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Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Mon, 26 Jan 2009 14:46:42 -0700

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Jan/26/t1233006448onydv2m3lv9ufkx.htm/, Retrieved Sun, 05 May 2024 14:06:29 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36981, Retrieved Sun, 05 May 2024 14:06:29 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

209

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Standard Deviation Plot] [standard deviatio...] [2009-01-08 21:49:18] [65364f12da24daf6c8f7985fc762862c]
- RMPD  [Classical Decomposition] [decompositie - te...] [2009-01-15 16:48:00] [74be16979710d4c4e7c6647856088456]
- RMP       [Exponential Smoothing] [opg10 oef2 - volk...] [2009-01-26 21:46:42] [9e20205489828c19845a9d736cd20362] [Current]

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Dataseries X:

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36981&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36981&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36981&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 Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.99995743816477
beta	0
gamma	0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.99995743816477 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36981&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]0.99995743816477[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36981&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36981&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
Parameter	Value
alpha	0.99995743816477
beta	0
gamma	0

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	93.36	93.89	-0.530000000000001
3	92.25	93.3600225577727	-1.11002255777267
4	91.07	92.2500472445972	-1.18004724459722
5	90.93	91.0700502249764	-0.140050224976378
6	90.68	90.9300059607946	-0.250005960794596
7	90.65	90.6800106407125	-0.0300106407125185
8	90.6	90.650001277308	-0.0500012773079561
9	90.02	90.6000021281461	-0.58000212814612
10	89.74	90.020024685955	-0.280024685955013
11	89.31	89.7400119183645	-0.430011918364528
12	89.16	89.3100183020964	-0.150018302096427
13	89.15	89.1600063850542	-0.0100063850542398
14	88.98	89.1500004258901	-0.170000425890109
15	88.25	88.9800072355301	-0.73000723553011
16	87.36	88.2500310704477	-0.890031070447677
17	87.13	87.3600378813558	-0.23003788135577
18	86.93	87.1300097908344	-0.200009790834386
19	86.93	86.9300085127838	-8.51278376501341e-06
20	86.93	86.9300000003623	-3.6231995181879e-10
21	86.98	86.93	0.049999999999983
22	86.16	86.9799978719083	-0.819997871908257
23	85.88	86.1600349006143	-0.280034900614311
24	85.91	85.8800119187993	0.0299880812006990
25	85.91	85.9099987236522	1.27634777413732e-06
26	85.6	85.9099999999457	-0.309999999945674
27	84.9	85.600013194169	-0.700013194168918
28	83.67	84.9000297938462	-1.23002979384623
29	83.41	83.6700523523254	-0.260052352325417
30	83.33	83.4100110683054	-0.0800110683053674
31	83.32	83.3300034054179	-0.0100034054179048
32	83.3	83.3200004257633	-0.0200004257632855
33	82.73	83.3000008512548	-0.570000851254818
34	82.2	82.7300242602823	-0.530024260282303
35	81.7	82.2000225588052	-0.500022558805242
36	81.52	81.7000212818778	-0.180021281877757
37	81.52	81.5200076620361	-7.66203612556637e-06
38	81.55	81.5200000003261	0.0299999996738904
39	81.89	81.549998723145	0.340001276855034
40	81.8	81.8899855289217	-0.0899855289216731
41	81.84	81.8000038299493	0.0399961700507419
42	81.77	81.8399982976896	-0.0699982976896081
43	81.77	81.770002979256	-2.97925602410487e-06
