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of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 13 Dec 2014 13:28:12 +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/2014/Dec/13/t14184773225d9n2fdq98dxc19.htm/, Retrieved Sat, 11 May 2024 16:30:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=267079, Retrieved Sat, 11 May 2024 16:30:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact105
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [] [2013-11-04 07:28:31] [0307e7a6407eb638caabc417e3a6b260]
- RM    [Multiple Regression] [] [2014-11-13 17:16:10] [d69b52d23ca73e15a0c741afa583703c]
-  MPD    [Multiple Regression] [huwelijken vs con...] [2014-12-13 10:56:41] [189b7d469e4e3b4e868a6af83e3b3816]
- RMPD        [Exponential Smoothing] [] [2014-12-13 13:28:12] [0ce3062f3159e08d115eba7e96d082ef] [Current]
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Dataseries X:
2132.00
1964.00
2209.00
1965.00
2631.00
2583.00
2714.00
2248.00
2364.00
3042.00
2316.00
2735.00
2493.00
2136.00
2467.00
2414.00
2556.00
2768.00
2998.00
2573.00
3005.00
3469.00
2540.00
3187.00
2689.00
2154.00
3065.00
2397.00
2787.00
3579.00
2915.00
3025.00
3245.00
3328.00
2840.00
3342.00
2261.00
2590.00
2624.00
1860.00
2577.00
2646.00
2639.00
2807.00
2350.00
3053.00
2203.00
2471.00
1967.00
2473.00
2397.00
1904.00
2732.00
2297.00
2734.00
2719.00
2296.00
3243.00
2166.00
2261.00
2408.00
2536.00
2324.00
2178.00
2803.00
2604.00
2782.00
2656.00
2801.00
3122.00
2393.00
2233.00
2451.00
2596.00
2467.00
2210.00
2948.00
2507.00
3019.00
2401.00
2818.00
3305.00
2101.00
2582.00
2407.00
2416.00
2463.00
2228.00
2616.00
2934.00
2668.00
2808.00
2664.00
3112.00
2321.00
2718.00
2297.00
2534.00
2647.00
2064.00
2642.00
2702.00
2348.00
2734.00
2709.00
3206.00
2214.00
2531.00
2119.00
2369.00
2682.00
1840.00
2622.00
2570.00
2447.00
2871.00
2485.00
2957.00
2102.00
2250.00
2051.00
2260.00
2327.00
1781.00
2631.00
2180.00
2150.00
2837.00
1976.00
2836.00
2203.00
1770.00




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' @ 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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267079&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' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267079&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267079&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' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.169446384646568
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.169446384646568 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267079&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]0.169446384646568[/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=267079&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267079&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
alpha0.169446384646568
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
219642132-168
322092103.53300737938105.466992620623
419652121.40400797849-156.404007978487
526312094.9019142823536.098085717701
625832185.74179672311397.25820327689
727142253.05576303957460.94423696043
822482331.16109751619-83.1610975161857
923642317.0697501988346.930249801173
1030422325.0219113582716.978088641804
1123162446.51125634936-130.511256349357
1227352424.39659580528310.603404194723
1324932477.0272197049915.9727802950106
1421362479.73374957873-343.733749578733
1524672421.4893084316145.5106915683928
1624142429.20093058064-15.2009305806364
1725562426.62518785048129.374812149516
1827682448.54728203355319.452717966452
1929982502.67739015848495.322609841517
2025732586.60801562983-13.6080156298308
2130052584.30218657914420.697813420858
2234692655.58791009202813.412089907977
2325402793.41764795474-253.417647954739
2431872750.47694370317436.523056296828
2526892824.44419740754-135.44419740754
2621542801.49366783548-647.493667835476
2730652691.77820673921373.221793260791
2823972755.01929027856-358.019290278558
2927872694.3542159071392.6457840928738
3035792710.05270907441868.94729092559
3129152857.2926859701857.7073140298189
3230252867.0709817002157.929018299802
3332452893.83148288188351.168517118119
3433282953.33571850924374.664281490757
3528403016.82122646406-176.821226464056
3633422986.85950891095355.140491089051
3722613047.0367811676-786.036781167596
3825902913.84569039952-323.845690399521
3926242858.97120897795-234.97120897795
4018602819.1561871206-959.156187120603
4125772656.63063890163-79.630638901629
4226462643.137515032652.86248496734834
