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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 29 Dec 2010 14:09:04 +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/Dec/29/t1293631630zq2qc1w4xwbo4mi.htm/, Retrieved Fri, 03 May 2024 14:02:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116854, Retrieved Fri, 03 May 2024 14:02:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact117
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2010-12-29 14:09:04] [0956ee981dded61b2e7128dae94e5715] [Current]
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Dataseries X:
3106.54
3125.67
3039.71
3051.67
3112.83
3228.01
3223.98
3328.8
3264.26
3394.14
3549.25
3744.63
3839.25
3912.28
3911.06
3675.8
3703.32
3795.91
3906.01
4070.78
4144.38
4140.3
4388.53
4433.57
4305.23
4471.65
4614.76
4697.86
4639.4
4384.47
4350.83
4325.29
4441.82
4162.5
4127.47
3722.23
3757.12
3719.52
3925.43
3751.41
3168.22
2994.38
3136
2672.2
2100.18
1881.46
1908.64
1900.09
1696.58
1748.74
1953.35
2071.37
2030.98
2169.14
2229.85
2480.93
2525.93
2475.14
2529.66
2453.37
2386.53
2517.3
2457.46
2589.73
2679.07
2506.13
2592.31




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116854&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116854&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116854&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0
gamma0.486860364521044

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.486860364521044 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116854&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]1[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.486860364521044[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116854&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116854&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0
gamma0.486860364521044







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
133839.253450.75455176768388.495448232321
143912.283852.9462559.3337499999998
153911.063843.472567.5875000000001
163675.83608.0383333333367.7616666666668
173703.323637.2666.059999999999
183795.913732.2341666666763.6758333333341
193906.013894.0529166666711.9570833333337
204070.783947.525123.255000000001
214144.383937.15833333333207.221666666666
224140.34211.94833333333-71.6483333333335
234388.534244.80083333333143.729166666666
244433.574535.64375-102.073750000000
254305.234476.10958333333-170.879583333333
264471.654318.92625152.72375
274614.764402.8425211.917500000001
284697.864311.73833333333386.121666666666
294639.44659.32-19.920000000001
304384.474668.31416666667-283.844166666665
314350.834482.61291666667-131.782916666667
324325.294392.345-67.0549999999994
334441.824191.66833333333250.151666666666
344162.54509.38833333333-346.888333333333
354127.474267.00083333333-139.530833333333
363722.234274.58375-552.35375
373757.123764.76958333333-7.6495833333338
383719.523770.81625-51.2962500000003
393925.433650.7125274.717500000001
403751.413622.40833333333129.001666666667
413168.223712.87-544.650000000001
422994.383197.13416666667-202.754166666665
4331363092.5229166666743.4770833333332
442672.23177.515-505.315
452100.182538.57833333333-438.398333333334
461881.462167.74833333333-286.288333333333
471908.641985.96083333333-77.3208333333334
481900.092055.75375-155.66375
491696.581942.62958333333-246.049583333333
501748.741710.2762538.4637499999997
511953.351679.9325273.417500000000
522071.371650.32833333333421.041666666667
532030.982032.83-1.85000000000082
542169.142059.89416666667109.245833333334
552229.852267.28291666667-37.4329166666666
