Home » date » 2010 » Dec » 09 »

MR monthly dummies lag 2

*The author of this computation has been verified*

R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Thu, 09 Dec 2010 18:16:30 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/09/t1291918699j61oqem75886vyx.htm/, Retrieved Thu, 09 Dec 2010 19:18:19 +0100

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/2010/Dec/09/t1291918699j61oqem75886vyx.htm/},
    year = {2010},
}
@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 = {2010},
    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 «

29462 27071 31514 26105 29462 27071 22397 26105 29462 23843 22397 26105 21705 23843 22397 18089 21705 23843 20764 18089 21705 25316 20764 18089 17704 25316 20764 15548 17704 25316 28029 15548 17704 29383 28029 15548 36438 29383 28029 32034 36438 29383 22679 32034 36438 24319 22679 32034 18004 24319 22679 17537 18004 24319 20366 17537 18004 22782 20366 17537 19169 22782 20366 13807 19169 22782 29743 13807 19169 25591 29743 13807 29096 25591 29743 26482 29096 25591 22405 26482 29096 27044 22405 26482 17970 27044 22405 18730 17970 27044 19684 18730 17970 19785 19684 18730 18479 19785 19684 10698 18479 19785 31956 10698 18479 29506 31956 10698 34506 29506 31956 27165 34506 29506 26736 27165 34506 23691 26736 27165 18157 23691 26736 17328 18157 23691 18205 17328 18157 20995 18205 17328 17382 20995 18205 9367 17382 20995 31124 9367 17382 26551 31124 9367 30651 26551 31124 25859 30651 26551 25100 25859 30651 25778 25100 25859 20418 25778 25100 18688 20418 25778 2 etc...

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits!

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Multiple Linear Regression - Estimated Regression Equation

y[t] = + 16510.6896674354 + 0.251370081323887Y1[t] + 0.291282697554051Y2[t] -992.075478863592M1[t] -4371.92634928235M2[t] -8944.9925952338M3[t] -5710.44611500409M4[t] -10306.7772526267M5[t] -10751.6786143463M6[t] -6642.18393311063M7[t] -4079.73917109206M8[t] -9912.24814850308M9[t] -15067.1659191166M10[t] + 4798.2828258261M11[t] + e[t]

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.D.	T-STAT H0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	16510.6896674354	3343.172545	4.9386	5e-06	3e-06
Y1	0.251370081323887	0.116551	2.1567	0.034565	0.017282
Y2	0.291282697554051	0.116045	2.5101	0.014455	0.007228
M1	-992.075478863592	2386.407136	-0.4157	0.678924	0.339462
M2	-4371.92634928235	2004.227409	-2.1814	0.032618	0.016309
M3	-8944.9925952338	2491.833178	-3.5897	0.00062	0.00031
M4	-5710.44611500409	2399.809757	-2.3795	0.020146	0.010073
M5	-10306.7772526267	1908.548033	-5.4003	1e-06	0
M6	-10751.6786143463	2423.762695	-4.4359	3.4e-05	1.7e-05
M7	-6642.18393311063	2101.60275	-3.1605	0.002352	0.001176
M8	-4079.73917109206	1809.599338	-2.2545	0.02739	0.013695
M9	-9912.24814850308	1747.228896	-5.6731	0	0
M10	-15067.1659191166	2335.655589	-6.4509	0	0
M11	4798.2828258261	2576.42146	1.8624	0.06687	0.033435

Multiple Linear Regression - Regression Statistics
Multiple R	0.953135347564555
R-squared	0.908466990777004
Adjusted R-squared	0.890968033131431
F-TEST (value)	51.9154917211224
F-TEST (DF numerator)	13
F-TEST (DF denominator)	68
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	1875.05245376751
Sum Squared Residuals	239075875.897811