4326392643.62255276147-4.6225527614738
4428072642.8392779082164.160722091796
4523502670.65571876763-320.655718767629
4630532616.32176650621436.678233493793
4722032690.31531442558-487.31531442558
4824712607.74149621326-136.74149621326
4919672584.57114404876-617.571144048761
5024732479.92594642765-6.92594642765289
5123972478.75236984523-81.7523698452314
5219042464.89972633867-560.899726338668
5327322369.85729556133362.142704438669
5422972431.22106755459-134.221067554594
5527342408.47779291407325.522207085935
5627192463.63635402695255.363645973052
5722962506.90680060725-210.906800607248
5832432471.16940574697771.830594253025
5921662601.95330950276-435.953309502762
6022612528.08259733281-267.082597332813
6124082482.82641681275-74.8264168127525
6225362470.1473510077765.8526489922256
6323242481.30584429891-157.305844298907
6421782454.65093769868-276.650937698681
6528032407.77343649656395.226563503444
6626042474.7431487985129.256851201498
6727822496.6452549254285.354745074605
6826562544.99758482003111.00241517997
6928012563.80654275931237.193457240687
7031222603.99811655057518.001883449432
7123932691.77166294119-298.771662941187
7222332641.14588482096-408.14588482096
7324512571.98704022967-120.987040229674
7425962551.4862236736744.5137763263333
7524672559.02892213913-92.0289221391295
7622102543.43495399973-333.434953999733
7729482486.93560652968461.064393470317
7825072565.06130109249-58.0613010924912
7930192555.22302353449463.776976465507
8024012633.80835547889-232.80835547889
8128182594.35982132748223.640178672521
8233052632.25484106525672.74515893475
8321012746.24907603522-645.249076035224
8425822636.91395290452-54.9139529045165
8524072627.60898211819-220.608982118194
8624162590.22758767771-174.227587677707
8724632560.70535284003-97.7053528400261
8822282544.14953404067-316.149534040666
8926162490.57913848978125.420861510222
9029342511.83125003194422.168749968057
9126682583.3662184247984.6337815752081
9228082597.70710673168210.292893268322
9326642633.3404772128630.6595227871385
9431122638.53562250413473.464377495869
9523212718.76244952974-397.762449529744
9627182651.3630405087766.6369594912344
9722972662.6544323784-365.654432378395
9825342600.69561078188-66.6956107818833
9926472589.394280663157.6057193369015
10020642599.1553615397-535.155361539701
10126422508.47522030257133.524779697428
10227022531.10051148303170.89948851697
10323482560.05881195018-212.058811950179
10427342524.12621293277209.873787067226
10527092559.6885673834149.311432616601
10632062584.98884982668621.011150173318
10722142690.21694404876-476.216944048757
10825312609.52370457226-78.5237045722579
10921192596.21814672343-477.218146723434
11023692515.35525707341-146.355257073412
11126822490.5558878883191.444112111697
11218402522.9954005475-682.995400547502
11326222407.26429919449214.735700805507
11425702443.65048735053126.349512649467
11524472465.05995547084-18.059955470841
11628712461.99976130943409.000238690571
11724852531.30337307513-46.3033730751299
11829572523.45743391061433.542566089392
11921022596.91965432485-494.919654324851
12022502513.05730820898-263.057308208976
12120512468.48319837811-417.483198378107
12222602397.74217976225-137.742179762251
12323272374.4022653882-47.4022653881993
12417812366.37012289411-585.370122894112
12526312267.18127188959363.818728110413
12621802328.82904003461-148.829040034609
12721502303.61049727033-153.610497270325
12828372277.58175386411559.418246135893
12919762372.37315317716-396.373153177158
13028362305.20915540033530.790844599672
13122032395.14974502124-192.149745021241
13217702362.59066541663-592.590665416632

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 1964 & 2132 & -168 \tabularnewline
3 & 2209 & 2103.53300737938 & 105.466992620623 \tabularnewline
4 & 1965 & 2121.40400797849 & -156.404007978487 \tabularnewline
5 & 2631 & 2094.9019142823 & 536.098085717701 \tabularnewline
6 & 2583 & 2185.74179672311 & 397.25820327689 \tabularnewline
7 & 2714 & 2253.05576303957 & 460.94423696043 \tabularnewline
8 & 2248 & 2331.16109751619 & -83.1610975161857 \tabularnewline
9 & 2364 & 2317.06975019883 & 46.930249801173 \tabularnewline
10 & 3042 & 2325.0219113582 & 716.978088641804 \tabularnewline
11 & 2316 & 2446.51125634936 & -130.511256349357 \tabularnewline
12 & 2735 & 2424.39659580528 & 310.603404194723 \tabularnewline
13 & 2493 & 2477.02721970499 & 15.9727802950106 \tabularnewline
14 & 2136 & 2479.73374957873 & -343.733749578733 \tabularnewline
15 & 2467 & 2421.48930843161 & 45.5106915683928 \tabularnewline
