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Author's title

Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Tue, 15 Aug 2017 16:02:56 +0200

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/2017/Aug/15/t1502805903asdj52b2fyk6c4j.htm/, Retrieved Mon, 20 May 2024 01:53:38 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=307286, Retrieved Mon, 20 May 2024 01:53:38 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

105

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

-       [Exponential Smoothing] [] [2017-08-15 14:02:56] [c81f1da0e4fa2d83805175b5d75ced6f] [Current]

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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	1 seconds
R Server	Big Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307286&T=0

[TABLE]
[ROW]

Summary of computational transaction[/C][/ROW] [ROW]

Raw Input[/C]

view raw input (R code) [/C][/ROW] [ROW]

Raw Output[/C]

view raw output of R engine [/C][/ROW] [ROW]

Computing time[/C]

1 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=307286&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307286&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	1 seconds
R Server	Big Analytics Cloud Computing Center

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.548594506058805
beta	FALSE
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.548594506058805 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307286&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]0.548594506058805[/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=307286&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307286&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	0.548594506058805
beta	FALSE
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
2	67600	70200	-2600
3	71500	68773.6542842471	2726.34571575289
4	57200	70269.3125655261	-13069.3125655261
5	74100	63099.5594941132	11000.4405058868
6	72800	69134.3407198694	3665.65928013057
7	78000	71145.3012620325	6854.69873796747
8	80600	74905.7513303697	5694.24866963029
9	89700	78029.5848666615	11670.4151333385
10	78000	84431.9104922366	-6431.91049223655
11	74100	80903.3997327336	-6803.3997327336
12	92300	77171.092016834	15128.907983166
13	78000	85470.7278190681	-7470.72781906807
14	58500	81372.3275812666	-22872.3275812666
15	68900	68824.6943294065	75.3056705935014
16	52000	68866.0066065692	-16866.0066065692
17	72800	59613.4080430538	13186.5919569462
18	59800	66847.4999442737	-7047.49994427372
19	79300	62981.2801933954	16318.7198066046
20	71500	71933.6402252117	-433.640225211697
21	75400	71695.7475800545	3704.25241994554
22	84500	73727.8801066916	10772.1198933084
23	83200	79637.4058987673	3562.59410123265
24	98800	81591.8254500211	17208.1745499789
25	71500	91032.1354674405	-19532.1354674405
26	59800	80316.9132584063	-20516.9132584063
27	66300	69061.4473635596	-2761.44736355956
28	48100	67546.5325111402	-19446.5325111402
29	68900	56878.2716136348	12021.7283863652
30	53300	63473.3257597259	-10173.3257597259
31	75400	57892.2951395938	17507.7048604062
32	71500	67496.9258397117	4003.07416028835
33	63700	69692.9903313918	-5992.9903313918
34	91000	66405.2687607267	24594.7312392733
35	81900	79897.8031965849	2002.19680341509
36	93600	80996.1973629869	12603.8026370131
37	70200	87910.5742451018	-17710.5742451018
38	65000	78194.6505150924	-13194.6505150924
39	58500	70956.1377331467	-12456.1377331467
40	48100	64122.7690060307	-16022.7690060307
41	63700	55332.7659574729	8367.23404252705
42	57200	59922.9845841115	-2722.98458411149
43	78000	58429.1702011851	19570.8297988149
44	75400	69165.6199078269	6234.3800921731
45	65000	72585.7665750755	-7585.76657507545
46	87100	68424.2567077445	18675.7432922555
47	80600	78669.6668744405	1930.33312555954
48	104000	79728.6370219857	24271.3629780143
49	83200	93043.7734062834	-9843.77340628344
50	50700	87643.5333967086	-36943.5333967086
51	50700	67376.5139408743	-16676.5139408743
52	50700	58227.8700126976	-7527.87001269759
53	59800	54098.1218814069	5701.87811859313
54	59800	57226.140891484	2573.85910851603
55	80600	58638.1458577853	21961.8541422147
56	74100	70686.2983830691	3413.70161693092
57	66300	72559.0363354414	-6259.03633544144
58	83200	69125.3633885958	14074.6366114042
59	76700	76846.6317083863	-146.631708386267
60	110500	76766.1903587515	33733.8096412485
61	87100	95272.372996374	-8172.37299637398
62	50700	90789.0540690999	-40089.0540690999
63	53300	68796.4192536973	-15496.4192536973
64	44200	60295.1687875351	-16095.1687875351
65	61100	51465.4476166042	9634.55238339581
66	70200	56750.9101224709	13449.0898775291
67	88400	64129.0069407744	24270.9930592256
68	87100	77443.940389657	9656.05961034304
69	70200	82741.2016420675	-12541.2016420675
70	81900	75861.1673218536	6038.8326781464
71	72800	79174.0377520931	-6374.03775209309
72	104000	75677.2756598834	28322.7243401166
73	79300	91214.9666294894	-11914.9666294894
74	63700	84678.4813966775	-20978.4813966775
75	57200	73169.8017570034	-15969.8017570034
76	42900	64408.8562502631	-21508.8562502631
77	63700	52609.2158797602	11090.7841202398
78	76700	58693.559116008	18006.440883992
79	89700	68571.7936586386	21128.2063413614
80	84500	80162.6115803863	4337.38841961371
81	62400	82542.0790380294	-20142.0790380294
82	89700	71492.2451371643	18207.7548628357
83	70200	81480.9194225814	-11280.9194225814
84	107900	75292.2690040612	32607.7309959388
85	89700	93180.6910834766	-3480.69108347662
86	65000	91271.2030777935	-26271.2030777935
87	59800	76858.9654017608	-17058.9654017608
88	40300	67500.5107033076	-27200.5107033076
89	63700	52578.4599694793	11121.5400305207
90	61100	58679.675729136	2420.32427086395
91	92300	60007.4523270128	32292.5476729872
92	92300	77722.9665670556	14577.0334329444
93	70200	85719.8470230044	-15519.8470230044
94	91000	77205.7442113111	13794.2557886889
95	67600	84773.1971521557	-17173.1971521557
96	105300	75352.0755430184	29947.9244569816
97	89700	91781.3423679826	-2081.34236798261
98	66300	90639.5293796799	-24339.5293796799
99	50700	77286.9972819307	-26586.9972819307
100	35100	62701.5166404631	-27601.5166404631
101	68900	47559.4762526144	21340.5237473856
102	66300	59266.7703368476	7033.22966315242
103	87100	63125.1614899028	23974.8385100972
104	100100	76277.6261801892	23822.3738198108
105	74100	89346.4495790165	-15246.4495790165
106	83200	80982.3311030655	2217.66889693451
107	62400	82198.9320761813	-19798.9320761813
108	107900	71337.3467133568	36562.6532866432

