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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: Wed, 21 Nov 2007 05:36:11 -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/21/t1195648242tlugvr8gym70xu1.htm/, Retrieved Wed, 21 Nov 2007 13:30:53 +0100

User-defined keywords:

textiel met monthly dummies en lineair trends

Dataseries X:

» Textbox « » Textfile « » CSV «

101.5 0 99.2 0 107.8 0 92.3 0 99.2 0 101.6 0 87 0 71.4 0 104.7 0 115.1 0 102.5 0 75.3 0 96.7 1 94.6 1 98.6 1 99.5 1 92 1 93.6 1 89.3 1 66.9 1 108.8 1 113.2 1 105.5 1 77.8 1 102.1 1 97 1 95.5 1 99.3 1 86.4 1 92.4 1 85.7 1 61.9 1 104.9 1 107.9 1 95.6 1 79.8 1 94.8 1 93.7 1 108.1 1 96.9 1 88.8 1 106.7 1 86.8 1 69.8 1 110.9 1 105.4 1 99.2 1 84.4 1 87.2 1 91.9 1 97.9 1 94.5 1 85 1 100.3 1 78.7 1 65.8 1 104.8 1 96 1 103.3 1 82.9 1 91.4 1 94.5 1 109.3 1 92.1 1 99.3 1 109.6 1 87.5 1 73.1 1 110.7 1 111.6 1 110.7 1 84 1 101.6 1 102.1 1 113.9 1 99 1 100.4 1 109.5 1 93 1 76.8 1 105.3 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	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

y[t] = + 81.0978124999999 -5.16078124999995x[t] + 16.3589279513888M1[t] + 15.9374317956349M2[t] + 24.1445070684524M3[t] + 15.8372966269841M4[t] + 12.5300861855159M5[t] + 21.3800186011905M6[t] + 6.18709387400795M7[t] -11.3772594246032M8[t] + 26.3012444196429M9[t] + 27.6858494543651M10[t] + 22.1929247271826M11[t] + 0.0929247271825398t + 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)	81.0978124999999	2.446634	33.1467	0	0
x	-5.16078124999995	2.000773	-2.5794	0.012098	0.006049
M1	16.3589279513888	2.801308	5.8397	0	0
M2	15.9374317956349	2.799488	5.693	0	0
M3	24.1445070684524	2.798001	8.6292	0	0
M4	15.8372966269841	2.796846	5.6626	0	0
M5	12.5300861855159	2.796024	4.4814	3e-05	1.5e-05
M6	21.3800186011905	2.795535	7.6479	0	0
M7	6.18709387400795	2.79538	2.2133	0.030285	0.015142
M8	-11.3772594246032	2.795558	-4.0698	0.000127	6.3e-05
M9	26.3012444196429	2.79607	9.4065	0	0
M10	27.6858494543651	2.901285	9.5426	0	0
M11	22.1929247271826	2.900803	7.6506	0	0
t	0.0929247271825398	0.030537	3.043	0.003344	0.001672

Multiple Linear Regression - Regression Statistics
Multiple R	0.924878815061786
R-squared	0.855400822550093
Adjusted R-squared	0.827344265731454
F-TEST (value)	30.4884461796049
F-TEST (DF numerator)	13
F-TEST (DF denominator)	67
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	5.02406007724201
Sum Squared Residuals	1691.15903720238