16 & 2414 & 2429.20093058064 & -15.2009305806364 \tabularnewline
17 & 2556 & 2426.62518785048 & 129.374812149516 \tabularnewline
18 & 2768 & 2448.54728203355 & 319.452717966452 \tabularnewline
19 & 2998 & 2502.67739015848 & 495.322609841517 \tabularnewline
20 & 2573 & 2586.60801562983 & -13.6080156298308 \tabularnewline
21 & 3005 & 2584.30218657914 & 420.697813420858 \tabularnewline
22 & 3469 & 2655.58791009202 & 813.412089907977 \tabularnewline
23 & 2540 & 2793.41764795474 & -253.417647954739 \tabularnewline
24 & 3187 & 2750.47694370317 & 436.523056296828 \tabularnewline
25 & 2689 & 2824.44419740754 & -135.44419740754 \tabularnewline
26 & 2154 & 2801.49366783548 & -647.493667835476 \tabularnewline
27 & 3065 & 2691.77820673921 & 373.221793260791 \tabularnewline
28 & 2397 & 2755.01929027856 & -358.019290278558 \tabularnewline
29 & 2787 & 2694.35421590713 & 92.6457840928738 \tabularnewline
30 & 3579 & 2710.05270907441 & 868.94729092559 \tabularnewline
31 & 2915 & 2857.29268597018 & 57.7073140298189 \tabularnewline
32 & 3025 & 2867.0709817002 & 157.929018299802 \tabularnewline
33 & 3245 & 2893.83148288188 & 351.168517118119 \tabularnewline
34 & 3328 & 2953.33571850924 & 374.664281490757 \tabularnewline
35 & 2840 & 3016.82122646406 & -176.821226464056 \tabularnewline
36 & 3342 & 2986.85950891095 & 355.140491089051 \tabularnewline
37 & 2261 & 3047.0367811676 & -786.036781167596 \tabularnewline
38 & 2590 & 2913.84569039952 & -323.845690399521 \tabularnewline
39 & 2624 & 2858.97120897795 & -234.97120897795 \tabularnewline
40 & 1860 & 2819.1561871206 & -959.156187120603 \tabularnewline
41 & 2577 & 2656.63063890163 & -79.630638901629 \tabularnewline
42 & 2646 & 2643.13751503265 & 2.86248496734834 \tabularnewline
43 & 2639 & 2643.62255276147 & -4.6225527614738 \tabularnewline
44 & 2807 & 2642.8392779082 & 164.160722091796 \tabularnewline
45 & 2350 & 2670.65571876763 & -320.655718767629 \tabularnewline
46 & 3053 & 2616.32176650621 & 436.678233493793 \tabularnewline
47 & 2203 & 2690.31531442558 & -487.31531442558 \tabularnewline
48 & 2471 & 2607.74149621326 & -136.74149621326 \tabularnewline
49 & 1967 & 2584.57114404876 & -617.571144048761 \tabularnewline
50 & 2473 & 2479.92594642765 & -6.92594642765289 \tabularnewline
51 & 2397 & 2478.75236984523 & -81.7523698452314 \tabularnewline
52 & 1904 & 2464.89972633867 & -560.899726338668 \tabularnewline
53 & 2732 & 2369.85729556133 & 362.142704438669 \tabularnewline
54 & 2297 & 2431.22106755459 & -134.221067554594 \tabularnewline
55 & 2734 & 2408.47779291407 & 325.522207085935 \tabularnewline
56 & 2719 & 2463.63635402695 & 255.363645973052 \tabularnewline
57 & 2296 & 2506.90680060725 & -210.906800607248 \tabularnewline
58 & 3243 & 2471.16940574697 & 771.830594253025 \tabularnewline
59 & 2166 & 2601.95330950276 & -435.953309502762 \tabularnewline
60 & 2261 & 2528.08259733281 & -267.082597332813 \tabularnewline
61 & 2408 & 2482.82641681275 & -74.8264168127525 \tabularnewline
62 & 2536 & 2470.14735100777 & 65.8526489922256 \tabularnewline
63 & 2324 & 2481.30584429891 & -157.305844298907 \tabularnewline
64 & 2178 & 2454.65093769868 & -276.650937698681 \tabularnewline
65 & 2803 & 2407.77343649656 & 395.226563503444 \tabularnewline
66 & 2604 & 2474.7431487985 & 129.256851201498 \tabularnewline
67 & 2782 & 2496.6452549254 & 285.354745074605 \tabularnewline
68 & 2656 & 2544.99758482003 & 111.00241517997 \tabularnewline
69 & 2801 & 2563.80654275931 & 237.193457240687 \tabularnewline
70 & 3122 & 2603.99811655057 & 518.001883449432 \tabularnewline
71 & 2393 & 2691.77166294119 & -298.771662941187 \tabularnewline
72 & 2233 & 2641.14588482096 & -408.14588482096 \tabularnewline
73 & 2451 & 2571.98704022967 & -120.987040229674 \tabularnewline
74 & 2596 & 2551.48622367367 & 44.5137763263333 \tabularnewline
75 & 2467 & 2559.02892213913 & -92.0289221391295 \tabularnewline
76 & 2210 & 2543.43495399973 & -333.434953999733 \tabularnewline
77 & 2948 & 2486.93560652968 & 461.064393470317 \tabularnewline
78 & 2507 & 2565.06130109249 & -58.0613010924912 \tabularnewline
79 & 3019 & 2555.22302353449 & 463.776976465507 \tabularnewline
80 & 2401 & 2633.80835547889 & -232.80835547889 \tabularnewline
81 & 2818 & 2594.35982132748 & 223.640178672521 \tabularnewline
82 & 3305 & 2632.25484106525 & 672.74515893475 \tabularnewline
83 & 2101 & 2746.24907603522 & -645.249076035224 \tabularnewline
84 & 2582 & 2636.91395290452 & -54.9139529045165 \tabularnewline
85 & 2407 & 2627.60898211819 & -220.608982118194 \tabularnewline