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 67600 & 70200 & -2600 \tabularnewline
3 & 71500 & 68773.6542842471 & 2726.34571575289 \tabularnewline
4 & 57200 & 70269.3125655261 & -13069.3125655261 \tabularnewline
5 & 74100 & 63099.5594941132 & 11000.4405058868 \tabularnewline
6 & 72800 & 69134.3407198694 & 3665.65928013057 \tabularnewline
7 & 78000 & 71145.3012620325 & 6854.69873796747 \tabularnewline
8 & 80600 & 74905.7513303697 & 5694.24866963029 \tabularnewline
9 & 89700 & 78029.5848666615 & 11670.4151333385 \tabularnewline
10 & 78000 & 84431.9104922366 & -6431.91049223655 \tabularnewline
11 & 74100 & 80903.3997327336 & -6803.3997327336 \tabularnewline
12 & 92300 & 77171.092016834 & 15128.907983166 \tabularnewline
13 & 78000 & 85470.7278190681 & -7470.72781906807 \tabularnewline
14 & 58500 & 81372.3275812666 & -22872.3275812666 \tabularnewline
15 & 68900 & 68824.6943294065 & 75.3056705935014 \tabularnewline
16 & 52000 & 68866.0066065692 & -16866.0066065692 \tabularnewline
17 & 72800 & 59613.4080430538 & 13186.5919569462 \tabularnewline
18 & 59800 & 66847.4999442737 & -7047.49994427372 \tabularnewline
19 & 79300 & 62981.2801933954 & 16318.7198066046 \tabularnewline
20 & 71500 & 71933.6402252117 & -433.640225211697 \tabularnewline
21 & 75400 & 71695.7475800545 & 3704.25241994554 \tabularnewline
22 & 84500 & 73727.8801066916 & 10772.1198933084 \tabularnewline
23 & 83200 & 79637.4058987673 & 3562.59410123265 \tabularnewline
24 & 98800 & 81591.8254500211 & 17208.1745499789 \tabularnewline
25 & 71500 & 91032.1354674405 & -19532.1354674405 \tabularnewline
26 & 59800 & 80316.9132584063 & -20516.9132584063 \tabularnewline
27 & 66300 & 69061.4473635596 & -2761.44736355956 \tabularnewline
28 & 48100 & 67546.5325111402 & -19446.5325111402 \tabularnewline
29 & 68900 & 56878.2716136348 & 12021.7283863652 \tabularnewline
30 & 53300 & 63473.3257597259 & -10173.3257597259 \tabularnewline
31 & 75400 & 57892.2951395938 & 17507.7048604062 \tabularnewline
32 & 71500 & 67496.9258397117 & 4003.07416028835 \tabularnewline
33 & 63700 & 69692.9903313918 & -5992.9903313918 \tabularnewline
34 & 91000 & 66405.2687607267 & 24594.7312392733 \tabularnewline
35 & 81900 & 79897.8031965849 & 2002.19680341509 \tabularnewline
36 & 93600 & 80996.1973629869 & 12603.8026370131 \tabularnewline
37 & 70200 & 87910.5742451018 & -17710.5742451018 \tabularnewline
38 & 65000 & 78194.6505150924 & -13194.6505150924 \tabularnewline
39 & 58500 & 70956.1377331467 & -12456.1377331467 \tabularnewline
40 & 48100 & 64122.7690060307 & -16022.7690060307 \tabularnewline
41 & 63700 & 55332.7659574729 & 8367.23404252705 \tabularnewline
42 & 57200 & 59922.9845841115 & -2722.98458411149 \tabularnewline
43 & 78000 & 58429.1702011851 & 19570.8297988149 \tabularnewline
44 & 75400 & 69165.6199078269 & 6234.3800921731 \tabularnewline
45 & 65000 & 72585.7665750755 & -7585.76657507545 \tabularnewline
46 & 87100 & 68424.2567077445 & 18675.7432922555 \tabularnewline
47 & 80600 & 78669.6668744405 & 1930.33312555954 \tabularnewline
48 & 104000 & 79728.6370219857 & 24271.3629780143 \tabularnewline
49 & 83200 & 93043.7734062834 & -9843.77340628344 \tabularnewline
50 & 50700 & 87643.5333967086 & -36943.5333967086 \tabularnewline
51 & 50700 & 67376.5139408743 & -16676.5139408743 \tabularnewline
52 & 50700 & 58227.8700126976 & -7527.87001269759 \tabularnewline
53 & 59800 & 54098.1218814069 & 5701.87811859313 \tabularnewline
