994[/C][/ROW]
[ROW][C]6[/C][C]136.7[/C][C]127.300103068043[/C][C]9.39989693195695[/C][/ROW]
[ROW][C]7[/C][C]133.8[/C][C]136.699307917442[/C][C]-2.89930791744203[/C][/ROW]
[ROW][C]8[/C][C]137.2[/C][C]133.800213466217[/C][C]3.39978653378282[/C][/ROW]
[ROW][C]9[/C][C]147.4[/C][C]137.199749685238[/C][C]10.2002503147617[/C][/ROW]
[ROW][C]10[/C][C]137.6[/C][C]147.399248990135[/C][C]-9.79924899013463[/C][/ROW]
[ROW][C]11[/C][C]123.6[/C][C]137.600721485497[/C][C]-14.0007214854967[/C][/ROW]
[ROW][C]12[/C][C]117.4[/C][C]123.601030825679[/C][C]-6.20103082567913[/C][/ROW]
[ROW][C]13[/C][C]113.7[/C][C]117.400456560886[/C][C]-3.70045656088644[/C][/ROW]
[ROW][C]14[/C][C]106.8[/C][C]113.700272452077[/C][C]-6.90027245207695[/C][/ROW]
[ROW][C]15[/C][C]103.3[/C][C]106.800508043678[/C][C]-3.5005080436779[/C][/ROW]
[ROW][C]16[/C][C]96.3[/C][C]103.300257730545[/C][C]-7.00025773054519[/C][/ROW]
[ROW][C]17[/C][C]96.2[/C][C]96.3005154052551[/C][C]-0.100515405255123[/C][/ROW]
[ROW][C]18[/C][C]94.7[/C][C]96.2000074006087[/C][C]-1.50000740060868[/C][/ROW]
[ROW][C]19[/C][C]94.6[/C][C]94.7001104404619[/C][C]-0.10011044046189[/C][/ROW]
[ROW][C]20[/C][C]95.7[/C][C]94.6000073707925[/C][C]1.09999262920752[/C][/ROW]
[ROW][C]21[/C][C]106.7[/C][C]95.6999190112702[/C][C]11.0000809887298[/C][/ROW]
[ROW][C]22[/C][C]100.2[/C][C]106.699190101312[/C][C]-6.49919010131245[/C][/ROW]
[ROW][C]23[/C][C]94.2[/C][C]100.200478513344[/C][C]-6.00047851334354[/C][/ROW]
[ROW][C]24[/C][C]97.6[/C][C]94.2004417948993[/C][C]3.3995582051007[/C][/ROW]
[ROW][C]25[/C][C]94.3[/C][C]97.5997497020493[/C][C]-3.29974970204934[/C][/ROW]
[ROW][C]26[/C][C]98[/C][C]94.3002429493888[/C][C]3.69975705061121[/C][/ROW]
[ROW][C]27[/C][C]93.6[/C][C]97.9997275994256[/C][C]-4.39972759942563[/C][/ROW]
[ROW][C]28[/C][C]86.3[/C][C]93.6003239370339[/C][C]-7.30032393703391[/C][/ROW]
[ROW][C]29[/C][C]90.7[/C][C]86.3005374981131[/C][C]4.39946250188692[/C][/ROW]
[ROW][C]30[/C][C]81.8[/C][C]90.6996760824843[/C][C]-8.89967608248432[/C][/ROW]
[ROW][C]31[/C][C]87.6[/C][C]81.8006552529919[/C][C]5.79934474700812[/C][/ROW]
[ROW][C]32[/C][C]73.8[/C][C]87.5995730138984[/C][C]-13.7995730138984[/C][/ROW]
[ROW][C]33[/C][C]63.3[/C][C]73.8010160157988[/C][C]-10.5010160157988[/C][/ROW]
[ROW][C]34[/C][C]59.1[/C][C]63.3007731542247[/C][C]-4.20077315422475[/C][/ROW]
[ROW][C]35[/C][C]52.9[/C][C]59.1003092886923[/C][C]-6.20030928869231[/C][/ROW]
[ROW][C]36[/C][C]54.6[/C][C]52.9004565077621[/C][C]1.69954349223789[/C][/ROW]
[ROW][C]37[/C][C]52.4[/C][C]54.5998748683719[/C][C]-2.19987486837186[/C][/ROW]
[ROW][C]38[/C][C]67.5[/C][C]52.4001619693319[/C][C]15.0998380306681[/C][/ROW]
[ROW][C]39[/C][C]90.4[/C][C]67.4988882500942[/C][C]22.9011117499058[/C][/ROW]
[ROW][C]40[/C][C]126[/C][C]90.3983138687462[/C][C]35.6016861312538[/C][/ROW]
[ROW][C]41[/C][C]144.3[/C][C]125.997378768493[/C][C]18.3026212315074[/C][/ROW]
[ROW][C]42[/C][C]167.8[/C][C]144.29865244002[/C][C]23.5013475599797[/C][/ROW]