86 & 2416 & 2590.22758767771 & -174.227587677707 \tabularnewline
87 & 2463 & 2560.70535284003 & -97.7053528400261 \tabularnewline
88 & 2228 & 2544.14953404067 & -316.149534040666 \tabularnewline
89 & 2616 & 2490.57913848978 & 125.420861510222 \tabularnewline
90 & 2934 & 2511.83125003194 & 422.168749968057 \tabularnewline
91 & 2668 & 2583.36621842479 & 84.6337815752081 \tabularnewline
92 & 2808 & 2597.70710673168 & 210.292893268322 \tabularnewline
93 & 2664 & 2633.34047721286 & 30.6595227871385 \tabularnewline
94 & 3112 & 2638.53562250413 & 473.464377495869 \tabularnewline
95 & 2321 & 2718.76244952974 & -397.762449529744 \tabularnewline
96 & 2718 & 2651.36304050877 & 66.6369594912344 \tabularnewline
97 & 2297 & 2662.6544323784 & -365.654432378395 \tabularnewline
98 & 2534 & 2600.69561078188 & -66.6956107818833 \tabularnewline
99 & 2647 & 2589.3942806631 & 57.6057193369015 \tabularnewline
100 & 2064 & 2599.1553615397 & -535.155361539701 \tabularnewline
101 & 2642 & 2508.47522030257 & 133.524779697428 \tabularnewline
102 & 2702 & 2531.10051148303 & 170.89948851697 \tabularnewline
103 & 2348 & 2560.05881195018 & -212.058811950179 \tabularnewline
104 & 2734 & 2524.12621293277 & 209.873787067226 \tabularnewline
105 & 2709 & 2559.6885673834 & 149.311432616601 \tabularnewline
106 & 3206 & 2584.98884982668 & 621.011150173318 \tabularnewline
107 & 2214 & 2690.21694404876 & -476.216944048757 \tabularnewline
108 & 2531 & 2609.52370457226 & -78.5237045722579 \tabularnewline
109 & 2119 & 2596.21814672343 & -477.218146723434 \tabularnewline
110 & 2369 & 2515.35525707341 & -146.355257073412 \tabularnewline
111 & 2682 & 2490.5558878883 & 191.444112111697 \tabularnewline
112 & 1840 & 2522.9954005475 & -682.995400547502 \tabularnewline
113 & 2622 & 2407.26429919449 & 214.735700805507 \tabularnewline
114 & 2570 & 2443.65048735053 & 126.349512649467 \tabularnewline
115 & 2447 & 2465.05995547084 & -18.059955470841 \tabularnewline
116 & 2871 & 2461.99976130943 & 409.000238690571 \tabularnewline
117 & 2485 & 2531.30337307513 & -46.3033730751299 \tabularnewline
118 & 2957 & 2523.45743391061 & 433.542566089392 \tabularnewline
119 & 2102 & 2596.91965432485 & -494.919654324851 \tabularnewline
120 & 2250 & 2513.05730820898 & -263.057308208976 \tabularnewline
121 & 2051 & 2468.48319837811 & -417.483198378107 \tabularnewline
122 & 2260 & 2397.74217976225 & -137.742179762251 \tabularnewline
123 & 2327 & 2374.4022653882 & -47.4022653881993 \tabularnewline
124 & 1781 & 2366.37012289411 & -585.370122894112 \tabularnewline
125 & 2631 & 2267.18127188959 & 363.818728110413 \tabularnewline
126 & 2180 & 2328.82904003461 & -148.829040034609 \tabularnewline
127 & 2150 & 2303.61049727033 & -153.610497270325 \tabularnewline
128 & 2837 & 2277.58175386411 & 559.418246135893 \tabularnewline
129 & 1976 & 2372.37315317716 & -396.373153177158 \tabularnewline
130 & 2836 & 2305.20915540033 & 530.790844599672 \tabularnewline
131 & 2203 & 2395.14974502124 & -192.149745021241 \tabularnewline
132 & 1770 & 2362.59066541663 & -592.590665416632 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267079&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]1964[/C][C]2132[/C][C]-168[/C][/ROW]
[ROW][C]3[/C][C]2209[/C][C]2103.53300737938[/C][C]105.466992620623[/C][/ROW]
[ROW][C]4[/C][C]1965[/C][C]2121.40400797849[/C][C]-156.404007978487[/C][/ROW]
[ROW][C]5[/C][C]2631[/C][C]2094.9019142823[/C][C]536.098085717701[/C][/ROW]
[ROW][C]6[/C][C]2583[/C][C]2185.74179672311[/C][C]397.25820327689[/C][/ROW]
[ROW][C]7[/C][C]2714[/C][C]2253.05576303957[/C][C]460.94423696043[/C][/ROW]
[ROW][C]8[/C][C]2248[/C][C]2331.16109751619[/C][C]-83.1610975161857[/C][/ROW]
[ROW][C]9[/C][C]2364[/C][C]2317.06975019883[/C][C]46.930249801173[/C][/ROW]
[ROW][C]10[/C][C]3042[/C][C]2325.0219113582[/C][C]716.978088641804[/C][/ROW]
[ROW][C]11[/C][C]2316[/C][C]2446.51125634936[/C][C]-130.511256349357[/C][/ROW]
[ROW][C]12[/C][C]2735[/C][C]2424.39659580528[/C][C]310.603404194723[/C][/ROW]
[ROW][C]13[/C][C]2493[/C][C]2477.02721970499[/C][C]15.9727802950106[/C][/ROW]
[ROW][C]14[/C][C]2136[/C][C]2479.73374957873[/C][C]-343.733749578733[/C][/ROW]
[ROW][C]15[/C][C]2467[/C][C]2421.48930843161[/C][C]45.5106915683928[/C][/ROW]
[ROW][C]16[/C][C]2414[/C][C]2429.20093058064[/C][C]-15.2009305806364[/C][/ROW]
[ROW][C]17[/C][C]2556[/C][C]2426.62518785048[/C][C]129.374812149516[/C][/ROW]
[ROW][C]18[/C][C]2768[/C][C]2448.54728203355[/C][C]319.452717966452[/C][/ROW]