54 & 59800 & 57226.140891484 & 2573.85910851603 \tabularnewline
55 & 80600 & 58638.1458577853 & 21961.8541422147 \tabularnewline
56 & 74100 & 70686.2983830691 & 3413.70161693092 \tabularnewline
57 & 66300 & 72559.0363354414 & -6259.03633544144 \tabularnewline
58 & 83200 & 69125.3633885958 & 14074.6366114042 \tabularnewline
59 & 76700 & 76846.6317083863 & -146.631708386267 \tabularnewline
60 & 110500 & 76766.1903587515 & 33733.8096412485 \tabularnewline
61 & 87100 & 95272.372996374 & -8172.37299637398 \tabularnewline
62 & 50700 & 90789.0540690999 & -40089.0540690999 \tabularnewline
63 & 53300 & 68796.4192536973 & -15496.4192536973 \tabularnewline
64 & 44200 & 60295.1687875351 & -16095.1687875351 \tabularnewline
65 & 61100 & 51465.4476166042 & 9634.55238339581 \tabularnewline
66 & 70200 & 56750.9101224709 & 13449.0898775291 \tabularnewline
67 & 88400 & 64129.0069407744 & 24270.9930592256 \tabularnewline
68 & 87100 & 77443.940389657 & 9656.05961034304 \tabularnewline
69 & 70200 & 82741.2016420675 & -12541.2016420675 \tabularnewline
70 & 81900 & 75861.1673218536 & 6038.8326781464 \tabularnewline
71 & 72800 & 79174.0377520931 & -6374.03775209309 \tabularnewline
72 & 104000 & 75677.2756598834 & 28322.7243401166 \tabularnewline
73 & 79300 & 91214.9666294894 & -11914.9666294894 \tabularnewline
74 & 63700 & 84678.4813966775 & -20978.4813966775 \tabularnewline
75 & 57200 & 73169.8017570034 & -15969.8017570034 \tabularnewline
76 & 42900 & 64408.8562502631 & -21508.8562502631 \tabularnewline
77 & 63700 & 52609.2158797602 & 11090.7841202398 \tabularnewline
78 & 76700 & 58693.559116008 & 18006.440883992 \tabularnewline
79 & 89700 & 68571.7936586386 & 21128.2063413614 \tabularnewline
80 & 84500 & 80162.6115803863 & 4337.38841961371 \tabularnewline
81 & 62400 & 82542.0790380294 & -20142.0790380294 \tabularnewline
82 & 89700 & 71492.2451371643 & 18207.7548628357 \tabularnewline
83 & 70200 & 81480.9194225814 & -11280.9194225814 \tabularnewline
84 & 107900 & 75292.2690040612 & 32607.7309959388 \tabularnewline
85 & 89700 & 93180.6910834766 & -3480.69108347662 \tabularnewline
86 & 65000 & 91271.2030777935 & -26271.2030777935 \tabularnewline
87 & 59800 & 76858.9654017608 & -17058.9654017608 \tabularnewline
88 & 40300 & 67500.5107033076 & -27200.5107033076 \tabularnewline
89 & 63700 & 52578.4599694793 & 11121.5400305207 \tabularnewline
90 & 61100 & 58679.675729136 & 2420.32427086395 \tabularnewline
91 & 92300 & 60007.4523270128 & 32292.5476729872 \tabularnewline
92 & 92300 & 77722.9665670556 & 14577.0334329444 \tabularnewline
93 & 70200 & 85719.8470230044 & -15519.8470230044 \tabularnewline
94 & 91000 & 77205.7442113111 & 13794.2557886889 \tabularnewline
95 & 67600 & 84773.1971521557 & -17173.1971521557 \tabularnewline
96 & 105300 & 75352.0755430184 & 29947.9244569816 \tabularnewline
97 & 89700 & 91781.3423679826 & -2081.34236798261 \tabularnewline
98 & 66300 & 90639.5293796799 & -24339.5293796799 \tabularnewline
99 & 50700 & 77286.9972819307 & -26586.9972819307 \tabularnewline
100 & 35100 & 62701.5166404631 & -27601.5166404631 \tabularnewline
101 & 68900 & 47559.4762526144 & 21340.5237473856 \tabularnewline
102 & 66300 & 59266.7703368476 & 7033.22966315242 \tabularnewline
103 & 87100 & 63125.1614899028 & 23974.8385100972 \tabularnewline
104 & 100100 & 76277.6261801892 & 23822.3738198108 \tabularnewline
