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

Title produced by software: Multiple Regression

Date of computation: Fri, 16 Nov 2007 06:58:03 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2007/Nov/16/t1195221211uvhit2j3hqxrp03.htm/, Retrieved Fri, 16 Nov 2007 14:53:31 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

102.3 0 105.8 0 106.7 0 109.6 0 111.9 0 113.3 0 114.6 0 115.7 0 117.3 0 119.8 0 120.6 0 121.4 0 123.5 0 125.2 0 126 0 126.8 0 128.1 0 128.2 0 129.3 0 130.6 0 131.4 0 131.1 0 131.2 0 131.2 0 131.5 0 133.5 0 133.7 0 133.5 0 134 0 135.9 0 135.9 0 137.2 0 138.4 0 140.9 0 143 0 144.1 0 146.8 0 149.1 0 149.6 0 151.2 0 153.3 0 156.9 0 157.2 0 158.5 0 160 0 162.5 0 162.9 0 164.7 0 165 0 167.2 0 168.6 0 169.5 0 169.8 0 171.9 0 172 0 173.7 0 173.9 0 175.9 0 175.6 0 176.1 0 176.3 0 179.4 0 179.7 0 179.9 0 180.4 0 182.5 0 183.6 0 183.9 0 184.5 0 187.6 0 188 0 188.5 0 188.6 0 191.9 0 193.5 0 194.9 0 194.9 0 196.2 0 196.2 0 198 0 198.6 0 201.3 0 203.5 0 204.1 0 204.8 1 206.5 1 207.8 1 208.6 1 209.7 1 210 1 211.7 1 212.4 1 213.7 1 214.8 1 216.4 1 217.5 1 218.6 1 220.4 1 221.8 1 222.5 1 223.4 1 225.5 1 226.5 1 227.8 1 228.5 1 229.1 1 229.9 1

Text written by user:

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 compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	6 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Multiple Linear Regression - Estimated Regression Equation

Y[t] = + 105.254791526706 -0.184143687937644X[t] + 1.17358473718674t + 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)	105.254791526706	0.47985	219.3495	0	0
X	-0.184143687937644	0.735517	-0.2504	0.802803	0.401402
t	1.17358473718674	0.009782	119.971	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.998215775607425
R-squared	0.996434734671533
Adjusted R-squared	0.996366171876754
F-TEST (value)	14533.1697445343
F-TEST (DF numerator)	2
F-TEST (DF denominator)	104
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	2.19604117057745
Sum Squared Residuals	501.550069578604