[ROW][C]43[/C][C]166.2[/C][C]167.798269675418[/C][C]-1.59826967541753[/C][/ROW]
[ROW][C]44[/C][C]156[/C][C]166.20011767518[/C][C]-10.2001176751802[/C][/ROW]
[ROW][C]45[/C][C]137[/C][C]156.0007510001[/C][C]-19.0007510000996[/C][/ROW]
[ROW][C]46[/C][C]129.3[/C][C]137.001398960909[/C][C]-7.70139896090882[/C][/ROW]
[ROW][C]47[/C][C]118[/C][C]129.300567027908[/C][C]-11.300567027908[/C][/ROW]
[ROW][C]48[/C][C]114.7[/C][C]118.000832022456[/C][C]-3.30083202245636[/C][/ROW]
[ROW][C]49[/C][C]112.8[/C][C]114.700243029076[/C][C]-1.90024302907638[/C][/ROW]
[ROW][C]50[/C][C]115.7[/C][C]112.800139908455[/C][C]2.89986009154508[/C][/ROW]
[ROW][C]51[/C][C]103.9[/C][C]115.699786493128[/C][C]-11.7997864931281[/C][/ROW]
[ROW][C]52[/C][C]96.9[/C][C]103.900868778294[/C][C]-7.00086877829389[/C][/ROW]
[ROW][C]53[/C][C]88.8[/C][C]96.9005154502445[/C][C]-8.10051545024452[/C][/ROW]
[ROW][C]54[/C][C]93[/C][C]88.8005964135026[/C][C]4.19940358649738[/C][/ROW]
[ROW][C]55[/C][C]86.3[/C][C]92.9996908121443[/C][C]-6.69969081214433[/C][/ROW]
[ROW][C]56[/C][C]82.3[/C][C]86.3004932755315[/C][C]-4.00049327553145[/C][/ROW]
[ROW][C]57[/C][C]82.4[/C][C]82.3002945427635[/C][C]0.0997054572364817[/C][/ROW]
[ROW][C]58[/C][C]76.6[/C][C]82.3999926590251[/C][C]-5.79999265902507[/C][/ROW]
[ROW][C]59[/C][C]72.7[/C][C]76.6004270338052[/C][C]-3.9004270338052[/C][/ROW]
[ROW][C]60[/C][C]67.5[/C][C]72.7002871752252[/C][C]-5.20028717522524[/C][/ROW]
[ROW][C]61[/C][C]77.3[/C][C]67.5003828795226[/C][C]9.79961712047735[/C][/ROW]
[ROW][C]62[/C][C]73.7[/C][C]77.2992784873991[/C][C]-3.59927848739909[/C][/ROW]
[ROW][C]63[/C][C]73[/C][C]73.7002650026783[/C][C]-0.700265002678265[/C][/ROW]
[ROW][C]64[/C][C]78.2[/C][C]73.0000515581392[/C][C]5.19994844186083[/C][/ROW]
[ROW][C]65[/C][C]90.7[/C][C]78.1996171454172[/C][C]12.5003828545829[/C][/ROW]
[ROW][C]66[/C][C]91.5[/C][C]90.6990796391701[/C][C]0.800920360829892[/C][/ROW]
[ROW][C]67[/C][C]86.3[/C][C]91.4999410309479[/C][C]-5.1999410309479[/C][/ROW]
[ROW][C]68[/C][C]86.8[/C][C]86.3003828540372[/C][C]0.499617145962787[/C][/ROW]
[ROW][C]69[/C][C]86.1[/C][C]86.7999632148826[/C][C]-0.699963214882587[/C][/ROW]
[ROW][C]70[/C][C]77.1[/C][C]86.1000515359196[/C][C]-9.00005153591957[/C][/ROW]
[ROW][C]71[/C][C]75.7[/C][C]77.1006626432964[/C][C]-1.40066264329637[/C][/ROW]
[ROW][C]72[/C][C]78.7[/C][C]75.700103126044[/C][C]2.99989687395596[/C][/ROW]
[ROW][C]73[/C][C]71.5[/C][C]78.6997791277588[/C][C]-7.19977912775883[/C][/ROW]
[ROW][C]74[/C][C]69.6[/C][C]71.5005300953395[/C][C]-1.90053009533951[/C][/ROW]
[ROW][C]75[/C][C]73.6[/C][C]69.6001399295906[/C][C]3.99986007040935[/C][/ROW]
[ROW][C]76[/C][C]78.1[/C][C]73.5997055038572[/C][C]4.50029449614277[/C][/ROW]
[ROW][C]77[/C][C]78.3[/C][C]78.0996686585663[/C][C]0.200331341433738[/C][/ROW]
[ROW][C]78[/C][C]71.5[/C][C]78.2999852502822[/C][C]-6.79998525028219[/C][/ROW]
[ROW][C]79[/C][C]68.7[/C][C]71.5005006598711[/C][C]-2.80050065987106[/C][/ROW]
[ROW][C]80[/C][C]61.2[/C][C]68.7002061913736[/C][C]-7.50020619137361[/C][/ROW]