105 & 74100 & 89346.4495790165 & -15246.4495790165 \tabularnewline
106 & 83200 & 80982.3311030655 & 2217.66889693451 \tabularnewline
107 & 62400 & 82198.9320761813 & -19798.9320761813 \tabularnewline
108 & 107900 & 71337.3467133568 & 36562.6532866432 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307286&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]67600[/C][C]70200[/C][C]-2600[/C][/ROW]
[ROW][C]3[/C][C]71500[/C][C]68773.6542842471[/C][C]2726.34571575289[/C][/ROW]
[ROW][C]4[/C][C]57200[/C][C]70269.3125655261[/C][C]-13069.3125655261[/C][/ROW]
[ROW][C]5[/C][C]74100[/C][C]63099.5594941132[/C][C]11000.4405058868[/C][/ROW]
[ROW][C]6[/C][C]72800[/C][C]69134.3407198694[/C][C]3665.65928013057[/C][/ROW]
[ROW][C]7[/C][C]78000[/C][C]71145.3012620325[/C][C]6854.69873796747[/C][/ROW]
[ROW][C]8[/C][C]80600[/C][C]74905.7513303697[/C][C]5694.24866963029[/C][/ROW]
[ROW][C]9[/C][C]89700[/C][C]78029.5848666615[/C][C]11670.4151333385[/C][/ROW]
[ROW][C]10[/C][C]78000[/C][C]84431.9104922366[/C][C]-6431.91049223655[/C][/ROW]
[ROW][C]11[/C][C]74100[/C][C]80903.3997327336[/C][C]-6803.3997327336[/C][/ROW]
[ROW][C]12[/C][C]92300[/C][C]77171.092016834[/C][C]15128.907983166[/C][/ROW]
[ROW][C]13[/C][C]78000[/C][C]85470.7278190681[/C][C]-7470.72781906807[/C][/ROW]
[ROW][C]14[/C][C]58500[/C][C]81372.3275812666[/C][C]-22872.3275812666[/C][/ROW]
[ROW][C]15[/C][C]68900[/C][C]68824.6943294065[/C][C]75.3056705935014[/C][/ROW]
[ROW][C]16[/C][C]52000[/C][C]68866.0066065692[/C][C]-16866.0066065692[/C][/ROW]
[ROW][C]17[/C][C]72800[/C][C]59613.4080430538[/C][C]13186.5919569462[/C][/ROW]
[ROW][C]18[/C][C]59800[/C][C]66847.4999442737[/C][C]-7047.49994427372[/C][/ROW]
[ROW][C]19[/C][C]79300[/C][C]62981.2801933954[/C][C]16318.7198066046[/C][/ROW]
[ROW][C]20[/C][C]71500[/C][C]71933.6402252117[/C][C]-433.640225211697[/C][/ROW]
[ROW][C]21[/C][C]75400[/C][C]71695.7475800545[/C][C]3704.25241994554[/C][/ROW]
[ROW][C]22[/C][C]84500[/C][C]73727.8801066916[/C][C]10772.1198933084[/C][/ROW]
[ROW][C]23[/C][C]83200[/C][C]79637.4058987673[/C][C]3562.59410123265[/C][/ROW]
[ROW][C]24[/C][C]98800[/C][C]81591.8254500211[/C][C]17208.1745499789[/C][/ROW]
[ROW][C]25[/C][C]71500[/C][C]91032.1354674405[/C][C]-19532.1354674405[/C][/ROW]
[ROW][C]26[/C][C]59800[/C][C]80316.9132584063[/C][C]-20516.9132584063[/C][/ROW]
[ROW][C]27[/C][C]66300[/C][C]69061.4473635596[/C][C]-2761.44736355956[/C][/ROW]
[ROW][C]28[/C][C]48100[/C][C]67546.5325111402[/C][C]-19446.5325111402[/C][/ROW]
[ROW][C]29[/C][C]68900[/C][C]56878.2716136348[/C][C]12021.7283863652[/C][/ROW]
[ROW][C]30[/C][C]53300[/C][C]63473.3257597259[/C][C]-10173.3257597259[/C][/ROW]
[ROW][C]31[/C][C]75400[/C][C]57892.2951395938[/C][C]17507.7048604062[/C][/ROW]
[ROW][C]32[/C][C]71500[/C][C]67496.9258397117[/C][C]4003.07416028835[/C][/ROW]
[ROW][C]33[/C][C]63700[/C][C]69692.9903313918[/C][C]-5992.9903313918[/C][/ROW]
[ROW][C]34[/C][C]91000[/C][C]66405.2687607267[/C][C]24594.7312392733[/C][/ROW]
[ROW][C]35[/C][C]81900[/C][C]79897.8031965849[/C][C]2002.19680341509[/C][/ROW]
[ROW][C]36[/C][C]93600[/C][C]80996.1973629869[/C][C]12603.8026370131[/C][/ROW]
[ROW][C]37[/C][C]70200[/C][C]87910.5742451018[/C][C]-17710.5742451018[/C][/ROW]
[ROW][C]38[/C][C]65000[/C][C]78194.6505150924[/C][C]-13194.6505150924[/C][/ROW]
[ROW][C]39[/C][C]58500[/C][C]70956.1377331467[/C][C]-12456.1377331467[/C][/ROW]
[ROW][C]40[/C][C]48100[/C][C]64122.7690060307[/C][C]-16022.7690060307[/C][/ROW]