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	102.3	106.428376263893	-4.12837626389348
2	105.8	107.60196100108	-1.80196100107999
3	106.7	108.775545738267	-2.07554573826671
4	109.6	109.949130475453	-0.349130475453471
5	111.9	111.122715212640	0.777284787359805
6	113.3	112.296299949827	1.00370005017306
7	114.6	113.469884687014	1.13011531298632
8	115.7	114.643469424200	1.05653057579959
9	117.3	115.817054161387	1.48294583861285
10	119.8	116.990638898574	2.80936110142611
11	120.6	118.164223635761	2.43577636423937
12	121.4	119.337808372947	2.06219162705265
13	123.5	120.511393110134	2.9886068898659
14	125.2	121.684977847321	3.51502215267917
15	126	122.858562584508	3.14143741549243
16	126.8	124.032147321694	2.76785267830569
17	128.1	125.205732058881	2.89426794111895
18	128.2	126.379316796068	1.82068320393220
19	129.3	127.552901533255	1.74709846674549
20	130.6	128.726486270441	1.87351372955874
21	131.4	129.900071007628	1.49992899237201
22	131.1	131.073655744815	0.0263442551852623
23	131.2	132.247240482001	-1.04724048200148
24	131.2	133.420825219188	-2.22082521918822
25	131.5	134.594409956375	-3.09440995637494
26	133.5	135.767994693562	-2.26799469356168
27	133.7	136.941579430748	-3.24157943074843
28	133.5	138.115164167935	-4.61516416793516
29	134	139.288748905122	-5.2887489051219
30	135.9	140.462333642309	-4.56233364230863
31	135.9	141.635918379495	-5.73591837949537
32	137.2	142.809503116682	-5.60950311668212
33	138.4	143.983087853869	-5.58308785386884
34	140.9	145.156672591056	-4.25667259105558
35	143	146.330257328242	-3.33025732824232
36	144.1	147.503842065429	-3.40384206542907
37	146.8	148.677426802616	-1.87742680261579
38	149.1	149.851011539803	-0.751011539802541
39	149.6	151.024596276989	-1.42459627698928
40	151.2	152.198181014176	-0.998181014176022
41	153.3	153.371765751363	-0.071765751362737
42	156.9	154.545350488549	2.35464951145052
43	157.2	155.718935225736	1.48106477426377
44	158.5	156.892519962923	1.60748003707704
45	160	158.066104700110	1.9338952998903
46	162.5	159.239689437296	3.26031056270356
47	162.9	160.413274174483	2.48672582551683
48	164.7	161.58685891167	3.11314108833008
49	165	162.760443648857	2.23955635114335
50	167.2	163.934028386043	3.26597161395661
51	168.6	165.10761312323	3.49238687676987
52	169.5	166.281197860417	3.21880213958314
53	169.8	167.454782597604	2.34521740239641
54	171.9	168.628367334790	3.27163266520967
55	172	169.801952071977	2.19804792802293
56	173.7	170.975536809164	2.72446319083618
57	173.9	172.149121546351	1.75087845364946
58	175.9	173.322706283537	2.57729371646272
59	175.6	174.496291020724	1.10370897927597
60	176.1	175.669875757911	0.430124242089237
61	176.3	176.843460495098	-0.543460495097485
62	179.4	178.017045232284	1.38295476771577
63	179.7	179.190629969471	0.509370030529018
64	179.9	180.364214706658	-0.464214706657703
65	180.4	181.537799443844	-1.13779944384444
66	182.5	182.711384181031	-0.211384181031187
67	183.6	183.884968918218	-0.284968918217928
68	183.9	185.058553655405	-1.15855365540466
69	184.5	186.232138392591	-1.7321383925914
70	187.6	187.405723129778	0.194276870221859
71	188	188.579307866965	-0.579307866964877
72	188.5	189.752892604152	-1.25289260415161
73	188.6	190.926477341338	-2.32647734133835
74	191.9	192.100062078525	-0.200062078525077
75	193.5	193.273646815712	0.226353184288174
76	194.9	194.447231552899	0.452768447101445
77	194.9	195.620816290085	-0.72081629008529
78	196.2	196.794401027272	-0.59440102727205
79	196.2	197.967985764459	-1.76798576445879
80	198	199.141570501646	-1.14157050164551
81	198.6	200.315155238832	-1.71515523883226
82	201.3	201.488739976019	-0.188739976018975
83	203.5	202.662324713206	0.837675286794278
84	204.1	203.835909450392	0.26409054960753
85	204.8	204.825350499642	-0.0253504996415309
86	206.5	205.998935236828	0.501064763171723
87	207.8	207.172519974015	0.627480025984995
88	208.6	208.346104711202	0.253895288798241
89	209.7	209.519689448389	0.180310551611498
90	210	210.693274185575	-0.693274185575227
91	211.7	211.866858922762	-0.166858922761978
92	212.4	213.040443659949	-0.640443659948698
93	213.7	214.214028397135	-0.514028397135453
94	214.8	215.387613134322	-0.587613134322168
95	216.4	216.561197871509	-0.161197871508911
96	217.5	217.734782608696	-0.234782608695654
97	218.6	218.908367345882	-0.308367345882397
98	220.4	220.081952083069	0.318047916930877
99	221.8	221.255536820256	0.544463179744145
100	222.5	222.429121557443	0.0708784425573961
101	223.4	223.602706294629	-0.202706294629335
102	225.5	224.776291031816	0.723708968183921
103	226.5	225.949875769003	0.550124230997184
104	227.8	227.123460506190	0.676539493810457
105	228.5	228.297045243376	0.202954756623709
106	229.1	229.470629980563	-0.370629980563035
107	229.9	230.64421471775	-0.74421471774976

Charts produced by software:

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/16/t1195221211uvhit2j3hqxrp03/72omx1195221473.ps (open in new window)

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Parameters:

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = 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

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

We may request personal information to be submitted to our servers in order to be able to:

personalize online software applications according to your needs
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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