44	82.98	81.7700000001268	1.20999999987320
45	83.13	82.9799485001794	0.150051499820606
46	82.84	83.1299936135328	-0.289993613532772
47	82.8	82.8400123426604	-0.040012342660404
48	82.8	82.8000017029987	-1.70299874469038e-06
49	82.8	82.8000000000725	-7.24895699022454e-11
50	82.98	82.8	0.180000000000007
51	81.91	82.9799923388697	-1.06999233886967
52	81.64	81.9100455408376	-0.270045540837614
53	81.4	81.6400114936338	-0.240011493633816
54	81.21	81.4000102153297	-0.190010215329664
55	81.21	81.2100080871835	-8.08718347400372e-06
56	81.23	81.2100000003442	0.0199999996558091
57	81.01	81.2299991487633	-0.219999148763307
58	80.55	81.0100093635675	-0.460009363567536
59	80.5	80.5500195788427	-0.0500195788427362
60	80.54	80.500002128925	0.0399978710749451
61	80.54	80.5399982976172	1.7023827894036e-06
62	80.72	80.5399999999276	0.180000000072440
63	80.63	80.7199923388696	-0.0899923388696493
64	80.36	80.630003830239	-0.270003830239091
65	79.88	80.3600114918585	-0.480011491858548
66	79.66	79.88002043017	-0.220020430170024
67	79.66	79.6600093644733	-9.36447329991097e-06
68	79.13	79.6600000003986	-0.530000000398573
69	78.81	79.1300225577727	-0.320022557772688
70	78.67	78.8100136207474	-0.140013620747368
71	78.43	78.6700059592366	-0.240005959236640
72	78.13	78.4300102150941	-0.300010215094105
73	78.13	78.1300127689853	-1.27689853428592e-05
74	78.07	78.1300000005435	-0.0600000005434822
75	76.94	78.0700025537101	-1.13000255371013
76	74.97	76.9400480949825	-1.97004809498250
77	75	74.9700838488624	0.0299161511375843
78	75.1	74.9999987267137	0.100001273286296
79	75.1	75.0999957437623	4.25623771604933e-06
80	75.02	75.0999999998188	-0.0799999998188525
81	73.87	75.0200034049468	-1.15000340494680
82	73.18	73.8700489462554	-0.69004894625543
83	72.55	73.1800293697496	-0.630029369749565
84	72.42	72.5500268152062	-0.130026815206222
85	72.4	72.4200055341799	-0.0200055341798731
86	72.45	72.4000008514723	0.0499991485277462
87	71.42	72.4499978719445	-1.02999787194447
88	70.89	71.4200438385997	-0.53004383859971
89	70.42	70.8900225596385	-0.470022559638522
90	69.57	70.4200200050227	-0.850020005022742
91	69.57	69.5700361784114	-3.61784113920294e-05
92	69.44	69.5700000015398	-0.130000001539813
93	68.25	69.4400055330386	-1.19000553303863
94	66.86	68.2500506488194	-1.39005064881943
95	66.5	66.8600591631067	-0.360059163106683
96	66.46	66.5000153247788	-0.0400153247787784

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 93.36 & 93.89 & -0.530000000000001 \tabularnewline
3 & 92.25 & 93.3600225577727 & -1.11002255777267 \tabularnewline
4 & 91.07 & 92.2500472445972 & -1.18004724459722 \tabularnewline
5 & 90.93 & 91.0700502249764 & -0.140050224976378 \tabularnewline
6 & 90.68 & 90.9300059607946 & -0.250005960794596 \tabularnewline
7 & 90.65 & 90.6800106407125 & -0.0300106407125185 \tabularnewline
8 & 90.6 & 90.650001277308 & -0.0500012773079561 \tabularnewline
9 & 90.02 & 90.6000021281461 & -0.58000212814612 \tabularnewline
10 & 89.74 & 90.020024685955 & -0.280024685955013 \tabularnewline
11 & 89.31 & 89.7400119183645 & -0.430011918364528 \tabularnewline
12 & 89.16 & 89.3100183020964 & -0.150018302096427 \tabularnewline
13 & 89.15 & 89.1600063850542 & -0.0100063850542398 \tabularnewline
14 & 88.98 & 89.1500004258901 & -0.170000425890109 \tabularnewline
15 & 88.25 & 88.9800072355301 & -0.73000723553011 \tabularnewline
16 & 87.36 & 88.2500310704477 & -0.890031070447677 \tabularnewline
17 & 87.13 & 87.3600378813558 & -0.23003788135577 \tabularnewline
18 & 86.93 & 87.1300097908344 & -0.200009790834386 \tabularnewline