562480.932271.365209.565000000001
572525.932347.30833333333178.621666666666
582475.142593.49833333333-118.358333333334
592529.662579.64083333333-49.9808333333335
602453.372676.77375-223.403749999999
612386.532495.90958333333-109.379583333333
622517.32400.22625117.073750000000
632457.462448.49258.96750000000065
642589.732154.43833333333435.291666666667
652679.072551.19127.879999999999
662506.132707.98416666667-201.854166666666
672592.312604.27291666667-11.9629166666668

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 3839.25 & 3450.75455176768 & 388.495448232321 \tabularnewline
14 & 3912.28 & 3852.94625 & 59.3337499999998 \tabularnewline
15 & 3911.06 & 3843.4725 & 67.5875000000001 \tabularnewline
16 & 3675.8 & 3608.03833333333 & 67.7616666666668 \tabularnewline
17 & 3703.32 & 3637.26 & 66.059999999999 \tabularnewline
18 & 3795.91 & 3732.23416666667 & 63.6758333333341 \tabularnewline
19 & 3906.01 & 3894.05291666667 & 11.9570833333337 \tabularnewline
20 & 4070.78 & 3947.525 & 123.255000000001 \tabularnewline
21 & 4144.38 & 3937.15833333333 & 207.221666666666 \tabularnewline
22 & 4140.3 & 4211.94833333333 & -71.6483333333335 \tabularnewline
23 & 4388.53 & 4244.80083333333 & 143.729166666666 \tabularnewline
24 & 4433.57 & 4535.64375 & -102.073750000000 \tabularnewline
25 & 4305.23 & 4476.10958333333 & -170.879583333333 \tabularnewline
26 & 4471.65 & 4318.92625 & 152.72375 \tabularnewline
27 & 4614.76 & 4402.8425 & 211.917500000001 \tabularnewline
28 & 4697.86 & 4311.73833333333 & 386.121666666666 \tabularnewline
29 & 4639.4 & 4659.32 & -19.920000000001 \tabularnewline
30 & 4384.47 & 4668.31416666667 & -283.844166666665 \tabularnewline
31 & 4350.83 & 4482.61291666667 & -131.782916666667 \tabularnewline
32 & 4325.29 & 4392.345 & -67.0549999999994 \tabularnewline
33 & 4441.82 & 4191.66833333333 & 250.151666666666 \tabularnewline
34 & 4162.5 & 4509.38833333333 & -346.888333333333 \tabularnewline
35 & 4127.47 & 4267.00083333333 & -139.530833333333 \tabularnewline
36 & 3722.23 & 4274.58375 & -552.35375 \tabularnewline
37 & 3757.12 & 3764.76958333333 & -7.6495833333338 \tabularnewline
38 & 3719.52 & 3770.81625 & -51.2962500000003 \tabularnewline
39 & 3925.43 & 3650.7125 & 274.717500000001 \tabularnewline
40 & 3751.41 & 3622.40833333333 & 129.001666666667 \tabularnewline
41 & 3168.22 & 3712.87 & -544.650000000001 \tabularnewline
42 & 2994.38 & 3197.13416666667 & -202.754166666665 \tabularnewline
43 & 3136 & 3092.52291666667 & 43.4770833333332 \tabularnewline
44 & 2672.2 & 3177.515 & -505.315 \tabularnewline
45 & 2100.18 & 2538.57833333333 & -438.398333333334 \tabularnewline
46 & 1881.46 & 2167.74833333333 & -286.288333333333 \tabularnewline
47 & 1908.64 & 1985.96083333333 & -77.3208333333334 \tabularnewline
48 & 1900.09 & 2055.75375 & -155.66375 \tabularnewline
49 & 1696.58 & 1942.62958333333 & -246.049583333333 \tabularnewline
50 & 1748.74 & 1710.27625 & 38.4637499999997 \tabularnewline
51 & 1953.35 & 1679.9325 & 273.417500000000 \tabularnewline
52 & 2071.37 & 1650.32833333333 & 421.041666666667 \tabularnewline
53 & 2030.98 & 2032.83 & -1.85000000000082 \tabularnewline
54 & 2169.14 & 2059.89416666667 & 109.245833333334 \tabularnewline
55 & 2229.85 & 2267.28291666667 & -37.4329166666666 \tabularnewline
56 & 2480.93 & 2271.365 & 209.565000000001 \tabularnewline
57 & 2525.93 & 2347.30833333333 & 178.621666666666 \tabularnewline
58 & 2475.14 & 2593.49833333333 & -118.358333333334 \tabularnewline
59 & 2529.66 & 2579.64083333333 & -49.9808333333335 \tabularnewline