[ROW][C]19[/C][C]2998[/C][C]2502.67739015848[/C][C]495.322609841517[/C][/ROW]
[ROW][C]20[/C][C]2573[/C][C]2586.60801562983[/C][C]-13.6080156298308[/C][/ROW]
[ROW][C]21[/C][C]3005[/C][C]2584.30218657914[/C][C]420.697813420858[/C][/ROW]
[ROW][C]22[/C][C]3469[/C][C]2655.58791009202[/C][C]813.412089907977[/C][/ROW]
[ROW][C]23[/C][C]2540[/C][C]2793.41764795474[/C][C]-253.417647954739[/C][/ROW]
[ROW][C]24[/C][C]3187[/C][C]2750.47694370317[/C][C]436.523056296828[/C][/ROW]
[ROW][C]25[/C][C]2689[/C][C]2824.44419740754[/C][C]-135.44419740754[/C][/ROW]
[ROW][C]26[/C][C]2154[/C][C]2801.49366783548[/C][C]-647.493667835476[/C][/ROW]
[ROW][C]27[/C][C]3065[/C][C]2691.77820673921[/C][C]373.221793260791[/C][/ROW]
[ROW][C]28[/C][C]2397[/C][C]2755.01929027856[/C][C]-358.019290278558[/C][/ROW]
[ROW][C]29[/C][C]2787[/C][C]2694.35421590713[/C][C]92.6457840928738[/C][/ROW]
[ROW][C]30[/C][C]3579[/C][C]2710.05270907441[/C][C]868.94729092559[/C][/ROW]
[ROW][C]31[/C][C]2915[/C][C]2857.29268597018[/C][C]57.7073140298189[/C][/ROW]
[ROW][C]32[/C][C]3025[/C][C]2867.0709817002[/C][C]157.929018299802[/C][/ROW]
[ROW][C]33[/C][C]3245[/C][C]2893.83148288188[/C][C]351.168517118119[/C][/ROW]
[ROW][C]34[/C][C]3328[/C][C]2953.33571850924[/C][C]374.664281490757[/C][/ROW]
[ROW][C]35[/C][C]2840[/C][C]3016.82122646406[/C][C]-176.821226464056[/C][/ROW]
[ROW][C]36[/C][C]3342[/C][C]2986.85950891095[/C][C]355.140491089051[/C][/ROW]
[ROW][C]37[/C][C]2261[/C][C]3047.0367811676[/C][C]-786.036781167596[/C][/ROW]
[ROW][C]38[/C][C]2590[/C][C]2913.84569039952[/C][C]-323.845690399521[/C][/ROW]
[ROW][C]39[/C][C]2624[/C][C]2858.97120897795[/C][C]-234.97120897795[/C][/ROW]
[ROW][C]40[/C][C]1860[/C][C]2819.1561871206[/C][C]-959.156187120603[/C][/ROW]
[ROW][C]41[/C][C]2577[/C][C]2656.63063890163[/C][C]-79.630638901629[/C][/ROW]
[ROW][C]42[/C][C]2646[/C][C]2643.13751503265[/C][C]2.86248496734834[/C][/ROW]
[ROW][C]43[/C][C]2639[/C][C]2643.62255276147[/C][C]-4.6225527614738[/C][/ROW]
[ROW][C]44[/C][C]2807[/C][C]2642.8392779082[/C][C]164.160722091796[/C][/ROW]
[ROW][C]45[/C][C]2350[/C][C]2670.65571876763[/C][C]-320.655718767629[/C][/ROW]
[ROW][C]46[/C][C]3053[/C][C]2616.32176650621[/C][C]436.678233493793[/C][/ROW]
[ROW][C]47[/C][C]2203[/C][C]2690.31531442558[/C][C]-487.31531442558[/C][/ROW]
[ROW][C]48[/C][C]2471[/C][C]2607.74149621326[/C][C]-136.74149621326[/C][/ROW]
[ROW][C]49[/C][C]1967[/C][C]2584.57114404876[/C][C]-617.571144048761[/C][/ROW]
[ROW][C]50[/C][C]2473[/C][C]2479.92594642765[/C][C]-6.92594642765289[/C][/ROW]
[ROW][C]51[/C][C]2397[/C][C]2478.75236984523[/C][C]-81.7523698452314[/C][/ROW]
[ROW][C]52[/C][C]1904[/C][C]2464.89972633867[/C][C]-560.899726338668[/C][/ROW]
[ROW][C]53[/C][C]2732[/C][C]2369.85729556133[/C][C]362.142704438669[/C][/ROW]
[ROW][C]54[/C][C]2297[/C][C]2431.22106755459[/C][C]-134.221067554594[/C][/ROW]
[ROW][C]55[/C][C]2734[/C][C]2408.47779291407[/C][C]325.522207085935[/C][/ROW]
[ROW][C]56[/C][C]2719[/C][C]2463.63635402695[/C][C]255.363645973052[/C][/ROW]
[ROW][C]57[/C][C]2296[/C][C]2506.90680060725[/C][C]-210.906800607248[/C][/ROW]
[ROW][C]58[/C][C]3243[/C][C]2471.16940574697[/C][C]771.830594253025[/C][/ROW]
[ROW][C]59[/C][C]2166[/C][C]2601.95330950276[/C][C]-435.953309502762[/C][/ROW]
[ROW][C]60[/C][C]2261[/C][C]2528.08259733281[/C][C]-267.082597332813[/C][/ROW]
[ROW][C]61[/C][C]2408[/C][C]2482.82641681275[/C][C]-74.8264168127525[/C][/ROW]
[ROW][C]62[/C][C]2536[/C][C]2470.14735100777[/C][C]65.8526489922256[/C][/ROW]
[ROW][C]63[/C][C]2324[/C][C]2481.30584429891[/C][C]-157.305844298907[/C][/ROW]
[ROW][C]64[/C][C]2178[/C][C]2454.65093769868[/C][C]-276.650937698681[/C][/ROW]
[ROW][C]65[/C][C]2803[/C][C]2407.77343649656[/C][C]395.226563503444[/C][/ROW]
[ROW][C]66[/C][C]2604[/C][C]2474.7431487985[/C][C]129.256851201498[/C][/ROW]
[ROW][C]67[/C][C]2782[/C][C]2496.6452549254[/C][C]285.354745074605[/C][/ROW]
[ROW][C]68[/C][C]2656[/C][C]2544.99758482003[/C][C]111.00241517997[/C][/ROW]
[ROW][C]69[/C][C]2801[/C][C]2563.80654275931[/C][C]237.193457240687[/C][/ROW]
[ROW][C]70[/C][C]3122[/C][C]2603.99811655057[/C][C]518.001883449432[/C][/ROW]
[ROW][C]71[/C][C]2393[/C][C]2691.77166294119[/C][C]-298.771662941187[/C][/ROW]
[ROW][C]72[/C][C]2233[/C][C]2641.14588482096[/C][C]-408.14588482096[/C][/ROW]
[ROW][C]73[/C][C]2451[/C][C]2571.98704022967[/C][C]-120.987040229674[/C][/ROW]
[ROW][C]74[/C][C]2596[/C][C]2551.48622367367[/C][C]44.5137763263333[/C][/ROW]
[ROW][C]75[/C][C]2467[/C][C]2559.02892213913[/C][C]-92.0289221391295[/C][/ROW]
[ROW][C]76[/C][C]2210[/C][C]2543.43495399973[/C][C]-333.434953999733[/C][/ROW]