[ROW][C]41[/C][C]63700[/C][C]55332.7659574729[/C][C]8367.23404252705[/C][/ROW]
[ROW][C]42[/C][C]57200[/C][C]59922.9845841115[/C][C]-2722.98458411149[/C][/ROW]
[ROW][C]43[/C][C]78000[/C][C]58429.1702011851[/C][C]19570.8297988149[/C][/ROW]
[ROW][C]44[/C][C]75400[/C][C]69165.6199078269[/C][C]6234.3800921731[/C][/ROW]
[ROW][C]45[/C][C]65000[/C][C]72585.7665750755[/C][C]-7585.76657507545[/C][/ROW]
[ROW][C]46[/C][C]87100[/C][C]68424.2567077445[/C][C]18675.7432922555[/C][/ROW]
[ROW][C]47[/C][C]80600[/C][C]78669.6668744405[/C][C]1930.33312555954[/C][/ROW]
[ROW][C]48[/C][C]104000[/C][C]79728.6370219857[/C][C]24271.3629780143[/C][/ROW]
[ROW][C]49[/C][C]83200[/C][C]93043.7734062834[/C][C]-9843.77340628344[/C][/ROW]
[ROW][C]50[/C][C]50700[/C][C]87643.5333967086[/C][C]-36943.5333967086[/C][/ROW]
[ROW][C]51[/C][C]50700[/C][C]67376.5139408743[/C][C]-16676.5139408743[/C][/ROW]
[ROW][C]52[/C][C]50700[/C][C]58227.8700126976[/C][C]-7527.87001269759[/C][/ROW]
[ROW][C]53[/C][C]59800[/C][C]54098.1218814069[/C][C]5701.87811859313[/C][/ROW]
[ROW][C]54[/C][C]59800[/C][C]57226.140891484[/C][C]2573.85910851603[/C][/ROW]
[ROW][C]55[/C][C]80600[/C][C]58638.1458577853[/C][C]21961.8541422147[/C][/ROW]
[ROW][C]56[/C][C]74100[/C][C]70686.2983830691[/C][C]3413.70161693092[/C][/ROW]
[ROW][C]57[/C][C]66300[/C][C]72559.0363354414[/C][C]-6259.03633544144[/C][/ROW]
[ROW][C]58[/C][C]83200[/C][C]69125.3633885958[/C][C]14074.6366114042[/C][/ROW]
[ROW][C]59[/C][C]76700[/C][C]76846.6317083863[/C][C]-146.631708386267[/C][/ROW]
[ROW][C]60[/C][C]110500[/C][C]76766.1903587515[/C][C]33733.8096412485[/C][/ROW]
[ROW][C]61[/C][C]87100[/C][C]95272.372996374[/C][C]-8172.37299637398[/C][/ROW]
[ROW][C]62[/C][C]50700[/C][C]90789.0540690999[/C][C]-40089.0540690999[/C][/ROW]
[ROW][C]63[/C][C]53300[/C][C]68796.4192536973[/C][C]-15496.4192536973[/C][/ROW]
[ROW][C]64[/C][C]44200[/C][C]60295.1687875351[/C][C]-16095.1687875351[/C][/ROW]
[ROW][C]65[/C][C]61100[/C][C]51465.4476166042[/C][C]9634.55238339581[/C][/ROW]
[ROW][C]66[/C][C]70200[/C][C]56750.9101224709[/C][C]13449.0898775291[/C][/ROW]
[ROW][C]67[/C][C]88400[/C][C]64129.0069407744[/C][C]24270.9930592256[/C][/ROW]
[ROW][C]68[/C][C]87100[/C][C]77443.940389657[/C][C]9656.05961034304[/C][/ROW]
[ROW][C]69[/C][C]70200[/C][C]82741.2016420675[/C][C]-12541.2016420675[/C][/ROW]
[ROW][C]70[/C][C]81900[/C][C]75861.1673218536[/C][C]6038.8326781464[/C][/ROW]
[ROW][C]71[/C][C]72800[/C][C]79174.0377520931[/C][C]-6374.03775209309[/C][/ROW]
[ROW][C]72[/C][C]104000[/C][C]75677.2756598834[/C][C]28322.7243401166[/C][/ROW]
[ROW][C]73[/C][C]79300[/C][C]91214.9666294894[/C][C]-11914.9666294894[/C][/ROW]
[ROW][C]74[/C][C]63700[/C][C]84678.4813966775[/C][C]-20978.4813966775[/C][/ROW]
[ROW][C]75[/C][C]57200[/C][C]73169.8017570034[/C][C]-15969.8017570034[/C][/ROW]
[ROW][C]76[/C][C]42900[/C][C]64408.8562502631[/C][C]-21508.8562502631[/C][/ROW]
[ROW][C]77[/C][C]63700[/C][C]52609.2158797602[/C][C]11090.7841202398[/C][/ROW]
[ROW][C]78[/C][C]76700[/C][C]58693.559116008[/C][C]18006.440883992[/C][/ROW]
[ROW][C]79[/C][C]89700[/C][C]68571.7936586386[/C][C]21128.2063413614[/C][/ROW]
[ROW][C]80[/C][C]84500[/C][C]80162.6115803863[/C][C]4337.38841961371[/C][/ROW]
[ROW][C]81[/C][C]62400[/C][C]82542.0790380294[/C][C]-20142.0790380294[/C][/ROW]
[ROW][C]82[/C][C]89700[/C][C]71492.2451371643[/C][C]18207.7548628357[/C][/ROW]
[ROW][C]83[/C][C]70200[/C][C]81480.9194225814[/C][C]-11280.9194225814[/C][/ROW]