19 & 86.93 & 86.9300085127838 & -8.51278376501341e-06 \tabularnewline
20 & 86.93 & 86.9300000003623 & -3.6231995181879e-10 \tabularnewline
21 & 86.98 & 86.93 & 0.049999999999983 \tabularnewline
22 & 86.16 & 86.9799978719083 & -0.819997871908257 \tabularnewline
23 & 85.88 & 86.1600349006143 & -0.280034900614311 \tabularnewline
24 & 85.91 & 85.8800119187993 & 0.0299880812006990 \tabularnewline
25 & 85.91 & 85.9099987236522 & 1.27634777413732e-06 \tabularnewline
26 & 85.6 & 85.9099999999457 & -0.309999999945674 \tabularnewline
27 & 84.9 & 85.600013194169 & -0.700013194168918 \tabularnewline
28 & 83.67 & 84.9000297938462 & -1.23002979384623 \tabularnewline
29 & 83.41 & 83.6700523523254 & -0.260052352325417 \tabularnewline
30 & 83.33 & 83.4100110683054 & -0.0800110683053674 \tabularnewline
31 & 83.32 & 83.3300034054179 & -0.0100034054179048 \tabularnewline
32 & 83.3 & 83.3200004257633 & -0.0200004257632855 \tabularnewline
33 & 82.73 & 83.3000008512548 & -0.570000851254818 \tabularnewline
34 & 82.2 & 82.7300242602823 & -0.530024260282303 \tabularnewline
35 & 81.7 & 82.2000225588052 & -0.500022558805242 \tabularnewline
36 & 81.52 & 81.7000212818778 & -0.180021281877757 \tabularnewline
37 & 81.52 & 81.5200076620361 & -7.66203612556637e-06 \tabularnewline
38 & 81.55 & 81.5200000003261 & 0.0299999996738904 \tabularnewline
39 & 81.89 & 81.549998723145 & 0.340001276855034 \tabularnewline
40 & 81.8 & 81.8899855289217 & -0.0899855289216731 \tabularnewline
41 & 81.84 & 81.8000038299493 & 0.0399961700507419 \tabularnewline
42 & 81.77 & 81.8399982976896 & -0.0699982976896081 \tabularnewline
43 & 81.77 & 81.770002979256 & -2.97925602410487e-06 \tabularnewline
44 & 82.98 & 81.7700000001268 & 1.20999999987320 \tabularnewline
45 & 83.13 & 82.9799485001794 & 0.150051499820606 \tabularnewline
46 & 82.84 & 83.1299936135328 & -0.289993613532772 \tabularnewline
47 & 82.8 & 82.8400123426604 & -0.040012342660404 \tabularnewline
48 & 82.8 & 82.8000017029987 & -1.70299874469038e-06 \tabularnewline
49 & 82.8 & 82.8000000000725 & -7.24895699022454e-11 \tabularnewline
50 & 82.98 & 82.8 & 0.180000000000007 \tabularnewline
51 & 81.91 & 82.9799923388697 & -1.06999233886967 \tabularnewline
52 & 81.64 & 81.9100455408376 & -0.270045540837614 \tabularnewline
53 & 81.4 & 81.6400114936338 & -0.240011493633816 \tabularnewline
54 & 81.21 & 81.4000102153297 & -0.190010215329664 \tabularnewline
55 & 81.21 & 81.2100080871835 & -8.08718347400372e-06 \tabularnewline
56 & 81.23 & 81.2100000003442 & 0.0199999996558091 \tabularnewline
57 & 81.01 & 81.2299991487633 & -0.219999148763307 \tabularnewline
58 & 80.55 & 81.0100093635675 & -0.460009363567536 \tabularnewline
59 & 80.5 & 80.5500195788427 & -0.0500195788427362 \tabularnewline
60 & 80.54 & 80.500002128925 & 0.0399978710749451 \tabularnewline
61 & 80.54 & 80.5399982976172 & 1.7023827894036e-06 \tabularnewline
62 & 80.72 & 80.5399999999276 & 0.180000000072440 \tabularnewline
63 & 80.63 & 80.7199923388696 & -0.0899923388696493 \tabularnewline
64 & 80.36 & 80.630003830239 & -0.270003830239091 \tabularnewline
65 & 79.88 & 80.3600114918585 & -0.480011491858548 \tabularnewline
66 & 79.66 & 79.88002043017 & -0.220020430170024 \tabularnewline
67 & 79.66 & 79.6600093644733 & -9.36447329991097e-06 \tabularnewline
68 & 79.13 & 79.6600000003986 & -0.530000000398573 \tabularnewline
69 & 78.81 & 79.1300225577727 & -0.320022557772688 \tabularnewline
70 & 78.67 & 78.8100136207474 & -0.140013620747368 \tabularnewline
71 & 78.43 & 78.6700059592366 & -0.240005959236640 \tabularnewline