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	29462	31502.9365908092	-2040.93659080918
2	26105	27429.9425596032	-1324.94255960315
3	22397	22709.4838804992	-312.483880499165
4	23843	24034.1140834909	-191.114083490946
5	21705	18721.1878409322	2983.81215906777
6	18089	18160.0520260053	-71.052026005286
7	20764	20737.8300858033	26.1699141967162
8	25316	22919.4115810078	2396.58841899221
9	17704	19010.3204297402	-1306.32042974019
10	15548	13267.8924393553	2280.10756064471
11	28029	30374.1433951823	-2345.14339518225
12	29383	28085.2050584330	1297.79494156696
13	36438	31068.9840178541	5369.0159821459
14	32034	29856.9458436636	2177.05415633645
15	22679	26231.8451908056	-3552.84519080555
16	24319	25832.0155602223	-1513.01556022225
17	18004	18922.9817203526	-918.981720352644
18	17537	17368.3819190613	168.618080938683
19	20366	19521.0365372649	844.963462735053
20	22782	22658.5782395911	123.421760408949
21	19169	18257.4181300390	911.581869961049
22	13807	12898.0392528928	908.96074710718
23	29743	30363.2372355140	-620.237235514046
24	25591	28008.9302013806	-2417.93020138058
25	29096	30615.0472130816	-1519.04721308157
26	26482	26906.8427174586	-424.842717458617
27	22405	22697.6409338535	-292.640933853485
28	27044	24145.9386211194	2898.06137888059
29	17970	19528.1537328304	-1558.15373283043
30	18730	18153.5806871311	576.419312868906
31	19684	19811.0174325675	-127.017432567508
32	19785	22834.6441023101	-3049.64410231014
33	18479	17305.4071965794	1173.59280342060
34	10698	11851.6196522098	-1153.61965220984
35	31956	29380.7425913658	2575.25740863421
36	29506	27659.6142846548	1846.38571534520
37	34506	32243.7696911517	2262.23030884830
38	27165	29407.1266183450	-2242.12661834495
39	26736	24445.1660931651	2290.83390683488
40	23691	25433.5685257626	-1742.56852576258
41	18157	19946.8552132580	-1789.85521325803
42	17328	17223.9160074399	104.083992560075
43	18205	19513.0664429940	-1308.06644299403
44	20995	22054.4894100613	-1059.48941006134
45	17382	17178.7578852989	203.242114701141
46	9367	11928.3187370379	-2561.31873703794
47	31124	28726.6318939069	2397.3681060931
48	26551	27062.7771065489	-511.777106548881
49	30651	31258.6238964747	-607.62389647465
50	25859	27577.3545835692	-1718.35458356915
51	25100	22993.9819678853	2106.01803211475
52	25778	24641.9118697111	1136.08813028889
53	20418	19994.9260797826	423.073920217445
54	18688	18400.1707511085	287.829248891461
55	20424	20513.5199327642	-89.5199327642223
56	24776	23008.4240891926	1767.57591080745
57	19814	18775.5444686569	1038.45553134309
58	12738	13640.9906542695	-902.9906542695
59	31566	30282.3999585012	1283.60004149882
60	30111	28155.7966559487	1955.20334405126
61	30019	32282.2483383066	-2263.24833830658
62	31934	28455.4550954649	3478.54490453512
63	25826	24336.9645470737	1489.03545292630
64	26835	26593.9489363931	241.051063606884
65	20205	20472.0954941661	-267.095494166143
66	17789	18654.5147351012	-865.514735101183
67	20520	20225.4950150750	294.504984924965
68	22518	22770.6924718986	-252.69247189855
69	15572	18235.9139639928	-2663.91396399277
70	11509	11916.9624382165	-407.962438216525
71	25447	28737.8449255298	-3290.84492552983
72	24090	26259.6766930340	-2169.67669303395
73	27786	28986.3902523222	-1200.39025232222
74	26195	26140.3325818957	54.6674181043054
75	20516	22243.9173867177	-1727.91738671772
76	22759	23587.5024033006	-828.502403300579
77	19028	17900.7999186780	1127.20008132203
78	16971	17171.3838741527	-200.383874152656
79	20036	19677.0345535310	358.965446469022
80	22485	22410.7601059386	74.2398940614242
81	18730	18086.6379256929	643.362074307082
82	14538	12701.1768260181	1836.82317398192

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/09/t1291918699j61oqem75886vyx/1sn6j1291918582.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/09/t1291918699j61oqem75886vyx/1sn6j1291918582.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/09/t1291918699j61oqem75886vyx/23e541291918582.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/09/t1291918699j61oqem75886vyx/23e541291918582.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/09/t1291918699j61oqem75886vyx/33e541291918582.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/09/t1291918699j61oqem75886vyx/33e541291918582.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/09/t1291918699j61oqem75886vyx/4vnnp1291918582.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/09/t1291918699j61oqem75886vyx/4vnnp1291918582.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/09/t1291918699j61oqem75886vyx/5vnnp1291918582.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/09/t1291918699j61oqem75886vyx/5vnnp1291918582.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/09/t1291918699j61oqem75886vyx/6vnnp1291918582.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/09/t1291918699j61oqem75886vyx/6vnnp1291918582.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/09/t1291918699j61oqem75886vyx/7ofms1291918582.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/09/t1291918699j61oqem75886vyx/7ofms1291918582.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/09/t1291918699j61oqem75886vyx/8ofms1291918582.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/09/t1291918699j61oqem75886vyx/8ofms1291918582.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/09/t1291918699j61oqem75886vyx/9z63d1291918582.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/09/t1291918699j61oqem75886vyx/9z63d1291918582.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

