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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: Thu, 22 Nov 2007 08:43:56 -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/22/t1195745793gzma47xdrxfbrq1.htm/, Retrieved Thu, 22 Nov 2007 16:36:33 +0100

User-defined keywords:

Inge & Florence

Dataseries X:

» Textbox « » Textfile « » CSV «

5,22 0 5,09 0 4,77 0 4,54 0 4,56 0 4,39 0 4,73 0 4,44 0 4,3 0 4,24 0 4,01 0 3,5 0 3,23 0 3,28 1 3,49 1 3,7 1 3,63 1 3,95 1 3,73 1 3,87 1 3,66 1 3,49 1 3,4 1 3,32 1 3,11 1 3,06 1 2,68 1 2,55 1 2,34 1 2,34 1 2,39 1 2,21 1 2,09 1 2,14 1 2,31 1 2,14 1 2,45 1 2,52 1 2,3 1 2,25 1 2,06 1 1,99 1 2,25 1 2,26 1 2,36 1 2,3 1 2,19 1 2,31 1 2,21 1 2,21 1 2,26 1 2,18 1 2,21 1 2,33 1 2,12 1 2,08 1 1,97 1 2,09 1 2,11 1 2,24 1 2,45 1 2,68 1 2,73 1 2,76 1 2,83 1 3,16 1 3,22 1 3,22 1 3,34 1 3,35 1 3,42 1 3,58 1 3,71 1 3,68 1 3,83 1 3,94 1 3,88 1 4,03 1 4,15 1 4,32 1 4,4 1 4,37 1 4,14 1 4,11 1 4,16 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

R1j[t] = + 4.13991071428571 -1.93200520833333Ter[t] + 0.138663969494047M1[t] + 0.302043340773809M2[t] + 0.224981863839285M3[t] + 0.193634672619047M4[t] + 0.123716052827380M5[t] + 0.209511718750000M6[t] + 0.255307384672619M7[t] + 0.216817336309524M8[t] + 0.165470145089285M9[t] + 0.134122953869047M10[t] + 0.0656329055059518M11[t] + 0.0113471912202381t + 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)	4.13991071428571	0.348767	11.8701	0	0
Ter	-1.93200520833333	0.293651	-6.5793	0	0
M1	0.138663969494047	0.390701	0.3549	0.723709	0.361854
M2	0.302043340773809	0.405036	0.7457	0.458299	0.229149
M3	0.224981863839285	0.404597	0.5561	0.579916	0.289958
M4	0.193634672619047	0.404204	0.4791	0.633374	0.316687
M5	0.123716052827380	0.403857	0.3063	0.760245	0.380123
M6	0.209511718750000	0.403556	0.5192	0.605261	0.302631
M7	0.255307384672619	0.403301	0.633	0.528739	0.264369
M8	0.216817336309524	0.403093	0.5379	0.592339	0.296169
M9	0.165470145089285	0.40293	0.4107	0.682553	0.341277
M10	0.134122953869047	0.402814	0.333	0.740142	0.370071
M11	0.0656329055059518	0.402745	0.163	0.87101	0.435505
t	0.0113471912202381	0.004324	2.6242	0.010627	0.005313

Multiple Linear Regression - Regression Statistics
Multiple R	0.635139796786672
R-squared	0.403402561462215
Adjusted R-squared	0.294166410744029
F-TEST (value)	3.69294010096473
F-TEST (DF numerator)	13
F-TEST (DF denominator)	71
p-value	0.000176111315490335
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.753422621986776
Sum Squared Residuals	40.3028409598214