72 & 78.13 & 78.4300102150941 & -0.300010215094105 \tabularnewline
73 & 78.13 & 78.1300127689853 & -1.27689853428592e-05 \tabularnewline
74 & 78.07 & 78.1300000005435 & -0.0600000005434822 \tabularnewline
75 & 76.94 & 78.0700025537101 & -1.13000255371013 \tabularnewline
76 & 74.97 & 76.9400480949825 & -1.97004809498250 \tabularnewline
77 & 75 & 74.9700838488624 & 0.0299161511375843 \tabularnewline
78 & 75.1 & 74.9999987267137 & 0.100001273286296 \tabularnewline
79 & 75.1 & 75.0999957437623 & 4.25623771604933e-06 \tabularnewline
80 & 75.02 & 75.0999999998188 & -0.0799999998188525 \tabularnewline
81 & 73.87 & 75.0200034049468 & -1.15000340494680 \tabularnewline
82 & 73.18 & 73.8700489462554 & -0.69004894625543 \tabularnewline
83 & 72.55 & 73.1800293697496 & -0.630029369749565 \tabularnewline
84 & 72.42 & 72.5500268152062 & -0.130026815206222 \tabularnewline
85 & 72.4 & 72.4200055341799 & -0.0200055341798731 \tabularnewline
86 & 72.45 & 72.4000008514723 & 0.0499991485277462 \tabularnewline
87 & 71.42 & 72.4499978719445 & -1.02999787194447 \tabularnewline
88 & 70.89 & 71.4200438385997 & -0.53004383859971 \tabularnewline
89 & 70.42 & 70.8900225596385 & -0.470022559638522 \tabularnewline
90 & 69.57 & 70.4200200050227 & -0.850020005022742 \tabularnewline
91 & 69.57 & 69.5700361784114 & -3.61784113920294e-05 \tabularnewline
92 & 69.44 & 69.5700000015398 & -0.130000001539813 \tabularnewline
93 & 68.25 & 69.4400055330386 & -1.19000553303863 \tabularnewline
94 & 66.86 & 68.2500506488194 & -1.39005064881943 \tabularnewline
95 & 66.5 & 66.8600591631067 & -0.360059163106683 \tabularnewline
96 & 66.46 & 66.5000153247788 & -0.0400153247787784 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36981&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]93.36[/C][C]93.89[/C][C]-0.530000000000001[/C][/ROW]
[ROW][C]3[/C][C]92.25[/C][C]93.3600225577727[/C][C]-1.11002255777267[/C][/ROW]
[ROW][C]4[/C][C]91.07[/C][C]92.2500472445972[/C][C]-1.18004724459722[/C][/ROW]
[ROW][C]5[/C][C]90.93[/C][C]91.0700502249764[/C][C]-0.140050224976378[/C][/ROW]
[ROW][C]6[/C][C]90.68[/C][C]90.9300059607946[/C][C]-0.250005960794596[/C][/ROW]
[ROW][C]7[/C][C]90.65[/C][C]90.6800106407125[/C][C]-0.0300106407125185[/C][/ROW]
[ROW][C]8[/C][C]90.6[/C][C]90.650001277308[/C][C]-0.0500012773079561[/C][/ROW]
[ROW][C]9[/C][C]90.02[/C][C]90.6000021281461[/C][C]-0.58000212814612[/C][/ROW]
[ROW][C]10[/C][C]89.74[/C][C]90.020024685955[/C][C]-0.280024685955013[/C][/ROW]
[ROW][C]11[/C][C]89.31[/C][C]89.7400119183645[/C][C]-0.430011918364528[/C][/ROW]
[ROW][C]12[/C][C]89.16[/C][C]89.3100183020964[/C][C]-0.150018302096427[/C][/ROW]
[ROW][C]13[/C][C]89.15[/C][C]89.1600063850542[/C][C]-0.0100063850542398[/C][/ROW]
[ROW][C]14[/C][C]88.98[/C][C]89.1500004258901[/C][C]-0.170000425890109[/C][/ROW]
[ROW][C]15[/C][C]88.25[/C][C]88.9800072355301[/C][C]-0.73000723553011[/C][/ROW]
[ROW][C]16[/C][C]87.36[/C][C]88.2500310704477[/C][C]-0.890031070447677[/C][/ROW]
[ROW][C]17[/C][C]87.13[/C][C]87.3600378813558[/C][C]-0.23003788135577[/C][/ROW]
[ROW][C]18[/C][C]86.93[/C][C]87.1300097908344[/C][C]-0.200009790834386[/C][/ROW]
[ROW][C]19[/C][C]86.93[/C][C]86.9300085127838[/C][C]-8.51278376501341e-06[/C][/ROW]
[ROW][C]20[/C][C]86.93[/C][C]86.9300000003623[/C][C]-3.6231995181879e-10[/C][/ROW]
[ROW][C]21[/C][C]86.98[/C][C]86.93[/C][C]0.049999999999983[/C][/ROW]
[ROW][C]22[/C][C]86.16[/C][C]86.9799978719083[/C][C]-0.819997871908257[/C][/ROW]
[ROW][C]23[/C][C]85.88[/C][C]86.1600349006143[/C][C]-0.280034900614311[/C][/ROW]