[ROW][C]77[/C][C]2948[/C][C]2486.93560652968[/C][C]461.064393470317[/C][/ROW]
[ROW][C]78[/C][C]2507[/C][C]2565.06130109249[/C][C]-58.0613010924912[/C][/ROW]
[ROW][C]79[/C][C]3019[/C][C]2555.22302353449[/C][C]463.776976465507[/C][/ROW]
[ROW][C]80[/C][C]2401[/C][C]2633.80835547889[/C][C]-232.80835547889[/C][/ROW]
[ROW][C]81[/C][C]2818[/C][C]2594.35982132748[/C][C]223.640178672521[/C][/ROW]
[ROW][C]82[/C][C]3305[/C][C]2632.25484106525[/C][C]672.74515893475[/C][/ROW]
[ROW][C]83[/C][C]2101[/C][C]2746.24907603522[/C][C]-645.249076035224[/C][/ROW]
[ROW][C]84[/C][C]2582[/C][C]2636.91395290452[/C][C]-54.9139529045165[/C][/ROW]
[ROW][C]85[/C][C]2407[/C][C]2627.60898211819[/C][C]-220.608982118194[/C][/ROW]
[ROW][C]86[/C][C]2416[/C][C]2590.22758767771[/C][C]-174.227587677707[/C][/ROW]
[ROW][C]87[/C][C]2463[/C][C]2560.70535284003[/C][C]-97.7053528400261[/C][/ROW]
[ROW][C]88[/C][C]2228[/C][C]2544.14953404067[/C][C]-316.149534040666[/C][/ROW]
[ROW][C]89[/C][C]2616[/C][C]2490.57913848978[/C][C]125.420861510222[/C][/ROW]
[ROW][C]90[/C][C]2934[/C][C]2511.83125003194[/C][C]422.168749968057[/C][/ROW]
[ROW][C]91[/C][C]2668[/C][C]2583.36621842479[/C][C]84.6337815752081[/C][/ROW]
[ROW][C]92[/C][C]2808[/C][C]2597.70710673168[/C][C]210.292893268322[/C][/ROW]
[ROW][C]93[/C][C]2664[/C][C]2633.34047721286[/C][C]30.6595227871385[/C][/ROW]
[ROW][C]94[/C][C]3112[/C][C]2638.53562250413[/C][C]473.464377495869[/C][/ROW]
[ROW][C]95[/C][C]2321[/C][C]2718.76244952974[/C][C]-397.762449529744[/C][/ROW]
[ROW][C]96[/C][C]2718[/C][C]2651.36304050877[/C][C]66.6369594912344[/C][/ROW]
[ROW][C]97[/C][C]2297[/C][C]2662.6544323784[/C][C]-365.654432378395[/C][/ROW]
[ROW][C]98[/C][C]2534[/C][C]2600.69561078188[/C][C]-66.6956107818833[/C][/ROW]
[ROW][C]99[/C][C]2647[/C][C]2589.3942806631[/C][C]57.6057193369015[/C][/ROW]
[ROW][C]100[/C][C]2064[/C][C]2599.1553615397[/C][C]-535.155361539701[/C][/ROW]
[ROW][C]101[/C][C]2642[/C][C]2508.47522030257[/C][C]133.524779697428[/C][/ROW]
[ROW][C]102[/C][C]2702[/C][C]2531.10051148303[/C][C]170.89948851697[/C][/ROW]
[ROW][C]103[/C][C]2348[/C][C]2560.05881195018[/C][C]-212.058811950179[/C][/ROW]
[ROW][C]104[/C][C]2734[/C][C]2524.12621293277[/C][C]209.873787067226[/C][/ROW]
[ROW][C]105[/C][C]2709[/C][C]2559.6885673834[/C][C]149.311432616601[/C][/ROW]
[ROW][C]106[/C][C]3206[/C][C]2584.98884982668[/C][C]621.011150173318[/C][/ROW]
[ROW][C]107[/C][C]2214[/C][C]2690.21694404876[/C][C]-476.216944048757[/C][/ROW]
[ROW][C]108[/C][C]2531[/C][C]2609.52370457226[/C][C]-78.5237045722579[/C][/ROW]
[ROW][C]109[/C][C]2119[/C][C]2596.21814672343[/C][C]-477.218146723434[/C][/ROW]
[ROW][C]110[/C][C]2369[/C][C]2515.35525707341[/C][C]-146.355257073412[/C][/ROW]
[ROW][C]111[/C][C]2682[/C][C]2490.5558878883[/C][C]191.444112111697[/C][/ROW]
[ROW][C]112[/C][C]1840[/C][C]2522.9954005475[/C][C]-682.995400547502[/C][/ROW]
[ROW][C]113[/C][C]2622[/C][C]2407.26429919449[/C][C]214.735700805507[/C][/ROW]
[ROW][C]114[/C][C]2570[/C][C]2443.65048735053[/C][C]126.349512649467[/C][/ROW]
[ROW][C]115[/C][C]2447[/C][C]2465.05995547084[/C][C]-18.059955470841[/C][/ROW]
[ROW][C]116[/C][C]2871[/C][C]2461.99976130943[/C][C]409.000238690571[/C][/ROW]
[ROW][C]117[/C][C]2485[/C][C]2531.30337307513[/C][C]-46.3033730751299[/C][/ROW]
[ROW][C]118[/C][C]2957[/C][C]2523.45743391061[/C][C]433.542566089392[/C][/ROW]
[ROW][C]119[/C][C]2102[/C][C]2596.91965432485[/C][C]-494.919654324851[/C][/ROW]
[ROW][C]120[/C][C]2250[/C][C]2513.05730820898[/C][C]-263.057308208976[/C][/ROW]
[ROW][C]121[/C][C]2051[/C][C]2468.48319837811[/C][C]-417.483198378107[/C][/ROW]
[ROW][C]122[/C][C]2260[/C][C]2397.74217976225[/C][C]-137.742179762251[/C][/ROW]
[ROW][C]123[/C][C]2327[/C][C]2374.4022653882[/C][C]-47.4022653881993[/C][/ROW]
[ROW][C]124[/C][C]1781[/C][C]2366.37012289411[/C][C]-585.370122894112[/C][/ROW]
[ROW][C]125[/C][C]2631[/C][C]2267.18127188959[/C][C]363.818728110413[/C][/ROW]
[ROW][C]126[/C][C]2180[/C][C]2328.82904003461[/C][C]-148.829040034609[/C][/ROW]
[ROW][C]127[/C][C]2150[/C][C]2303.61049727033[/C][C]-153.610497270325[/C][/ROW]
[ROW][C]128[/C][C]2837[/C][C]2277.58175386411[/C][C]559.418246135893[/C][/ROW]
[ROW][C]129[/C][C]1976[/C][C]2372.37315317716[/C][C]-396.373153177158[/C][/ROW]
[ROW][C]130[/C][C]2836[/C][C]2305.20915540033[/C][C]530.790844599672[/C][/ROW]
[ROW][C]131[/C][C]2203[/C][C]2395.14974502124[/C][C]-192.149745021241[/C][/ROW]