[ROW][C]81[/C][C]64.7[/C][C]61.2005522147661[/C][C]3.49944778523386[/C][/ROW]
[ROW][C]82[/C][C]64.6[/C][C]64.6997423475181[/C][C]-0.0997423475180597[/C][/ROW]
[ROW][C]83[/C][C]56.3[/C][C]64.600007343691[/C][C]-8.30000734369105[/C][/ROW]
[ROW][C]84[/C][C]54.5[/C][C]56.3006111014147[/C][C]-1.80061110141472[/C][/ROW]
[ROW][C]85[/C][C]49.5[/C][C]54.5001325728937[/C][C]-5.00013257289372[/C][/ROW]
[ROW][C]86[/C][C]54[/C][C]49.5003681428175[/C][C]4.49963185718246[/C][/ROW]
[ROW][C]87[/C][C]59.2[/C][C]53.9996687073541[/C][C]5.20033129264588[/C][/ROW]
[ROW][C]88[/C][C]52.4[/C][C]59.1996171172291[/C][C]-6.79961711722914[/C][/ROW]
[ROW][C]89[/C][C]52.8[/C][C]52.4005006327667[/C][C]0.399499367233325[/C][/ROW]
[ROW][C]90[/C][C]47.8[/C][C]52.7999705862154[/C][C]-4.99997058621536[/C][/ROW]
[ROW][C]91[/C][C]45.2[/C][C]47.800368130891[/C][C]-2.600368130891[/C][/ROW]
[ROW][C]92[/C][C]47.1[/C][C]45.2001914562937[/C][C]1.89980854370631[/C][/ROW]
[ROW][C]93[/C][C]42.6[/C][C]47.0998601235348[/C][C]-4.49986012353475[/C][/ROW]
[ROW][C]94[/C][C]42.1[/C][C]42.6003313094524[/C][C]-0.500331309452349[/C][/ROW]
[ROW][C]95[/C][C]39.4[/C][C]42.1000368376989[/C][C]-2.70003683769886[/C][/ROW]
[ROW][C]96[/C][C]39.6[/C][C]39.4001987945628[/C][C]0.199801205437183[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204778&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204778&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
2133.71321.69999999999999
3127133.699874834761-6.69987483476072
4128.7127.000493289081.69950671091958
5127.3128.69987487108-1.39987487107994
6136.7127.3001030680439.39989693195695
7133.8136.699307917442-2.89930791744203
8137.2133.8002134662173.39978653378282
9147.4137.19974968523810.2002503147617
10137.6147.399248990135-9.79924899013463
11123.6137.600721485497-14.0007214854967
12117.4123.601030825679-6.20103082567913
13113.7117.400456560886-3.70045656088644
14106.8113.700272452077-6.90027245207695
15103.3106.800508043678-3.5005080436779
1696.3103.300257730545-7.00025773054519
1796.296.3005154052551-0.100515405255123
1894.796.2000074006087-1.50000740060868
1994.694.7001104404619-0.10011044046189
2095.794.60000737079251.09999262920752
21106.795.699919011270211.0000809887298
22100.2106.699190101312-6.49919010131245
2394.2100.200478513344-6.00047851334354
2497.694.20044179489933.3995582051007
2594.397.5997497020493-3.29974970204934
269894.30024294938883.69975705061121
2793.697.9997275994256-4.39972759942563
2886.393.6003239370339-7.30032393703391
2990.786.30053749811314.39946250188692
3081.890.6996760824843-8.89967608248432
3187.681.80065525299195.79934474700812
3273.887.5995730138984-13.7995730138984
3363.373.8010160157988-10.5010160157988
3459.163.3007731542247-4.20077315422475
3552.959.1003092886923-6.20030928869231
3654.652.90045650776211.69954349223789
3752.454.5998748683719-2.19987486837186
3867.552.400161969331915.0998380306681
3990.467.498888250094222.9011117499058
4012690.398313868746235.6016861312538