[ROW][C]24[/C][C]85.91[/C][C]85.8800119187993[/C][C]0.0299880812006990[/C][/ROW]
[ROW][C]25[/C][C]85.91[/C][C]85.9099987236522[/C][C]1.27634777413732e-06[/C][/ROW]
[ROW][C]26[/C][C]85.6[/C][C]85.9099999999457[/C][C]-0.309999999945674[/C][/ROW]
[ROW][C]27[/C][C]84.9[/C][C]85.600013194169[/C][C]-0.700013194168918[/C][/ROW]
[ROW][C]28[/C][C]83.67[/C][C]84.9000297938462[/C][C]-1.23002979384623[/C][/ROW]
[ROW][C]29[/C][C]83.41[/C][C]83.6700523523254[/C][C]-0.260052352325417[/C][/ROW]
[ROW][C]30[/C][C]83.33[/C][C]83.4100110683054[/C][C]-0.0800110683053674[/C][/ROW]
[ROW][C]31[/C][C]83.32[/C][C]83.3300034054179[/C][C]-0.0100034054179048[/C][/ROW]
[ROW][C]32[/C][C]83.3[/C][C]83.3200004257633[/C][C]-0.0200004257632855[/C][/ROW]
[ROW][C]33[/C][C]82.73[/C][C]83.3000008512548[/C][C]-0.570000851254818[/C][/ROW]
[ROW][C]34[/C][C]82.2[/C][C]82.7300242602823[/C][C]-0.530024260282303[/C][/ROW]
[ROW][C]35[/C][C]81.7[/C][C]82.2000225588052[/C][C]-0.500022558805242[/C][/ROW]
[ROW][C]36[/C][C]81.52[/C][C]81.7000212818778[/C][C]-0.180021281877757[/C][/ROW]
[ROW][C]37[/C][C]81.52[/C][C]81.5200076620361[/C][C]-7.66203612556637e-06[/C][/ROW]
[ROW][C]38[/C][C]81.55[/C][C]81.5200000003261[/C][C]0.0299999996738904[/C][/ROW]
[ROW][C]39[/C][C]81.89[/C][C]81.549998723145[/C][C]0.340001276855034[/C][/ROW]
[ROW][C]40[/C][C]81.8[/C][C]81.8899855289217[/C][C]-0.0899855289216731[/C][/ROW]
[ROW][C]41[/C][C]81.84[/C][C]81.8000038299493[/C][C]0.0399961700507419[/C][/ROW]
[ROW][C]42[/C][C]81.77[/C][C]81.8399982976896[/C][C]-0.0699982976896081[/C][/ROW]
[ROW][C]43[/C][C]81.77[/C][C]81.770002979256[/C][C]-2.97925602410487e-06[/C][/ROW]
[ROW][C]44[/C][C]82.98[/C][C]81.7700000001268[/C][C]1.20999999987320[/C][/ROW]
[ROW][C]45[/C][C]83.13[/C][C]82.9799485001794[/C][C]0.150051499820606[/C][/ROW]
[ROW][C]46[/C][C]82.84[/C][C]83.1299936135328[/C][C]-0.289993613532772[/C][/ROW]
[ROW][C]47[/C][C]82.8[/C][C]82.8400123426604[/C][C]-0.040012342660404[/C][/ROW]
[ROW][C]48[/C][C]82.8[/C][C]82.8000017029987[/C][C]-1.70299874469038e-06[/C][/ROW]
[ROW][C]49[/C][C]82.8[/C][C]82.8000000000725[/C][C]-7.24895699022454e-11[/C][/ROW]
[ROW][C]50[/C][C]82.98[/C][C]82.8[/C][C]0.180000000000007[/C][/ROW]
[ROW][C]51[/C][C]81.91[/C][C]82.9799923388697[/C][C]-1.06999233886967[/C][/ROW]
[ROW][C]52[/C][C]81.64[/C][C]81.9100455408376[/C][C]-0.270045540837614[/C][/ROW]
[ROW][C]53[/C][C]81.4[/C][C]81.6400114936338[/C][C]-0.240011493633816[/C][/ROW]
[ROW][C]54[/C][C]81.21[/C][C]81.4000102153297[/C][C]-0.190010215329664[/C][/ROW]
[ROW][C]55[/C][C]81.21[/C][C]81.2100080871835[/C][C]-8.08718347400372e-06[/C][/ROW]
[ROW][C]56[/C][C]81.23[/C][C]81.2100000003442[/C][C]0.0199999996558091[/C][/ROW]
[ROW][C]57[/C][C]81.01[/C][C]81.2299991487633[/C][C]-0.219999148763307[/C][/ROW]
[ROW][C]58[/C][C]80.55[/C][C]81.0100093635675[/C][C]-0.460009363567536[/C][/ROW]
[ROW][C]59[/C][C]80.5[/C][C]80.5500195788427[/C][C]-0.0500195788427362[/C][/ROW]
[ROW][C]60[/C][C]80.54[/C][C]80.500002128925[/C][C]0.0399978710749451[/C][/ROW]
[ROW][C]61[/C][C]80.54[/C][C]80.5399982976172[/C][C]1.7023827894036e-06[/C][/ROW]
[ROW][C]62[/C][C]80.72[/C][C]80.5399999999276[/C][C]0.180000000072440[/C][/ROW]
[ROW][C]63[/C][C]80.63[/C][C]80.7199923388696[/C][C]-0.0899923388696493[/C][/ROW]
[ROW][C]64[/C][C]80.36[/C][C]80.630003830239[/C][C]-0.270003830239091[/C][/ROW]
[ROW][C]65[/C][C]79.88[/C][C]80.3600114918585[/C][C]-0.480011491858548[/C][/ROW]
[ROW][C]66[/C][C]79.66[/C][C]79.88002043017[/C][C]-0.220020430170024[/C][/ROW]
[ROW][C]67[/C][C]79.66[/C][C]79.6600093644733[/C][C]-9.36447329991097e-06[/C][/ROW]