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

library(lattice)

par1 <- as.numeric(par1)

x <- t(y)

k <- length(x[1,])

n <- length(x[,1])

x1 <- cbind(x[,par1], x[,1:k!=par1])

mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])

colnames(x1) <- mycolnames #colnames(x)[par1]

x <- x1

if (par3 == 'First Differences'){

x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))

for (i in 1:n-1) {

for (j in 1:k) {

x2[i,j] <- x[i+1,j] - x[i,j]

}

}

x <- x2

}

if (par2 == 'Include Monthly Dummies'){

x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))

for (i in 1:11){

x2[seq(i,n,12),i] <- 1

}

x <- cbind(x, x2)

}

if (par2 == 'Include Quarterly Dummies'){

x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))

for (i in 1:3){

x2[seq(i,n,4),i] <- 1

}

x <- cbind(x, x2)

}

k <- length(x[1,])

if (par3 == 'Linear Trend'){

x <- cbind(x, c(1:n))

colnames(x)[k+1] <- 't'

}

x

k <- length(x[1,])

df <- as.data.frame(x)

(mylm <- lm(df))

(mysum <- summary(mylm))

bitmap(file='test0.png')

plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')

points(x[,1]-mysum$resid)

grid()

dev.off()

bitmap(file='test1.png')

plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')

grid()

dev.off()

bitmap(file='test2.png')

hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')

grid()

dev.off()

bitmap(file='test3.png')

densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')

dev.off()

bitmap(file='test4.png')

qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')

grid()

dev.off()

(myerror <- as.ts(mysum$resid))

bitmap(file='test5.png')

dum <- cbind(lag(myerror,k=1),myerror)

dum

dum1 <- dum[2:length(myerror),]

dum1

z <- as.data.frame(dum1)

z

plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')

lines(lowess(z))

abline(lm(z))

grid()

dev.off()

bitmap(file='test6.png')

acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')

grid()

dev.off()

bitmap(file='test7.png')

pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')

grid()

dev.off()

bitmap(file='test8.png')

opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))

plot(mylm, las = 1, sub='Residual Diagnostics')

par(opar)

dev.off()

load(file='createtable')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)

a<-table.row.end(a)

myeq <- colnames(x)[1]

myeq <- paste(myeq, '[t] = ', sep='')

for (i in 1:k){

if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')

myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')

if (rownames(mysum$coefficients)[i] != '(Intercept)') {

myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')

if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')

}

}

myeq <- paste(myeq, ' + e[t]')

a<-table.row.start(a)

a<-table.element(a, myeq)

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,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'Variable',header=TRUE)

a<-table.element(a,'Parameter',header=TRUE)

a<-table.element(a,'S.D.',header=TRUE)

a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE)

a<-table.element(a,'2-tail p-value',header=TRUE)

a<-table.element(a,'1-tail p-value',header=TRUE)

a<-table.row.end(a)

for (i in 1:k){

a<-table.row.start(a)

a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)

a<-table.element(a,mysum$coefficients[i,1])

a<-table.element(a, round(mysum$coefficients[i,2],6))

a<-table.element(a, round(mysum$coefficients[i,3],4))

a<-table.element(a, round(mysum$coefficients[i,4],6))

a<-table.element(a, round(mysum$coefficients[i,4]/2,6))

a<-table.row.end(a)

}

a<-table.end(a)

table.save(a,file='mytable2.tab')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'Multiple R',1,TRUE)

a<-table.element(a, sqrt(mysum$r.squared))

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'R-squared',1,TRUE)

a<-table.element(a, mysum$r.squared)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'Adjusted R-squared',1,TRUE)

a<-table.element(a, mysum$adj.r.squared)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'F-TEST (value)',1,TRUE)

a<-table.element(a, mysum$fstatistic[1])

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)

a<-table.element(a, mysum$fstatistic[2])

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)

a<-table.element(a, mysum$fstatistic[3])

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'p-value',1,TRUE)

a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'Residual Standard Deviation',1,TRUE)

a<-table.element(a, mysum$sigma)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'Sum Squared Residuals',1,TRUE)

a<-table.element(a, sum(myerror*myerror))

a<-table.row.end(a)

a<-table.end(a)

table.save(a,file='mytable3.tab')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a, 'Time or Index', 1, TRUE)

a<-table.element(a, 'Actuals', 1, TRUE)

a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE)

a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE)

a<-table.row.end(a)

for (i in 1:n) {

a<-table.row.start(a)

a<-table.element(a,i, 1, TRUE)

a<-table.element(a,x[i])

a<-table.element(a,x[i]-mysum$resid[i])

a<-table.element(a,mysum$resid[i])

a<-table.row.end(a)

}

a<-table.end(a)

table.save(a,file='mytable4.tab')

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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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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