41144.3125.99737876849318.3026212315074
42167.8144.2986524400223.5013475599797
43166.2167.798269675418-1.59826967541753
44156166.20011767518-10.2001176751802
45137156.0007510001-19.0007510000996
46129.3137.001398960909-7.70139896090882
47118129.300567027908-11.300567027908
48114.7118.000832022456-3.30083202245636
49112.8114.700243029076-1.90024302907638
50115.7112.8001399084552.89986009154508
51103.9115.699786493128-11.7997864931281
5296.9103.900868778294-7.00086877829389
5388.896.9005154502445-8.10051545024452
549388.80059641350264.19940358649738
5586.392.9996908121443-6.69969081214433
5682.386.3004932755315-4.00049327553145
5782.482.30029454276350.0997054572364817
5876.682.3999926590251-5.79999265902507
5972.776.6004270338052-3.9004270338052
6067.572.7002871752252-5.20028717522524
6177.367.50038287952269.79961712047735
6273.777.2992784873991-3.59927848739909
637373.7002650026783-0.700265002678265
6478.273.00005155813925.19994844186083
6590.778.199617145417212.5003828545829
6691.590.69907963917010.800920360829892
6786.391.4999410309479-5.1999410309479
6886.886.30038285403720.499617145962787
6986.186.7999632148826-0.699963214882587
7077.186.1000515359196-9.00005153591957
7175.777.1006626432964-1.40066264329637
7278.775.7001031260442.99989687395596
7371.578.6997791277588-7.19977912775883
7469.671.5005300953395-1.90053009533951
7573.669.60013992959063.99986007040935
7678.173.59970550385724.50029449614277
7778.378.09966865856630.200331341433738
7871.578.2999852502822-6.79998525028219
7968.771.5005006598711-2.80050065987106
8061.268.7002061913736-7.50020619137361
8164.761.20055221476613.49944778523386
8264.664.6997423475181-0.0997423475180597
8356.364.600007343691-8.30000734369105
8454.556.3006111014147-1.80061110141472
8549.554.5001325728937-5.00013257289372
865449.50036814281754.49963185718246
8759.253.99966870735415.20033129264588
8852.459.1996171172291-6.79961711722914
8952.852.40050063276670.399499367233325
9047.852.7999705862154-4.99997058621536
9145.247.800368130891-2.600368130891
9247.145.20019145629371.89980854370631
9342.647.0998601235348-4.49986012353475
9442.142.6003313094524-0.500331309452349
9539.442.1000368376989-2.70003683769886
9639.639.40019879456280.199801205437183







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
9739.599985289314323.540437282788455.6595332958402
9839.599985289314316.889190767712762.3107798109159
9939.599985289314311.785397508243267.4145730703854
10039.59998528931437.4826628750872571.7173077035414
10139.59998528931433.6918594027143275.5081111759143
10239.59998528931430.26470074329363178.935269835335
10339.5999852893143-2.8869034640989482.0868740427275
10439.5999852893143-5.8203496012764385.020320179905
10539.5999852893143-8.5755056495636787.7754762281923
10639.5999852893143-11.181399418375790.3813699970043
10739.5999852893143-13.659944662375692.8599152410042
10839.5999852893143-16.028166253653795.2281368322823