[ROW][C]68[/C][C]79.13[/C][C]79.6600000003986[/C][C]-0.530000000398573[/C][/ROW]
[ROW][C]69[/C][C]78.81[/C][C]79.1300225577727[/C][C]-0.320022557772688[/C][/ROW]
[ROW][C]70[/C][C]78.67[/C][C]78.8100136207474[/C][C]-0.140013620747368[/C][/ROW]
[ROW][C]71[/C][C]78.43[/C][C]78.6700059592366[/C][C]-0.240005959236640[/C][/ROW]
[ROW][C]72[/C][C]78.13[/C][C]78.4300102150941[/C][C]-0.300010215094105[/C][/ROW]
[ROW][C]73[/C][C]78.13[/C][C]78.1300127689853[/C][C]-1.27689853428592e-05[/C][/ROW]
[ROW][C]74[/C][C]78.07[/C][C]78.1300000005435[/C][C]-0.0600000005434822[/C][/ROW]
[ROW][C]75[/C][C]76.94[/C][C]78.0700025537101[/C][C]-1.13000255371013[/C][/ROW]
[ROW][C]76[/C][C]74.97[/C][C]76.9400480949825[/C][C]-1.97004809498250[/C][/ROW]
[ROW][C]77[/C][C]75[/C][C]74.9700838488624[/C][C]0.0299161511375843[/C][/ROW]
[ROW][C]78[/C][C]75.1[/C][C]74.9999987267137[/C][C]0.100001273286296[/C][/ROW]
[ROW][C]79[/C][C]75.1[/C][C]75.0999957437623[/C][C]4.25623771604933e-06[/C][/ROW]
[ROW][C]80[/C][C]75.02[/C][C]75.0999999998188[/C][C]-0.0799999998188525[/C][/ROW]
[ROW][C]81[/C][C]73.87[/C][C]75.0200034049468[/C][C]-1.15000340494680[/C][/ROW]
[ROW][C]82[/C][C]73.18[/C][C]73.8700489462554[/C][C]-0.69004894625543[/C][/ROW]
[ROW][C]83[/C][C]72.55[/C][C]73.1800293697496[/C][C]-0.630029369749565[/C][/ROW]
[ROW][C]84[/C][C]72.42[/C][C]72.5500268152062[/C][C]-0.130026815206222[/C][/ROW]
[ROW][C]85[/C][C]72.4[/C][C]72.4200055341799[/C][C]-0.0200055341798731[/C][/ROW]
[ROW][C]86[/C][C]72.45[/C][C]72.4000008514723[/C][C]0.0499991485277462[/C][/ROW]
[ROW][C]87[/C][C]71.42[/C][C]72.4499978719445[/C][C]-1.02999787194447[/C][/ROW]
[ROW][C]88[/C][C]70.89[/C][C]71.4200438385997[/C][C]-0.53004383859971[/C][/ROW]
[ROW][C]89[/C][C]70.42[/C][C]70.8900225596385[/C][C]-0.470022559638522[/C][/ROW]
[ROW][C]90[/C][C]69.57[/C][C]70.4200200050227[/C][C]-0.850020005022742[/C][/ROW]
[ROW][C]91[/C][C]69.57[/C][C]69.5700361784114[/C][C]-3.61784113920294e-05[/C][/ROW]
[ROW][C]92[/C][C]69.44[/C][C]69.5700000015398[/C][C]-0.130000001539813[/C][/ROW]
[ROW][C]93[/C][C]68.25[/C][C]69.4400055330386[/C][C]-1.19000553303863[/C][/ROW]
[ROW][C]94[/C][C]66.86[/C][C]68.2500506488194[/C][C]-1.39005064881943[/C][/ROW]
[ROW][C]95[/C][C]66.5[/C][C]66.8600591631067[/C][C]-0.360059163106683[/C][/ROW]
[ROW][C]96[/C][C]66.46[/C][C]66.5000153247788[/C][C]-0.0400153247787784[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36981&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36981&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
t	Observed	Fitted	Residuals
2	93.36	93.89	-0.530000000000001
3	92.25	93.3600225577727	-1.11002255777267
4	91.07	92.2500472445972	-1.18004724459722
5	90.93	91.0700502249764	-0.140050224976378
6	90.68	90.9300059607946	-0.250005960794596
7	90.65	90.6800106407125	-0.0300106407125185
8	90.6	90.650001277308	-0.0500012773079561
9	90.02	90.6000021281461	-0.58000212814612
10	89.74	90.020024685955	-0.280024685955013
11	89.31	89.7400119183645	-0.430011918364528
12	89.16	89.3100183020964	-0.150018302096427
13	89.15	89.1600063850542	-0.0100063850542398
14	88.98	89.1500004258901	-0.170000425890109
15	88.25	88.9800072355301	-0.73000723553011
16	87.36	88.2500310704477	-0.890031070447677
17	87.13	87.3600378813558	-0.23003788135577
18	86.93	87.1300097908344	-0.200009790834386
19	86.93	86.9300085127838	-8.51278376501341e-06
20	86.93	86.9300000003623	-3.6231995181879e-10
21	86.98	86.93	0.049999999999983
22	86.16	86.9799978719083	-0.819997871908257
23	85.88	86.1600349006143	-0.280034900614311
24	85.91	85.8800119187993	0.0299880812006990