60 & 2453.37 & 2676.77375 & -223.403749999999 \tabularnewline
61 & 2386.53 & 2495.90958333333 & -109.379583333333 \tabularnewline
62 & 2517.3 & 2400.22625 & 117.073750000000 \tabularnewline
63 & 2457.46 & 2448.4925 & 8.96750000000065 \tabularnewline
64 & 2589.73 & 2154.43833333333 & 435.291666666667 \tabularnewline
65 & 2679.07 & 2551.19 & 127.879999999999 \tabularnewline
66 & 2506.13 & 2707.98416666667 & -201.854166666666 \tabularnewline
67 & 2592.31 & 2604.27291666667 & -11.9629166666668 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116854&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]3839.25[/C][C]3450.75455176768[/C][C]388.495448232321[/C][/ROW]
[ROW][C]14[/C][C]3912.28[/C][C]3852.94625[/C][C]59.3337499999998[/C][/ROW]
[ROW][C]15[/C][C]3911.06[/C][C]3843.4725[/C][C]67.5875000000001[/C][/ROW]
[ROW][C]16[/C][C]3675.8[/C][C]3608.03833333333[/C][C]67.7616666666668[/C][/ROW]
[ROW][C]17[/C][C]3703.32[/C][C]3637.26[/C][C]66.059999999999[/C][/ROW]
[ROW][C]18[/C][C]3795.91[/C][C]3732.23416666667[/C][C]63.6758333333341[/C][/ROW]
[ROW][C]19[/C][C]3906.01[/C][C]3894.05291666667[/C][C]11.9570833333337[/C][/ROW]
[ROW][C]20[/C][C]4070.78[/C][C]3947.525[/C][C]123.255000000001[/C][/ROW]
[ROW][C]21[/C][C]4144.38[/C][C]3937.15833333333[/C][C]207.221666666666[/C][/ROW]
[ROW][C]22[/C][C]4140.3[/C][C]4211.94833333333[/C][C]-71.6483333333335[/C][/ROW]
[ROW][C]23[/C][C]4388.53[/C][C]4244.80083333333[/C][C]143.729166666666[/C][/ROW]
[ROW][C]24[/C][C]4433.57[/C][C]4535.64375[/C][C]-102.073750000000[/C][/ROW]
[ROW][C]25[/C][C]4305.23[/C][C]4476.10958333333[/C][C]-170.879583333333[/C][/ROW]
[ROW][C]26[/C][C]4471.65[/C][C]4318.92625[/C][C]152.72375[/C][/ROW]
[ROW][C]27[/C][C]4614.76[/C][C]4402.8425[/C][C]211.917500000001[/C][/ROW]
[ROW][C]28[/C][C]4697.86[/C][C]4311.73833333333[/C][C]386.121666666666[/C][/ROW]
[ROW][C]29[/C][C]4639.4[/C][C]4659.32[/C][C]-19.920000000001[/C][/ROW]
[ROW][C]30[/C][C]4384.47[/C][C]4668.31416666667[/C][C]-283.844166666665[/C][/ROW]
[ROW][C]31[/C][C]4350.83[/C][C]4482.61291666667[/C][C]-131.782916666667[/C][/ROW]
[ROW][C]32[/C][C]4325.29[/C][C]4392.345[/C][C]-67.0549999999994[/C][/ROW]
[ROW][C]33[/C][C]4441.82[/C][C]4191.66833333333[/C][C]250.151666666666[/C][/ROW]
[ROW][C]34[/C][C]4162.5[/C][C]4509.38833333333[/C][C]-346.888333333333[/C][/ROW]
[ROW][C]35[/C][C]4127.47[/C][C]4267.00083333333[/C][C]-139.530833333333[/C][/ROW]
[ROW][C]36[/C][C]3722.23[/C][C]4274.58375[/C][C]-552.35375[/C][/ROW]
[ROW][C]37[/C][C]3757.12[/C][C]3764.76958333333[/C][C]-7.6495833333338[/C][/ROW]
[ROW][C]38[/C][C]3719.52[/C][C]3770.81625[/C][C]-51.2962500000003[/C][/ROW]
[ROW][C]39[/C][C]3925.43[/C][C]3650.7125[/C][C]274.717500000001[/C][/ROW]
[ROW][C]40[/C][C]3751.41[/C][C]3622.40833333333[/C][C]129.001666666667[/C][/ROW]
[ROW][C]41[/C][C]3168.22[/C][C]3712.87[/C][C]-544.650000000001[/C][/ROW]
[ROW][C]42[/C][C]2994.38[/C][C]3197.13416666667[/C][C]-202.754166666665[/C][/ROW]
[ROW][C]43[/C][C]3136[/C][C]3092.52291666667[/C][C]43.4770833333332[/C][/ROW]
[ROW][C]44[/C][C]2672.2[/C][C]3177.515[/C][C]-505.315[/C][/ROW]
[ROW][C]45[/C][C]2100.18[/C][C]2538.57833333333[/C][C]-438.398333333334[/C][/ROW]
[ROW][C]46[/C][C]1881.46[/C][C]2167.74833333333[/C][C]-286.288333333333[/C][/ROW]
[ROW][C]47[/C][C]1908.64[/C][C]1985.96083333333[/C][C]-77.3208333333334[/C][/ROW]
[ROW][C]48[/C][C]1900.09[/C][C]2055.75375[/C][C]-155.66375[/C][/ROW]
[ROW][C]49[/C][C]1696.58[/C][C]1942.62958333333[/C][C]-246.049583333333[/C][/ROW]
[ROW][C]50[/C][C]1748.74[/C][C]1710.27625[/C][C]38.4637499999997[/C][/ROW]
[ROW][C]51[/C][C]1953.35[/C][C]1679.9325[/C][C]273.417500000000[/C][/ROW]