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 39.5999852893143 & 23.5404372827884 & 55.6595332958402 \tabularnewline
98 & 39.5999852893143 & 16.8891907677127 & 62.3107798109159 \tabularnewline
99 & 39.5999852893143 & 11.7853975082432 & 67.4145730703854 \tabularnewline
100 & 39.5999852893143 & 7.48266287508725 & 71.7173077035414 \tabularnewline
101 & 39.5999852893143 & 3.69185940271432 & 75.5081111759143 \tabularnewline
102 & 39.5999852893143 & 0.264700743293631 & 78.935269835335 \tabularnewline
103 & 39.5999852893143 & -2.88690346409894 & 82.0868740427275 \tabularnewline
104 & 39.5999852893143 & -5.82034960127643 & 85.020320179905 \tabularnewline
105 & 39.5999852893143 & -8.57550564956367 & 87.7754762281923 \tabularnewline
106 & 39.5999852893143 & -11.1813994183757 & 90.3813699970043 \tabularnewline
107 & 39.5999852893143 & -13.6599446623756 & 92.8599152410042 \tabularnewline
108 & 39.5999852893143 & -16.0281662536537 & 95.2281368322823 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204778&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]97[/C][C]39.5999852893143[/C][C]23.5404372827884[/C][C]55.6595332958402[/C][/ROW]
[ROW][C]98[/C][C]39.5999852893143[/C][C]16.8891907677127[/C][C]62.3107798109159[/C][/ROW]
[ROW][C]99[/C][C]39.5999852893143[/C][C]11.7853975082432[/C][C]67.4145730703854[/C][/ROW]
[ROW][C]100[/C][C]39.5999852893143[/C][C]7.48266287508725[/C][C]71.7173077035414[/C][/ROW]
[ROW][C]101[/C][C]39.5999852893143[/C][C]3.69185940271432[/C][C]75.5081111759143[/C][/ROW]
[ROW][C]102[/C][C]39.5999852893143[/C][C]0.264700743293631[/C][C]78.935269835335[/C][/ROW]
[ROW][C]103[/C][C]39.5999852893143[/C][C]-2.88690346409894[/C][C]82.0868740427275[/C][/ROW]
[ROW][C]104[/C][C]39.5999852893143[/C][C]-5.82034960127643[/C][C]85.020320179905[/C][/ROW]
[ROW][C]105[/C][C]39.5999852893143[/C][C]-8.57550564956367[/C][C]87.7754762281923[/C][/ROW]
[ROW][C]106[/C][C]39.5999852893143[/C][C]-11.1813994183757[/C][C]90.3813699970043[/C][/ROW]
[ROW][C]107[/C][C]39.5999852893143[/C][C]-13.6599446623756[/C][C]92.8599152410042[/C][/ROW]
[ROW][C]108[/C][C]39.5999852893143[/C][C]-16.0281662536537[/C][C]95.2281368322823[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204778&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204778&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
9739.599985289314323.540437282788455.6595332958402
9839.599985289314316.889190767712762.3107798109159
9939.599985289314311.785397508243267.4145730703854
10039.59998528931437.4826628750872571.7173077035414
10139.59998528931433.6918594027143275.5081111759143
10239.59998528931430.26470074329363178.935269835335
10339.5999852893143-2.8869034640989482.0868740427275
10439.5999852893143-5.8203496012764385.020320179905
10539.5999852893143-8.5755056495636787.7754762281923
10639.5999852893143-11.181399418375790.3813699970043
10739.5999852893143-13.659944662375692.8599152410042
10839.5999852893143-16.028166253653795.2281368322823



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