[ROW][C]132[/C][C]1770[/C][C]2362.59066541663[/C][C]-592.590665416632[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267079&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267079&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
219642132-168
322092103.53300737938105.466992620623
419652121.40400797849-156.404007978487
526312094.9019142823536.098085717701
625832185.74179672311397.25820327689
727142253.05576303957460.94423696043
822482331.16109751619-83.1610975161857
923642317.0697501988346.930249801173
1030422325.0219113582716.978088641804
1123162446.51125634936-130.511256349357
1227352424.39659580528310.603404194723
1324932477.0272197049915.9727802950106
1421362479.73374957873-343.733749578733
1524672421.4893084316145.5106915683928
1624142429.20093058064-15.2009305806364
1725562426.62518785048129.374812149516
1827682448.54728203355319.452717966452
1929982502.67739015848495.322609841517
2025732586.60801562983-13.6080156298308
2130052584.30218657914420.697813420858
2234692655.58791009202813.412089907977
2325402793.41764795474-253.417647954739
2431872750.47694370317436.523056296828
2526892824.44419740754-135.44419740754
2621542801.49366783548-647.493667835476
2730652691.77820673921373.221793260791
2823972755.01929027856-358.019290278558
2927872694.3542159071392.6457840928738
3035792710.05270907441868.94729092559
3129152857.2926859701857.7073140298189
3230252867.0709817002157.929018299802
3332452893.83148288188351.168517118119
3433282953.33571850924374.664281490757
3528403016.82122646406-176.821226464056
3633422986.85950891095355.140491089051
3722613047.0367811676-786.036781167596
3825902913.84569039952-323.845690399521
3926242858.97120897795-234.97120897795
4018602819.1561871206-959.156187120603
4125772656.63063890163-79.630638901629
4226462643.137515032652.86248496734834
4326392643.62255276147-4.6225527614738
4428072642.8392779082164.160722091796
4523502670.65571876763-320.655718767629
4630532616.32176650621436.678233493793
4722032690.31531442558-487.31531442558
4824712607.74149621326-136.74149621326
4919672584.57114404876-617.571144048761
5024732479.92594642765-6.92594642765289
5123972478.75236984523-81.7523698452314
5219042464.89972633867-560.899726338668
5327322369.85729556133362.142704438669
5422972431.22106755459-134.221067554594
5527342408.47779291407325.522207085935
5627192463.63635402695255.363645973052
5722962506.90680060725-210.906800607248
5832432471.16940574697771.830594253025
5921662601.95330950276-435.953309502762
6022612528.08259733281-267.082597332813
6124082482.82641681275-74.8264168127525
6225362470.1473510077765.8526489922256
6323242481.30584429891-157.305844298907
6421782454.65093769868-276.650937698681
6528032407.77343649656395.226563503444
6626042474.7431487985129.256851201498
6727822496.6452549254285.354745074605
6826562544.99758482003111.00241517997
6928012563.80654275931237.193457240687
7031222603.99811655057518.001883449432
7123932691.77166294119-298.771662941187
7222332641.14588482096-408.14588482096
7324512571.98704022967-120.987040229674
7425962551.4862236736744.5137763263333
7524672559.02892213913-92.0289221391295
7622102543.43495399973-333.434953999733
7729482486.93560652968461.064393470317
7825072565.06130109249-58.0613010924912
7930192555.22302353449463.776976465507
8024012633.80835547889-232.80835547889
8128182594.35982132748223.640178672521
8233052632.25484106525672.74515893475
8321012746.24907603522-645.249076035224
8425822636.91395290452-54.9139529045165
8524072627.60898211819-220.608982118194
8624162590.22758767771-174.227587677707
8724632560.70535284003-97.7053528400261
8822282544.14953404067-316.149534040666
8926162490.57913848978125.420861510222
9029342511.83125003194422.168749968057
9126682583.3662184247984.6337815752081
9228082597.70710673168210.292893268322
9326642633.3404772128630.6595227871385
9431122638.53562250413473.464377495869
9523212718.76244952974-397.762449529744
9627182651.3630405087766.6369594912344
9722972662.6544323784-365.654432378395
9825342600.69561078188-66.6956107818833
9926472589.394280663157.6057193369015
10020642599.1553615397-535.155361539701
10126422508.47522030257133.524779697428
10227022531.10051148303170.89948851697
10323482560.05881195018-212.058811950179
10427342524.12621293277209.873787067226
10527092559.6885673834149.311432616601
10632062584.98884982668621.011150173318
10722142690.21694404876-476.216944048757
10825312609.52370457226-78.5237045722579
10921192596.21814672343-477.218146723434
11023692515.35525707341-146.355257073412
11126822490.5558878883191.444112111697
11218402522.9954005475-682.995400547502