[ROW][C]52[/C][C]2071.37[/C][C]1650.32833333333[/C][C]421.041666666667[/C][/ROW]
[ROW][C]53[/C][C]2030.98[/C][C]2032.83[/C][C]-1.85000000000082[/C][/ROW]
[ROW][C]54[/C][C]2169.14[/C][C]2059.89416666667[/C][C]109.245833333334[/C][/ROW]
[ROW][C]55[/C][C]2229.85[/C][C]2267.28291666667[/C][C]-37.4329166666666[/C][/ROW]
[ROW][C]56[/C][C]2480.93[/C][C]2271.365[/C][C]209.565000000001[/C][/ROW]
[ROW][C]57[/C][C]2525.93[/C][C]2347.30833333333[/C][C]178.621666666666[/C][/ROW]
[ROW][C]58[/C][C]2475.14[/C][C]2593.49833333333[/C][C]-118.358333333334[/C][/ROW]
[ROW][C]59[/C][C]2529.66[/C][C]2579.64083333333[/C][C]-49.9808333333335[/C][/ROW]
[ROW][C]60[/C][C]2453.37[/C][C]2676.77375[/C][C]-223.403749999999[/C][/ROW]
[ROW][C]61[/C][C]2386.53[/C][C]2495.90958333333[/C][C]-109.379583333333[/C][/ROW]
[ROW][C]62[/C][C]2517.3[/C][C]2400.22625[/C][C]117.073750000000[/C][/ROW]
[ROW][C]63[/C][C]2457.46[/C][C]2448.4925[/C][C]8.96750000000065[/C][/ROW]
[ROW][C]64[/C][C]2589.73[/C][C]2154.43833333333[/C][C]435.291666666667[/C][/ROW]
[ROW][C]65[/C][C]2679.07[/C][C]2551.19[/C][C]127.879999999999[/C][/ROW]
[ROW][C]66[/C][C]2506.13[/C][C]2707.98416666667[/C][C]-201.854166666666[/C][/ROW]
[ROW][C]67[/C][C]2592.31[/C][C]2604.27291666667[/C][C]-11.9629166666668[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116854&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116854&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
133839.253450.75455176768388.495448232321
143912.283852.9462559.3337499999998
153911.063843.472567.5875000000001
163675.83608.0383333333367.7616666666668
173703.323637.2666.059999999999
183795.913732.2341666666763.6758333333341
193906.013894.0529166666711.9570833333337
204070.783947.525123.255000000001
214144.383937.15833333333207.221666666666
224140.34211.94833333333-71.6483333333335
234388.534244.80083333333143.729166666666
244433.574535.64375-102.073750000000
254305.234476.10958333333-170.879583333333
264471.654318.92625152.72375
274614.764402.8425211.917500000001
284697.864311.73833333333386.121666666666
294639.44659.32-19.920000000001
304384.474668.31416666667-283.844166666665
314350.834482.61291666667-131.782916666667
324325.294392.345-67.0549999999994
334441.824191.66833333333250.151666666666
344162.54509.38833333333-346.888333333333
354127.474267.00083333333-139.530833333333
363722.234274.58375-552.35375
373757.123764.76958333333-7.6495833333338
383719.523770.81625-51.2962500000003
393925.433650.7125274.717500000001
403751.413622.40833333333129.001666666667
413168.223712.87-544.650000000001
422994.383197.13416666667-202.754166666665
4331363092.5229166666743.4770833333332
442672.23177.515-505.315
452100.182538.57833333333-438.398333333334
461881.462167.74833333333-286.288333333333
471908.641985.96083333333-77.3208333333334
481900.092055.75375-155.66375
491696.581942.62958333333-246.049583333333
501748.741710.2762538.4637499999997
511953.351679.9325273.417500000000
522071.371650.32833333333421.041666666667
532030.982032.83-1.85000000000082
542169.142059.89416666667109.245833333334
552229.852267.28291666667-37.4329166666666
562480.932271.365209.565000000001
572525.932347.30833333333178.621666666666
582475.142593.49833333333-118.358333333334
592529.662579.64083333333-49.9808333333335
602453.372676.77375-223.403749999999
612386.532495.90958333333-109.379583333333
622517.32400.22625117.073750000000
632457.462448.49258.96750000000065
642589.732154.43833333333435.291666666667
652679.072551.19127.879999999999
662506.132707.98416666667-201.854166666666