25	85.91	85.9099987236522	1.27634777413732e-06
26	85.6	85.9099999999457	-0.309999999945674
27	84.9	85.600013194169	-0.700013194168918
28	83.67	84.9000297938462	-1.23002979384623
29	83.41	83.6700523523254	-0.260052352325417
30	83.33	83.4100110683054	-0.0800110683053674
31	83.32	83.3300034054179	-0.0100034054179048
32	83.3	83.3200004257633	-0.0200004257632855
33	82.73	83.3000008512548	-0.570000851254818
34	82.2	82.7300242602823	-0.530024260282303
35	81.7	82.2000225588052	-0.500022558805242
36	81.52	81.7000212818778	-0.180021281877757
37	81.52	81.5200076620361	-7.66203612556637e-06
38	81.55	81.5200000003261	0.0299999996738904
39	81.89	81.549998723145	0.340001276855034
40	81.8	81.8899855289217	-0.0899855289216731
41	81.84	81.8000038299493	0.0399961700507419
42	81.77	81.8399982976896	-0.0699982976896081
43	81.77	81.770002979256	-2.97925602410487e-06
44	82.98	81.7700000001268	1.20999999987320
45	83.13	82.9799485001794	0.150051499820606
46	82.84	83.1299936135328	-0.289993613532772
47	82.8	82.8400123426604	-0.040012342660404
48	82.8	82.8000017029987	-1.70299874469038e-06
49	82.8	82.8000000000725	-7.24895699022454e-11
50	82.98	82.8	0.180000000000007
51	81.91	82.9799923388697	-1.06999233886967
52	81.64	81.9100455408376	-0.270045540837614
53	81.4	81.6400114936338	-0.240011493633816
54	81.21	81.4000102153297	-0.190010215329664
55	81.21	81.2100080871835	-8.08718347400372e-06
56	81.23	81.2100000003442	0.0199999996558091
57	81.01	81.2299991487633	-0.219999148763307
58	80.55	81.0100093635675	-0.460009363567536
59	80.5	80.5500195788427	-0.0500195788427362
60	80.54	80.500002128925	0.0399978710749451
61	80.54	80.5399982976172	1.7023827894036e-06
62	80.72	80.5399999999276	0.180000000072440
63	80.63	80.7199923388696	-0.0899923388696493
64	80.36	80.630003830239	-0.270003830239091
65	79.88	80.3600114918585	-0.480011491858548
66	79.66	79.88002043017	-0.220020430170024
67	79.66	79.6600093644733	-9.36447329991097e-06
68	79.13	79.6600000003986	-0.530000000398573
69	78.81	79.1300225577727	-0.320022557772688
70	78.67	78.8100136207474	-0.140013620747368
71	78.43	78.6700059592366	-0.240005959236640
72	78.13	78.4300102150941	-0.300010215094105
73	78.13	78.1300127689853	-1.27689853428592e-05
74	78.07	78.1300000005435	-0.0600000005434822
75	76.94	78.0700025537101	-1.13000255371013
76	74.97	76.9400480949825	-1.97004809498250
77	75	74.9700838488624	0.0299161511375843
78	75.1	74.9999987267137	0.100001273286296
79	75.1	75.0999957437623	4.25623771604933e-06
80	75.02	75.0999999998188	-0.0799999998188525
81	73.87	75.0200034049468	-1.15000340494680
82	73.18	73.8700489462554	-0.69004894625543
83	72.55	73.1800293697496	-0.630029369749565
84	72.42	72.5500268152062	-0.130026815206222
85	72.4	72.4200055341799	-0.0200055341798731
86	72.45	72.4000008514723	0.0499991485277462
87	71.42	72.4499978719445	-1.02999787194447
88	70.89	71.4200438385997	-0.53004383859971
89	70.42	70.8900225596385	-0.470022559638522
90	69.57	70.4200200050227	-0.850020005022742
91	69.57	69.5700361784114	-3.61784113920294e-05
92	69.44	69.5700000015398	-0.130000001539813
93	68.25	69.4400055330386	-1.19000553303863
94	66.86	68.2500506488194	-1.39005064881943
95	66.5	66.8600591631067	-0.360059163106683
96	66.46	66.5000153247788	-0.0400153247787784

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
97	66.4600017031257	65.5931755140823	67.326827892169
98	66.4600017031257	65.2341504378777	67.6858529683736
99	66.4600017031257	64.9586573032598	67.9613461029915
100	66.4600017031257	64.7264046653147	68.1935987409367
101	66.4600017031257	64.5217854169477	68.3982179893036