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	5.22	4.28992187500000	0.930078124999995
2	5.09	4.4646484375	0.625351562499999
3	4.77	4.39893415178571	0.371065848214286
4	4.54	4.37893415178571	0.161065848214286
5	4.56	4.32036272321429	0.239637276785714
6	4.39	4.41750558035714	-0.0275055803571429
7	4.73	4.4746484375	0.255351562500001
8	4.44	4.44750558035714	-0.00750558035714218
9	4.3	4.40750558035714	-0.107505580357143
10	4.24	4.38750558035714	-0.147505580357143
11	4.01	4.33036272321428	-0.320362723214285
12	3.5	4.27607700892857	-0.776077008928572
13	3.23	4.42608816964286	-1.19608816964286
14	3.28	2.66880952380952	0.611190476190477
15	3.49	2.60309523809524	0.886904761904762
16	3.7	2.58309523809524	1.11690476190476
17	3.63	2.52452380952381	1.10547619047619
18	3.95	2.62166666666667	1.32833333333333
19	3.73	2.67880952380952	1.05119047619048
20	3.87	2.65166666666667	1.21833333333333
21	3.66	2.61166666666667	1.04833333333333
22	3.49	2.59166666666667	0.898333333333334
23	3.4	2.53452380952381	0.865476190476191
24	3.32	2.48023809523810	0.839761904761904
25	3.11	2.63024925595238	0.47975074404762
26	3.06	2.80497581845238	0.255024181547619
27	2.68	2.73926153273809	-0.059261532738095
28	2.55	2.71926153273809	-0.169261532738095
29	2.34	2.66069010416667	-0.320690104166667
30	2.34	2.75783296130952	-0.417832961309524
31	2.39	2.81497581845238	-0.424975818452381
32	2.21	2.78783296130952	-0.577832961309524
33	2.09	2.74783296130952	-0.657832961309524
34	2.14	2.72783296130952	-0.587832961309524
35	2.31	2.67069010416667	-0.360690104166667
36	2.14	2.61640438988095	-0.476404389880953
37	2.45	2.76641555059524	-0.316415550595237
38	2.52	2.94114211309524	-0.421142113095238
39	2.3	2.87542782738095	-0.575427827380953
40	2.25	2.85542782738095	-0.605427827380952
41	2.06	2.79685639880952	-0.736856398809524
42	1.99	2.89399925595238	-0.903999255952381
43	2.25	2.95114211309524	-0.701142113095238
44	2.26	2.92399925595238	-0.663999255952381
45	2.36	2.88399925595238	-0.523999255952381
46	2.3	2.86399925595238	-0.563999255952381
47	2.19	2.80685639880952	-0.616856398809524
48	2.31	2.75257068452381	-0.44257068452381
49	2.21	2.90258184523809	-0.692581845238095
50	2.21	3.07730840773810	-0.867308407738095
51	2.26	3.01159412202381	-0.75159412202381
52	2.18	2.99159412202381	-0.81159412202381
53	2.21	2.93302269345238	-0.723022693452381
54	2.33	3.03016555059524	-0.700165550595238
55	2.12	3.08730840773810	-0.967308407738096
56	2.08	3.06016555059524	-0.980165550595238
57	1.97	3.02016555059524	-1.05016555059524
58	2.09	3.00016555059524	-0.910165550595238
59	2.11	2.94302269345238	-0.833022693452381
60	2.24	2.88873697916667	-0.648736979166667
61	2.45	3.03874813988095	-0.588748139880952
62	2.68	3.21347470238095	-0.533474702380952
63	2.73	3.14776041666667	-0.417760416666667
64	2.76	3.12776041666667	-0.367760416666667
65	2.83	3.06918898809524	-0.239188988095238
66	3.16	3.16633184523810	-0.00633184523809523
67	3.22	3.22347470238095	-0.00347470238095259
68	3.22	3.19633184523810	0.0236681547619047
69	3.34	3.15633184523810	0.183668154761904
70	3.35	3.13633184523810	0.213668154761905
71	3.42	3.07918898809524	0.340811011904762
72	3.58	3.02490327380952	0.555096726190475
73	3.71	3.17491443452381	0.535085565476191
74	3.68	3.34964099702381	0.330359002976190
75	3.83	3.28392671130952	0.546073288690476
76	3.94	3.26392671130952	0.676073288690476
77	3.88	3.20535528273810	0.674644717261905
78	4.03	3.30249813988095	0.727501860119048
79	4.15	3.35964099702381	0.790359002976191
80	4.32	3.33249813988095	0.987501860119048
81	4.4	3.29249813988095	1.10750186011905
82	4.37	3.27249813988095	1.09750186011905
83	4.14	3.21535528273809	0.924644717261905
84	4.11	3.16106956845238	0.948930431547619
85	4.16	3.31108072916667	0.848919270833334

Charts produced by software:

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Parameters:

par1 = 1 ; par2 = Include Monthly 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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