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	101.5	97.5496651785718	3.95033482142816
2	99.2	97.22109375	1.97890625
3	107.8	105.52109375	2.27890625000002
4	92.3	97.3068080357142	-5.00680803571423
5	99.2	94.0925223214286	5.10747767857144
6	101.6	103.035379464286	-1.43537946428569
7	87	87.9353794642857	-0.935379464285681
8	71.4	70.4639508928571	0.936049107142891
9	104.7	108.235379464286	-3.5353794642857
10	115.1	109.712909226190	5.38709077380959
11	102.5	104.312909226190	-1.81290922619042
12	75.3	82.2129092261904	-6.91290922619044
13	96.7	93.5039806547618	3.19601934523818
14	94.6	93.1754092261905	1.42459077380952
15	98.6	101.475409226190	-2.87540922619048
16	99.5	93.2611235119048	6.23887648809523
17	92	90.046837797619	1.95316220238095
18	93.6	98.9896949404762	-5.38969494047620
19	89.3	83.8896949404762	5.41030505952381
20	66.9	66.4182663690476	0.481733630952386
21	108.8	104.189694940476	4.61030505952381
22	113.2	105.667224702381	7.53277529761904
23	105.5	100.267224702381	5.23277529761904
24	77.8	78.167224702381	-0.367224702380958
25	102.1	94.6190773809523	7.48092261904768
26	97	94.290505952381	2.70949404761905
27	95.5	102.590505952381	-7.09050595238095
28	99.3	94.3762202380952	4.92377976190475
29	86.4	91.1619345238095	-4.76193452380952
30	92.4	100.104791666667	-7.70479166666666
31	85.7	85.0047916666667	0.695208333333334
32	61.9	67.5333630952381	-5.6333630952381
33	104.9	105.304791666667	-0.404791666666663
34	107.9	106.782321428571	1.11767857142857
35	95.6	101.382321428571	-5.78232142857144
36	79.8	79.2823214285714	0.517678571428565
37	94.8	95.7341741071428	-0.934174107142794
38	93.7	95.4056026785714	-1.70560267857143
39	108.1	103.705602678571	4.39439732142857
40	96.9	95.4913169642857	1.40868303571428
41	88.8	92.27703125	-3.47703125000001
42	106.7	101.219888392857	5.48011160714286
43	86.8	86.1198883928571	0.680111607142851
44	69.8	68.6484598214286	1.15154017857142
45	110.9	106.419888392857	4.48011160714286
46	105.4	107.897418154762	-2.49741815476191
47	99.2	102.497418154762	-3.29741815476191
48	84.4	80.3974181547619	4.00258184523809
49	87.2	96.8492708333333	-9.64927083333327
50	91.9	96.520699404762	-4.6206994047619
51	97.9	104.820699404762	-6.9206994047619
52	94.5	96.6064136904762	-2.1064136904762
53	85	93.3921279761905	-8.39212797619048
54	100.3	102.334985119048	-2.03498511904762
55	78.7	87.2349851190476	-8.53498511904762
56	65.8	69.763556547619	-3.96355654761906
57	104.8	107.534985119048	-2.73498511904763
58	96	109.012514880952	-13.0125148809524
59	103.3	103.612514880952	-0.312514880952395
60	82.9	81.5125148809524	1.38748511904762
61	91.4	97.9643675595238	-6.56436755952374
62	94.5	97.6357961309524	-3.13579613095239
63	109.3	105.935796130952	3.36420386904761
64	92.1	97.7215104166667	-5.62151041666668
65	99.3	94.507224702381	4.79277529761904
66	109.6	103.450081845238	6.1499181547619
67	87.5	88.3500818452381	-0.850081845238102
68	73.1	70.8786532738095	2.22134672619046
69	110.7	108.650081845238	2.0499181547619
70	111.6	110.127611607143	1.47238839285712
71	110.7	104.727611607143	5.97238839285714
72	84	82.627611607143	1.37238839285713
73	101.6	99.0794642857142	2.52053571428577
74	102.1	98.7508928571429	3.34910714285713
75	113.9	107.050892857143	6.84910714285714
76	99	98.8366071428571	0.163392857142846
77	100.4	95.6223214285714	4.77767857142857
78	109.5	104.565178571429	4.93482142857142
79	93	89.4651785714286	3.53482142857142
80	76.8	71.99375	4.80624999999999
81	105.3	109.765178571429	-4.46517857142858

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

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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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