[ROW][C]84[/C][C]107900[/C][C]75292.2690040612[/C][C]32607.7309959388[/C][/ROW]
[ROW][C]85[/C][C]89700[/C][C]93180.6910834766[/C][C]-3480.69108347662[/C][/ROW]
[ROW][C]86[/C][C]65000[/C][C]91271.2030777935[/C][C]-26271.2030777935[/C][/ROW]
[ROW][C]87[/C][C]59800[/C][C]76858.9654017608[/C][C]-17058.9654017608[/C][/ROW]
[ROW][C]88[/C][C]40300[/C][C]67500.5107033076[/C][C]-27200.5107033076[/C][/ROW]
[ROW][C]89[/C][C]63700[/C][C]52578.4599694793[/C][C]11121.5400305207[/C][/ROW]
[ROW][C]90[/C][C]61100[/C][C]58679.675729136[/C][C]2420.32427086395[/C][/ROW]
[ROW][C]91[/C][C]92300[/C][C]60007.4523270128[/C][C]32292.5476729872[/C][/ROW]
[ROW][C]92[/C][C]92300[/C][C]77722.9665670556[/C][C]14577.0334329444[/C][/ROW]
[ROW][C]93[/C][C]70200[/C][C]85719.8470230044[/C][C]-15519.8470230044[/C][/ROW]
[ROW][C]94[/C][C]91000[/C][C]77205.7442113111[/C][C]13794.2557886889[/C][/ROW]
[ROW][C]95[/C][C]67600[/C][C]84773.1971521557[/C][C]-17173.1971521557[/C][/ROW]
[ROW][C]96[/C][C]105300[/C][C]75352.0755430184[/C][C]29947.9244569816[/C][/ROW]
[ROW][C]97[/C][C]89700[/C][C]91781.3423679826[/C][C]-2081.34236798261[/C][/ROW]
[ROW][C]98[/C][C]66300[/C][C]90639.5293796799[/C][C]-24339.5293796799[/C][/ROW]
[ROW][C]99[/C][C]50700[/C][C]77286.9972819307[/C][C]-26586.9972819307[/C][/ROW]
[ROW][C]100[/C][C]35100[/C][C]62701.5166404631[/C][C]-27601.5166404631[/C][/ROW]
[ROW][C]101[/C][C]68900[/C][C]47559.4762526144[/C][C]21340.5237473856[/C][/ROW]
[ROW][C]102[/C][C]66300[/C][C]59266.7703368476[/C][C]7033.22966315242[/C][/ROW]
[ROW][C]103[/C][C]87100[/C][C]63125.1614899028[/C][C]23974.8385100972[/C][/ROW]
[ROW][C]104[/C][C]100100[/C][C]76277.6261801892[/C][C]23822.3738198108[/C][/ROW]
[ROW][C]105[/C][C]74100[/C][C]89346.4495790165[/C][C]-15246.4495790165[/C][/ROW]
[ROW][C]106[/C][C]83200[/C][C]80982.3311030655[/C][C]2217.66889693451[/C][/ROW]
[ROW][C]107[/C][C]62400[/C][C]82198.9320761813[/C][C]-19798.9320761813[/C][/ROW]
[ROW][C]108[/C][C]107900[/C][C]71337.3467133568[/C][C]36562.6532866432[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307286&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307286&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	67600	70200	-2600
3	71500	68773.6542842471	2726.34571575289
4	57200	70269.3125655261	-13069.3125655261
5	74100	63099.5594941132	11000.4405058868
6	72800	69134.3407198694	3665.65928013057
7	78000	71145.3012620325	6854.69873796747
8	80600	74905.7513303697	5694.24866963029
9	89700	78029.5848666615	11670.4151333385
10	78000	84431.9104922366	-6431.91049223655
11	74100	80903.3997327336	-6803.3997327336
12	92300	77171.092016834	15128.907983166
13	78000	85470.7278190681	-7470.72781906807
14	58500	81372.3275812666	-22872.3275812666
15	68900	68824.6943294065	75.3056705935014
16	52000	68866.0066065692	-16866.0066065692
17	72800	59613.4080430538	13186.5919569462
18	59800	66847.4999442737	-7047.49994427372
19	79300	62981.2801933954	16318.7198066046
20	71500	71933.6402252117	-433.640225211697
21	75400	71695.7475800545	3704.25241994554
22	84500	73727.8801066916	10772.1198933084
23	83200	79637.4058987673	3562.59410123265
24	98800	81591.8254500211	17208.1745499789
25	71500	91032.1354674405	-19532.1354674405
26	59800	80316.9132584063	-20516.9132584063
27	66300	69061.4473635596	-2761.44736355956
28	48100	67546.5325111402	-19446.5325111402
29	68900	56878.2716136348	12021.7283863652
30	53300	63473.3257597259	-10173.3257597259