11326222407.26429919449214.735700805507
11425702443.65048735053126.349512649467
11524472465.05995547084-18.059955470841
11628712461.99976130943409.000238690571
11724852531.30337307513-46.3033730751299
11829572523.45743391061433.542566089392
11921022596.91965432485-494.919654324851
12022502513.05730820898-263.057308208976
12120512468.48319837811-417.483198378107
12222602397.74217976225-137.742179762251
12323272374.4022653882-47.4022653881993
12417812366.37012289411-585.370122894112
12526312267.18127188959363.818728110413
12621802328.82904003461-148.829040034609
12721502303.61049727033-153.610497270325
12828372277.58175386411559.418246135893
12919762372.37315317716-396.373153177158
13028362305.20915540033530.790844599672
13122032395.14974502124-192.149745021241
13217702362.59066541663-592.590665416632







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1332262.178319586481554.95223278932969.40440638366
1342262.178319586481544.871118106232979.48552106673
1352262.178319586481534.929734339032989.42690483393
1362262.178319586481525.12242740912999.23421176386
1372262.178319586481515.443914565273008.91272460769
1382262.178319586481505.889251113743018.46738805921
1392262.178319586481496.453800885183027.90283828778
1402262.178319586481487.133209938453037.22342923451
1412262.178319586481477.923383077753046.4332560952
1422262.178319586481468.820462823673055.53617634929
1432262.178319586481459.82081053193064.53582864106
1442262.178319586481450.920989397563073.4356497754

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
133 & 2262.17831958648 & 1554.9522327893 & 2969.40440638366 \tabularnewline
134 & 2262.17831958648 & 1544.87111810623 & 2979.48552106673 \tabularnewline
135 & 2262.17831958648 & 1534.92973433903 & 2989.42690483393 \tabularnewline
136 & 2262.17831958648 & 1525.1224274091 & 2999.23421176386 \tabularnewline
137 & 2262.17831958648 & 1515.44391456527 & 3008.91272460769 \tabularnewline
138 & 2262.17831958648 & 1505.88925111374 & 3018.46738805921 \tabularnewline
139 & 2262.17831958648 & 1496.45380088518 & 3027.90283828778 \tabularnewline
140 & 2262.17831958648 & 1487.13320993845 & 3037.22342923451 \tabularnewline
141 & 2262.17831958648 & 1477.92338307775 & 3046.4332560952 \tabularnewline
142 & 2262.17831958648 & 1468.82046282367 & 3055.53617634929 \tabularnewline
143 & 2262.17831958648 & 1459.8208105319 & 3064.53582864106 \tabularnewline
144 & 2262.17831958648 & 1450.92098939756 & 3073.4356497754 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=267079&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]133[/C][C]2262.17831958648[/C][C]1554.9522327893[/C][C]2969.40440638366[/C][/ROW]
[ROW][C]134[/C][C]2262.17831958648[/C][C]1544.87111810623[/C][C]2979.48552106673[/C][/ROW]
[ROW][C]135[/C][C]2262.17831958648[/C][C]1534.92973433903[/C][C]2989.42690483393[/C][/ROW]
[ROW][C]136[/C][C]2262.17831958648[/C][C]1525.1224274091[/C][C]2999.23421176386[/C][/ROW]
[ROW][C]137[/C][C]2262.17831958648[/C][C]1515.44391456527[/C][C]3008.91272460769[/C][/ROW]
[ROW][C]138[/C][C]2262.17831958648[/C][C]1505.88925111374[/C][C]3018.46738805921[/C][/ROW]
[ROW][C]139[/C][C]2262.17831958648[/C][C]1496.45380088518[/C][C]3027.90283828778[/C][/ROW]
[ROW][C]140[/C][C]2262.17831958648[/C][C]1487.13320993845[/C][C]3037.22342923451[/C][/ROW]
[ROW][C]141[/C][C]2262.17831958648[/C][C]1477.92338307775[/C][C]3046.4332560952[/C][/ROW]
[ROW][C]142[/C][C]2262.17831958648[/C][C]1468.82046282367[/C][C]3055.53617634929[/C][/ROW]
[ROW][C]143[/C][C]2262.17831958648[/C][C]1459.8208105319[/C][C]3064.53582864106[/C][/ROW]
[ROW][C]144[/C][C]2262.17831958648[/C][C]1450.92098939756[/C][C]3073.4356497754[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=267079&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=267079&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
1332262.178319586481554.95223278932969.40440638366
1342262.178319586481544.871118106232979.48552106673
1352262.178319586481534.929734339032989.42690483393
1362262.178319586481525.12242740912999.23421176386
1372262.178319586481515.443914565273008.91272460769
1382262.178319586481505.889251113743018.46738805921
1392262.178319586481496.453800885183027.90283828778
1402262.178319586481487.133209938453037.22342923451
1412262.178319586481477.923383077753046.4332560952
1422262.178319586481468.820462823673055.53617634929
1432262.178319586481459.82081053193064.53582864106
1442262.178319586481450.920989397563073.4356497754



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