102	66.4600017031257	64.3367951529982	68.5832082532531
103	66.4600017031257	64.1666788438224	68.7533245624289
104	66.4600017031257	64.0083383046345	68.9116651016168
105	66.4600017031257	63.8596215189988	69.0603818872525
106	66.4600017031257	63.7189616113907	69.2010417948606
107	66.4600017031257	63.5851757141314	69.33482769212
108	66.4600017031257	63.4573448546837	69.4626585515676

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 66.4600017031257 & 65.5931755140823 & 67.326827892169 \tabularnewline
98 & 66.4600017031257 & 65.2341504378777 & 67.6858529683736 \tabularnewline
99 & 66.4600017031257 & 64.9586573032598 & 67.9613461029915 \tabularnewline
100 & 66.4600017031257 & 64.7264046653147 & 68.1935987409367 \tabularnewline
101 & 66.4600017031257 & 64.5217854169477 & 68.3982179893036 \tabularnewline
102 & 66.4600017031257 & 64.3367951529982 & 68.5832082532531 \tabularnewline
103 & 66.4600017031257 & 64.1666788438224 & 68.7533245624289 \tabularnewline
104 & 66.4600017031257 & 64.0083383046345 & 68.9116651016168 \tabularnewline
105 & 66.4600017031257 & 63.8596215189988 & 69.0603818872525 \tabularnewline
106 & 66.4600017031257 & 63.7189616113907 & 69.2010417948606 \tabularnewline
107 & 66.4600017031257 & 63.5851757141314 & 69.33482769212 \tabularnewline
108 & 66.4600017031257 & 63.4573448546837 & 69.4626585515676 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36981&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]66.4600017031257[/C][C]65.5931755140823[/C][C]67.326827892169[/C][/ROW]
[ROW][C]98[/C][C]66.4600017031257[/C][C]65.2341504378777[/C][C]67.6858529683736[/C][/ROW]
[ROW][C]99[/C][C]66.4600017031257[/C][C]64.9586573032598[/C][C]67.9613461029915[/C][/ROW]
[ROW][C]100[/C][C]66.4600017031257[/C][C]64.7264046653147[/C][C]68.1935987409367[/C][/ROW]
[ROW][C]101[/C][C]66.4600017031257[/C][C]64.5217854169477[/C][C]68.3982179893036[/C][/ROW]
[ROW][C]102[/C][C]66.4600017031257[/C][C]64.3367951529982[/C][C]68.5832082532531[/C][/ROW]
[ROW][C]103[/C][C]66.4600017031257[/C][C]64.1666788438224[/C][C]68.7533245624289[/C][/ROW]
[ROW][C]104[/C][C]66.4600017031257[/C][C]64.0083383046345[/C][C]68.9116651016168[/C][/ROW]
[ROW][C]105[/C][C]66.4600017031257[/C][C]63.8596215189988[/C][C]69.0603818872525[/C][/ROW]
[ROW][C]106[/C][C]66.4600017031257[/C][C]63.7189616113907[/C][C]69.2010417948606[/C][/ROW]
[ROW][C]107[/C][C]66.4600017031257[/C][C]63.5851757141314[/C][C]69.33482769212[/C][/ROW]
[ROW][C]108[/C][C]66.4600017031257[/C][C]63.4573448546837[/C][C]69.4626585515676[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36981&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36981&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
t	Forecast	95% Lower Bound	95% Upper Bound
97	66.4600017031257	65.5931755140823	67.326827892169
98	66.4600017031257	65.2341504378777	67.6858529683736
99	66.4600017031257	64.9586573032598	67.9613461029915
100	66.4600017031257	64.7264046653147	68.1935987409367
101	66.4600017031257	64.5217854169477	68.3982179893036
102	66.4600017031257	64.3367951529982	68.5832082532531
103	66.4600017031257	64.1666788438224	68.7533245624289
104	66.4600017031257	64.0083383046345	68.9116651016168
105	66.4600017031257	63.8596215189988	69.0603818872525
106	66.4600017031257	63.7189616113907	69.2010417948606
107	66.4600017031257	63.5851757141314	69.33482769212
108	66.4600017031257	63.4573448546837	69.4626585515676

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ;

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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code