31	75400	57892.2951395938	17507.7048604062
32	71500	67496.9258397117	4003.07416028835
33	63700	69692.9903313918	-5992.9903313918
34	91000	66405.2687607267	24594.7312392733
35	81900	79897.8031965849	2002.19680341509
36	93600	80996.1973629869	12603.8026370131
37	70200	87910.5742451018	-17710.5742451018
38	65000	78194.6505150924	-13194.6505150924
39	58500	70956.1377331467	-12456.1377331467
40	48100	64122.7690060307	-16022.7690060307
41	63700	55332.7659574729	8367.23404252705
42	57200	59922.9845841115	-2722.98458411149
43	78000	58429.1702011851	19570.8297988149
44	75400	69165.6199078269	6234.3800921731
45	65000	72585.7665750755	-7585.76657507545
46	87100	68424.2567077445	18675.7432922555
47	80600	78669.6668744405	1930.33312555954
48	104000	79728.6370219857	24271.3629780143
49	83200	93043.7734062834	-9843.77340628344
50	50700	87643.5333967086	-36943.5333967086
51	50700	67376.5139408743	-16676.5139408743
52	50700	58227.8700126976	-7527.87001269759
53	59800	54098.1218814069	5701.87811859313
54	59800	57226.140891484	2573.85910851603
55	80600	58638.1458577853	21961.8541422147
56	74100	70686.2983830691	3413.70161693092
57	66300	72559.0363354414	-6259.03633544144
58	83200	69125.3633885958	14074.6366114042
59	76700	76846.6317083863	-146.631708386267
60	110500	76766.1903587515	33733.8096412485
61	87100	95272.372996374	-8172.37299637398
62	50700	90789.0540690999	-40089.0540690999
63	53300	68796.4192536973	-15496.4192536973
64	44200	60295.1687875351	-16095.1687875351
65	61100	51465.4476166042	9634.55238339581
66	70200	56750.9101224709	13449.0898775291
67	88400	64129.0069407744	24270.9930592256
68	87100	77443.940389657	9656.05961034304
69	70200	82741.2016420675	-12541.2016420675
70	81900	75861.1673218536	6038.8326781464
71	72800	79174.0377520931	-6374.03775209309
72	104000	75677.2756598834	28322.7243401166
73	79300	91214.9666294894	-11914.9666294894
74	63700	84678.4813966775	-20978.4813966775
75	57200	73169.8017570034	-15969.8017570034
76	42900	64408.8562502631	-21508.8562502631
77	63700	52609.2158797602	11090.7841202398
78	76700	58693.559116008	18006.440883992
79	89700	68571.7936586386	21128.2063413614
80	84500	80162.6115803863	4337.38841961371
81	62400	82542.0790380294	-20142.0790380294
82	89700	71492.2451371643	18207.7548628357
83	70200	81480.9194225814	-11280.9194225814
84	107900	75292.2690040612	32607.7309959388
85	89700	93180.6910834766	-3480.69108347662
86	65000	91271.2030777935	-26271.2030777935
87	59800	76858.9654017608	-17058.9654017608
88	40300	67500.5107033076	-27200.5107033076
89	63700	52578.4599694793	11121.5400305207
90	61100	58679.675729136	2420.32427086395
91	92300	60007.4523270128	32292.5476729872
92	92300	77722.9665670556	14577.0334329444
93	70200	85719.8470230044	-15519.8470230044
94	91000	77205.7442113111	13794.2557886889
95	67600	84773.1971521557	-17173.1971521557
96	105300	75352.0755430184	29947.9244569816
97	89700	91781.3423679826	-2081.34236798261
98	66300	90639.5293796799	-24339.5293796799
99	50700	77286.9972819307	-26586.9972819307
100	35100	62701.5166404631	-27601.5166404631
101	68900	47559.4762526144	21340.5237473856
102	66300	59266.7703368476	7033.22966315242
103	87100	63125.1614899028	23974.8385100972
104	100100	76277.6261801892	23822.3738198108
105	74100	89346.4495790165	-15246.4495790165
106	83200	80982.3311030655	2217.66889693451
107	62400	82198.9320761813	-19798.9320761813
108	107900	71337.3467133568	36562.6532866432