672592.312604.27291666667-11.9629166666668







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
682633.8252183.294926640183084.35507335982
692500.203333333331863.057593330933137.34907333573
702567.771666666671787.430689269733348.11264406361
712672.27251771.212353280363573.33264671964
722819.386251811.970380059483826.80211994052
732861.925833333331758.357039823113965.49462684356
742875.622083333331683.631551067574067.6126155991
752806.814583333331532.523103328534081.10606333813
762503.792916666671152.202696587213855.38313674612
772465.252916666671040.551730446893889.95410288644
782494.16708333333999.9278732275223988.40629343914
792592.311031.628045206124152.99195479388

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
68 & 2633.825 & 2183.29492664018 & 3084.35507335982 \tabularnewline
69 & 2500.20333333333 & 1863.05759333093 & 3137.34907333573 \tabularnewline
70 & 2567.77166666667 & 1787.43068926973 & 3348.11264406361 \tabularnewline
71 & 2672.2725 & 1771.21235328036 & 3573.33264671964 \tabularnewline
72 & 2819.38625 & 1811.97038005948 & 3826.80211994052 \tabularnewline
73 & 2861.92583333333 & 1758.35703982311 & 3965.49462684356 \tabularnewline
74 & 2875.62208333333 & 1683.63155106757 & 4067.6126155991 \tabularnewline
75 & 2806.81458333333 & 1532.52310332853 & 4081.10606333813 \tabularnewline
76 & 2503.79291666667 & 1152.20269658721 & 3855.38313674612 \tabularnewline
77 & 2465.25291666667 & 1040.55173044689 & 3889.95410288644 \tabularnewline
78 & 2494.16708333333 & 999.927873227522 & 3988.40629343914 \tabularnewline
79 & 2592.31 & 1031.62804520612 & 4152.99195479388 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116854&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]68[/C][C]2633.825[/C][C]2183.29492664018[/C][C]3084.35507335982[/C][/ROW]
[ROW][C]69[/C][C]2500.20333333333[/C][C]1863.05759333093[/C][C]3137.34907333573[/C][/ROW]
[ROW][C]70[/C][C]2567.77166666667[/C][C]1787.43068926973[/C][C]3348.11264406361[/C][/ROW]
[ROW][C]71[/C][C]2672.2725[/C][C]1771.21235328036[/C][C]3573.33264671964[/C][/ROW]
[ROW][C]72[/C][C]2819.38625[/C][C]1811.97038005948[/C][C]3826.80211994052[/C][/ROW]
[ROW][C]73[/C][C]2861.92583333333[/C][C]1758.35703982311[/C][C]3965.49462684356[/C][/ROW]
[ROW][C]74[/C][C]2875.62208333333[/C][C]1683.63155106757[/C][C]4067.6126155991[/C][/ROW]
[ROW][C]75[/C][C]2806.81458333333[/C][C]1532.52310332853[/C][C]4081.10606333813[/C][/ROW]
[ROW][C]76[/C][C]2503.79291666667[/C][C]1152.20269658721[/C][C]3855.38313674612[/C][/ROW]
[ROW][C]77[/C][C]2465.25291666667[/C][C]1040.55173044689[/C][C]3889.95410288644[/C][/ROW]
[ROW][C]78[/C][C]2494.16708333333[/C][C]999.927873227522[/C][C]3988.40629343914[/C][/ROW]
[ROW][C]79[/C][C]2592.31[/C][C]1031.62804520612[/C][C]4152.99195479388[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116854&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116854&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
682633.8252183.294926640183084.35507335982
692500.203333333331863.057593330933137.34907333573
702567.771666666671787.430689269733348.11264406361
712672.27251771.212353280363573.33264671964
722819.386251811.970380059483826.80211994052
732861.925833333331758.357039823113965.49462684356
742875.622083333331683.631551067574067.6126155991
752806.814583333331532.523103328534081.10606333813
762503.792916666671152.202696587213855.38313674612
772465.252916666671040.551730446893889.95410288644
782494.16708333333999.9278732275223988.40629343914
792592.311031.628045206124152.99195479388



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