Home » date » 2009 » Jun » 08 »

Wim Gabriels Opgave 10 Aantal kinderen

*Unverified author*
R Software Module: rwasp_exponentialsmoothing.wasp (opens new window with default values)
Title produced by software: Exponential Smoothing
Date of computation: Mon, 08 Jun 2009 00:00:56 -0600
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Jun/08/t1244440912p3t0mbax5cn9y4o.htm/, Retrieved Mon, 08 Jun 2009 08:01:52 +0200
 
BibTeX entries for LaTeX users:
@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2009/Jun/08/t1244440912p3t0mbax5cn9y4o.htm/},
    year = {2009},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2009},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}
 
Original text written by user:
 
IsPrivate?
No (this computation is public)
 
User-defined keywords:
 
Dataseries X:
» Textbox « » Textfile « » CSV «
374 572 402 589 507 628 698 451 694 488 526 343 494 447 470 366 517 483 485 530 308 481 437 468 502 408 479 436 410 451 344 411 427 454 365 499 416 430 470 325 452 442 488 446 523 594 439 588 503 444 525 375 472 436 458 514 472 360 450 549 361 466 387 457 470 396 471 422 404 414 342 459 379 0 410 319 411 371 365 429 333 392 469 432 534 379 436 448 358 492 387 529 475 439 459 361 394 425 341 455 403 471 523 389 531 468 398 446 355 435 353 400 332 389 355 384 406 356 336 351 278 265 229 387 435 317 490 472 440 429 350 489 494 436 436 375 429 434 472 362 440 433 400 442 316 432 401 434 488 377 484 377 300 389 337 376 377 331 339 356 280 249 196 268 379 401 404 397 419 421 407 296 468 475 422 456 339 446 419 346 327 326 403 359 358 421 322 367 394 356 418 344 372 358 373 379 348 369 341 390 279 325 354 346 358 2 etc...
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24


Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.414557442391802
beta0.42808673791782
gamma0


Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3402770-368
4589750.13517330477-161.135173304770
5507787.431597891926-280.431597891926
6628725.505575535757-97.5055755357569
7698722.108919722086-24.1089197220864
8451744.860867179445-293.860867179445
9694603.63466494062190.3653350593786
10488637.729118039311-149.729118039311
11526545.718719735167-19.7187197351666
12343504.105686608735-161.105686608735
13494375.288764816466118.711235183534
14447383.53930300654763.4606969934532
15470380.14746991782889.8525300821722
16366403.642385565233-37.6423855652331
17517367.603071020089149.396928979911
18483435.6152528892247.38474711078
19485469.74673281970415.2532671802959
20530493.2648132088336.7351867911696
21308532.207649862887-224.207649862887
22481423.18533496456957.8146650354306
23437441.337638377616-4.33763837761632
24468432.95445616049435.0455438395059
25502447.11727675607054.8827232439295
26408479.243594884934-71.2435948849337
27479446.43995464312432.5600453568756
28436462.447204706612-26.4472047066124
29410449.299066104806-39.2990661048055
30451423.84882329945427.1511767005456
31344430.764448670474-86.7644486704736
32411375.0577169616235.9422830383803
33427376.59852683953350.4014731604668
34454393.07807680714260.9219231928583
35365424.730560746699-59.7305607466989
36499395.765483387355103.234516612645
37416452.679464498736-36.6794644987363
38430445.081685674965-15.0816856749649
39470443.7609321794626.2390678205404
40325464.226561233473-139.226561233473
41452391.38912576034260.6108742396581
42442412.15218876231129.8478112376894
43488425.45918292827762.540817071723
44446463.418208591089-17.4182085910890
45523465.13847581170957.8615241882912
46594508.33500119886585.6649988011354
47439578.260335121002-139.260335121002
48588530.22714760542457.7728523945759
49503574.128282777477-71.1282827774771
50444551.969602563426-107.969602563426
51525495.37708690771429.6229130922860
52375501.081648620284-126.081648620284
53472419.86245111983152.1375488801692
54436421.77801889060814.2219811093923
55458410.49933168433947.5006683156609
56514421.44635133779992.5536486622015
57472467.4955953838344.50440461616597
58360477.842751129987-117.842751129987
59450416.55683722270533.4431627772954
60549423.922667346261125.077332653739
61361491.473166427359-130.473166427359
62466429.92868238213336.0713176178674
63387443.827905733219-56.8279057332193
64457409.13001266431947.869987335681
65470426.33073154503143.6692684549686
66396449.539845266822-53.5398452668218
67471422.94866616433948.0513338356614
68422447.000370551779-25.0003705517790
69404436.33121786563-32.3312178656303
70414416.885298394651-2.88529839465144
71342409.134360056257-67.1343600562572
72459362.83439223069296.1656077693078
73379401.297819394436-22.2978193944359
740386.694234247537-386.694234247537
75410152.402114317796257.597885682204
76319230.92109408518388.0789059148174
77411254.795778124263156.204221875737
78371334.63334219868536.3666578013147
79365371.245217255435-6.24521725543542
80429389.08370525532839.9162947446716
81333433.142598452336-100.142598452336
82392401.367074327659-9.36707432765928
83469405.56087701512163.4391229848786
84432451.195352510068-19.1953525100681
85534459.16655833510874.8334416648924
86379519.398532792012-140.398532792012
87436465.488448113148-29.4884481131483
88448452.323751523444-4.32375152344417
89358448.823945954042-90.8239459540422
90492393.34662928748098.6533707125195
91387433.926217084165-46.9262170841647
92529405.826869768349123.173130231651
93475470.1025824647724.8974175352277
94439486.215345969249-47.2153459692489
95459472.345231284514-13.3452312845136
96361470.147892652825-109.147892652825
97394408.864748544057-14.8647485440567
98425384.02938797812940.9706120218706
99341389.611904571463-48.6119045714626
100455349.430335540514105.569664459486
101403391.90096684866711.0990331513332
102471397.17780190672573.8221980932748
103523441.55796210836181.442037891639
104389503.550220543469-114.550220543469
105531463.96359793127467.0364020687263
106468511.551779704992-43.5517797049924
107398505.565823889688-107.565823889688
108446453.953034708604-7.95303470860352
109355442.224071062313-87.224071062313
110435382.15335495482652.8466450451735
111353389.528508086365-36.5285080863655
112400353.36993826423146.6300617357691
113332359.960648325647-27.9606483256466
114389330.66714479402458.3328552059761
115355347.4993855494857.5006144505154
116384344.58985070467439.4101492953259
117406361.90263397520444.0973660247957
118356388.984344937379-32.9843449373792
119336378.257641272367-42.2576412723665
120351356.187306076081-5.18730607608086
121278348.564180949568-70.5641809495677
122265301.315804517564-36.3158045175635
123229261.820507134276-32.8205071342757
124387217.949669347639169.050330652361
125435287.76666757384147.23333242616
126317374.668257363186-57.6682573631857
127490366.392181861234123.607818138766
128472455.20170478291816.7982952170824
129440502.713680442812-62.7136804428118
130429506.133794754521-77.133794754521
131350489.887275439723-139.887275439723
132489422.800522461966.1994775380996
133494452.89675914926941.1032408507314
134436479.883614209673-43.8836142096733
135436463.850662682705-27.8506626827051
136375449.521729702813-74.521729702813
137429402.61984478224326.3801552177574
138434402.22918216224831.7708178377523
139472409.71151606687762.2884839331227
140362440.899297500119-78.8992975001186
141440399.55464777771640.4453522222845
142433414.86290765449218.1370923455081
143400424.141839454671-24.141839454671
144442411.60935662636830.3906433736319
145316427.077042831573-111.077042831573
146432364.18578804303567.814211956965
147401387.48998808125813.5100119187421
148434390.67955295421843.3204470457815
149488413.91518555682474.0848144431758
150377463.051991546825-86.0519915468253
151484430.53154333812653.4684566618744
152377465.339197473833-88.3391974738332
153300425.68218119533-125.682181195330
154389348.23997085626540.7600291437346
155337347.031159013989-10.0311590139888
156376322.98628699857353.013713001427
157377334.48529626997942.5147037300212
158331349.176800616027-18.1768006160268
159339335.4824161738303.51758382616953
160356331.40585370227824.5941462977224
161280340.431375189584-60.431375189584
162249303.484386695785-54.484386695785
163196259.333610777014-63.3336107770138
164268200.27472618344567.725273816555
165379207.566247820736171.433752179264
166401288.274646388287112.725353611713
167404364.65002023444239.349979765558
168397417.590391648103-20.590391648103
169419442.027930363722-23.0279303637218
170421461.368282065122-40.3682820651225
171407466.356042442276-59.3560424422764
172296452.938573770878-156.938573770878
173468371.21619430900996.783805690991
174475411.85220298746463.1477970125359
175422449.750775181982-27.7507751819823
176456445.04183362810.9581663719998
177339458.324679788104-119.324679788104
178446396.42166401693749.5783359830633
179419413.3371463803055.66285361969483
180346413.052105750209-67.0521057502089
181327370.723032118796-43.7230321187964
182326330.30582421735-4.30582421735022
183403305.46517347030397.5348265296965
184359340.15249093362918.8475090663707
185358345.56419760249612.4358023975043
186421350.52482241666770.4751775833326
187322392.053088312526-70.0530883125255
188367362.8922362920194.10776370798061
189394365.20430803624028.7956919637596
190356382.86121608779-26.8612160877901
191418372.67817152099245.3218284790083
192344400.462253525217-56.4622535252172
193372376.030825863563-4.03082586356294
194358372.619900022055-14.6199000220552
195373362.22465156136310.7753484386365
196379364.26945619054614.730543809454
197348370.568095186032-22.5680951860323
198369357.39922395573811.6007760442625
199341360.454062215021-19.4540622150207
200390347.18244097928242.8175590207181
201279367.324667963994-88.3246679639938
202325317.4262352381137.57376476188665
203354308.62730136370645.3726986362943
204346323.55033282373322.449667176267
205358332.95451581943125.0454841805686
206296347.879549573472-51.8795495734723
207356321.70785375331834.2921462466824
208337337.344984412000-0.344984412000372
209360338.56181158197621.4381884180243
210474352.613576358413121.386423641587
211362429.641654894946-67.6416548949456
212440416.30260598307323.6973940169275
213443445.034334177473-2.03433417747328
214435462.737756689107-27.7377566891066
215429464.863110308055-35.8631103080554
216341457.255535897682-116.255535897682
217434395.68921506438138.3107849356192
218329404.998395445181-75.998395445181
219416353.43268183753862.567318162462
220430370.41402173742759.585978262573
221307396.733942578553-89.7339425785531
222408345.22740634113562.7725936588649
223322368.083624918235-46.0836249182352
224324337.634386321525-13.6343863215249
225303318.217573675988-15.2175736759884
226369295.44382873389573.556171266105
227328322.5256598916515.4743401083494
228258322.355173466588-64.3551734665884
229372281.81545231873190.184547681269
230298321.346062644296-23.3460626442964
231376309.66856848546366.3314315145369
232306346.939156801154-40.9391568011537
233359332.47459374208826.5254062579118
234418350.68533955225367.3146604477474
235311397.751674352301-86.7516743523007
236355365.553143675449-10.5531436754488
237335363.070451062104-28.0704510621043
238345348.344262385095-3.34426238509525
239318343.275004561111-25.2750045611108
240291324.628726662234-33.6287266622341
241340296.55137722193343.4486227780671
2420308.137693522865-308.137693522865
243356119.287154461142236.712845538858
244419198.317071785815220.682928214185
245296309.865503994514-13.8655039945142
246361321.71947496623239.2805250337682
247371362.5765067977468.42349320225406
248392392.136414653600-0.136414653599502
249383418.123539964606-35.1235399646057
250286423.373238867818-137.373238867818
251362361.8554102792760.144589720723957
252358357.3722808315930.627719168407396


Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
253353.200835442998184.111170231117522.290500654879
254348.769164401409152.268901197122545.269427605695
255344.337493359819108.664586309650580.010400409988
256339.90582231822954.9841786314051624.827466005053
257335.474151276640-7.05928699747852678.007589550758
258331.04248023505-76.1295842866999738.2145447568
259326.61080919346-151.26059143605804.48220982297
260322.179138151871-231.757720794500876.11599709824
261317.747467110281-317.110726293215952.605660513776
262313.315796068691-406.933225285391033.56481742277
263308.884125027102-500.9233557450991118.69160579930
264304.452453985512-598.8383996802581207.74330765128
 
Charts produced by software:
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/08/t1244440912p3t0mbax5cn9y4o/13cz41244440850.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/08/t1244440912p3t0mbax5cn9y4o/13cz41244440850.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/08/t1244440912p3t0mbax5cn9y4o/2d34m1244440850.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/08/t1244440912p3t0mbax5cn9y4o/2d34m1244440850.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/08/t1244440912p3t0mbax5cn9y4o/3mb291244440850.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/08/t1244440912p3t0mbax5cn9y4o/3mb291244440850.ps (open in new window)


 
Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
 
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
 
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=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')
 




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Software written by Ed van Stee & Patrick Wessa


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  • enforce strict security rules with respect to the data that you upload (e.g. statistical data)
  • manage user sessions of online applications
  • alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

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