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
109	91395.4174333422	58411.3196805245	124379.51518616
110	91395.4174333422	53773.9352334695	129016.899633215
111	91395.4174333422	49648.5475954341	133142.28727125
112	91395.4174333422	45895.6772185767	136895.157648108
113	91395.4174333422	42429.5969259817	140361.237940703
114	91395.4174333422	39193.1493187578	143597.685547926
115	91395.4174333422	36145.9648147428	146644.870051941
116	91395.4174333422	33258.2758369173	149532.559029767
117	91395.4174333422	30507.3853469735	152283.449519711
118	91395.4174333422	27875.5176404539	154915.31722623
119	91395.4174333422	25348.4425741825	157442.392292502
120	91395.4174333422	22914.5580170471	159876.276849637

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 91395.4174333422 & 58411.3196805245 & 124379.51518616 \tabularnewline
110 & 91395.4174333422 & 53773.9352334695 & 129016.899633215 \tabularnewline
111 & 91395.4174333422 & 49648.5475954341 & 133142.28727125 \tabularnewline
112 & 91395.4174333422 & 45895.6772185767 & 136895.157648108 \tabularnewline
113 & 91395.4174333422 & 42429.5969259817 & 140361.237940703 \tabularnewline
114 & 91395.4174333422 & 39193.1493187578 & 143597.685547926 \tabularnewline
115 & 91395.4174333422 & 36145.9648147428 & 146644.870051941 \tabularnewline
116 & 91395.4174333422 & 33258.2758369173 & 149532.559029767 \tabularnewline
117 & 91395.4174333422 & 30507.3853469735 & 152283.449519711 \tabularnewline
118 & 91395.4174333422 & 27875.5176404539 & 154915.31722623 \tabularnewline
119 & 91395.4174333422 & 25348.4425741825 & 157442.392292502 \tabularnewline
120 & 91395.4174333422 & 22914.5580170471 & 159876.276849637 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307286&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]109[/C][C]91395.4174333422[/C][C]58411.3196805245[/C][C]124379.51518616[/C][/ROW]
[ROW][C]110[/C][C]91395.4174333422[/C][C]53773.9352334695[/C][C]129016.899633215[/C][/ROW]
[ROW][C]111[/C][C]91395.4174333422[/C][C]49648.5475954341[/C][C]133142.28727125[/C][/ROW]
[ROW][C]112[/C][C]91395.4174333422[/C][C]45895.6772185767[/C][C]136895.157648108[/C][/ROW]
[ROW][C]113[/C][C]91395.4174333422[/C][C]42429.5969259817[/C][C]140361.237940703[/C][/ROW]
[ROW][C]114[/C][C]91395.4174333422[/C][C]39193.1493187578[/C][C]143597.685547926[/C][/ROW]
[ROW][C]115[/C][C]91395.4174333422[/C][C]36145.9648147428[/C][C]146644.870051941[/C][/ROW]
[ROW][C]116[/C][C]91395.4174333422[/C][C]33258.2758369173[/C][C]149532.559029767[/C][/ROW]
[ROW][C]117[/C][C]91395.4174333422[/C][C]30507.3853469735[/C][C]152283.449519711[/C][/ROW]
[ROW][C]118[/C][C]91395.4174333422[/C][C]27875.5176404539[/C][C]154915.31722623[/C][/ROW]
[ROW][C]119[/C][C]91395.4174333422[/C][C]25348.4425741825[/C][C]157442.392292502[/C][/ROW]
[ROW][C]120[/C][C]91395.4174333422[/C][C]22914.5580170471[/C][C]159876.276849637[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307286&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307286&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
109	91395.4174333422	58411.3196805245	124379.51518616
110	91395.4174333422	53773.9352334695	129016.899633215
111	91395.4174333422	49648.5475954341	133142.28727125
112	91395.4174333422	45895.6772185767	136895.157648108
113	91395.4174333422	42429.5969259817	140361.237940703
114	91395.4174333422	39193.1493187578	143597.685547926
115	91395.4174333422	36145.9648147428	146644.870051941
116	91395.4174333422	33258.2758369173	149532.559029767
117	91395.4174333422	30507.3853469735	152283.449519711
118	91395.4174333422	27875.5176404539	154915.31722623
119	91395.4174333422	25348.4425741825	157442.392292502
120	91395.4174333422	22914.5580170471	159876.276849637

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):

Parameters (R input):

par1 = 12 ; par2 = Single ; par3 = additive ; par4 = 12 ;

R code (references can be found in the software module):

par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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