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Paper

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

Title produced by software: Multiple Regression

Date of computation: Tue, 04 Dec 2007 08:10:23 -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/Dec/04/t1196781019jtp168vfdh4bcqq.htm/, Retrieved Tue, 04 Dec 2007 16:10:29 +0100

User-defined keywords:

Paper regressie, alle variabelen

Dataseries X:

» Textbox « » Textfile « » CSV «

106,7 97,3 0 104,8 93,5 110,2 101 0 105,6 94,7 125,9 113,2 0 118,3 112,9 100,1 101 0 89,9 99,2 106,4 105,7 0 90,2 105,6 114,8 113,9 0 107 113 81,3 86,4 0 64,5 83,1 87 96,5 0 92,6 81,1 104,2 103,3 0 95,8 96,9 108 114,9 0 94,3 104,3 105 105,8 0 91,2 97,7 94,5 94,2 0 86,3 102,6 92 98,4 0 77,6 89,9 95,9 99,4 0 82,5 96 108,8 108,8 0 97,7 112,7 103,4 112,6 0 83,3 107,1 102,1 104,4 0 84,2 106,2 110,1 112,2 0 92,8 121 83,2 81,1 0 77,4 101,2 82,7 97,1 0 72,5 83,2 106,8 112,6 0 88,8 105,1 113,7 113,8 0 93,4 113,3 102,5 107,8 0 92,6 99,1 96,6 103,2 0 90,7 100,3 92,1 103,3 0 81,6 93,5 95,6 101,2 0 84,1 98,8 102,3 107,7 0 88,1 106,2 98,6 110,4 0 85,3 98,3 98,2 101,9 0 82,9 102,1 104,5 115,9 0 84,8 117,1 84 89,9 0 71,2 101,5 73,8 88,6 0 68,9 80,5 103,9 117,2 0 94,3 105,9 106 123,9 0 97,6 109,5 97,2 100 0 85,6 97,2 102,6 103,6 0 91,9 114,5 89 94,1 0 75,8 93,5 93,8 98,7 0 79,8 100,9 116,7 119,5 0 99 121,1 106,8 112,7 0 88,5 116,5 98,5 104,4 0 86,7 109,3 118,7 124,7 0 97,9 118,1 90 89,1 0 94,3 108,3 91,9 97 0 72,9 105,4 113,3 121,6 0 91,8 116,2 113,1 118,8 0 93,2 111,2 104,1 114 0 86,5 105,8 108,7 111,5 0 98,9 122,7 96,7 97,2 0 77,2 99,5 101 102,5 0 79,4 107,9 116,9 113,4 0 90,4 124,6 105,8 109,8 0 81,4 115 99 104,9 0 85,8 110,3 129,4 126,1 0 103,6 132,7 83 80 0 73,6 99,7 88,9 96,8 0 75,7 96,5 115,9 117,2 1 99,2 118,7 104,2 112,3 1 88,7 112,9 113,4 117,3 1 94,6 130,5 112,2 111,1 1 98,7 137,9 100,8 102,2 1 84,2 115 107,3 104,3 1 87,7 116,8 126,6 122,9 1 103,3 140,9 102,9 107,6 1 88,2 120,7 117,9 121,3 1 93,4 134,2 128,8 131,5 1 106,3 147,3 87,5 89 1 73,1 112,4 93,8 104,4 1 78,6 107,1 122,7 128,9 1 101,6 128,4 126,2 135,9 1 101,4 137,7 124,6 133,3 1 98,5 135 116,7 121,3 1 99 151 115,2 120,5 1 89,5 137,4 111,1 120,4 1 83,5 132,4 129,9 137,9 1 97,4 161,3 113,3 126,1 1 87,8 139,8 118,5 133,2 1 90,4 146 133,5 146,6 1 97,1 154,6 102,1 103,4 1 79,4 142,1 102,4 117,2 1 85 120,5

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	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

metaal[t] = + 20.8675860424059 + 1.12593999912943Totaal[t] + 1.60887221363666conjunctuur[t] -0.339736946221387elektrische[t] + 0.00158058220510757mac[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)	20.8675860424059	6.164896	3.3849	0.001136	0.000568
Totaal	1.12593999912943	0.137513	8.1879	0	0
conjunctuur	1.60887221363666	2.003933	0.8029	0.424594	0.212297
elektrische	-0.339736946221387	0.117824	-2.8834	0.00513	0.002565
mac	0.00158058220510757	0.083851	0.0188	0.985011	0.492505

Multiple Linear Regression - Regression Statistics
Multiple R	0.919833866017206
R-squared	0.846094341072158
Adjusted R-squared	0.837886039262674
F-TEST (value)	103.077879043687
F-TEST (DF numerator)	4
F-TEST (DF denominator)	75
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	5.31645716657112
Sum Squared Residuals	2119.85376029891

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	97.3	105.548736421692	-8.24873642169238
2	101	109.219633560315	-8.2196335603146
3	113.2	122.610998925768	-9.41099892576796
4	101	103.188622244706	-2.18862224470599
5	105.7	110.190238881468	-4.49023888146771
6	113.9	113.952250485953	-0.052250485953429
7	86.4	90.6248213215937	-4.22482132159366
8	96.5	87.4929099634003	9.00709003659976
9	103.3	105.796892919359	-2.49689291935876
10	114.9	110.596766643700	4.30323335629953
11	105.8	108.261699337045	-2.46169933704477
12	94.2	98.1117852354756	-3.91178523547554
13	98.4	98.2325732757732	0.16742672422684
14	99.4	100.968669787344	-1.56866978734431
15	108.8	110.355689916374	-1.55568991637421
16	112.6	109.158974686315	3.44102531368534
17	104.4	107.388066911863	-2.98806691186252
18	112.2	113.497241784030	-1.29724178402966
19	81.1	88.4101092515961	-7.31010925159615
20	97.1	89.4833998088243	7.6166001911757
21	112.6	111.115456314727	1.48454368527312
22	113.8	117.334613130183	-3.53461313018347
23	107.8	104.973430429598	2.8265695704016
24	103.2	98.9777813312015	4.22221866879851
25	103.3	96.991909586739	6.30809041326106
26	101.2	100.091734303826	1.10826569617444
27	107.7	106.288280821425	1.41171917857499
28	110.4	103.061079674646	7.33892032535437
29	101.9	103.432078558305	-1.53207855830461
30	115.9	109.903709088076	5.99629091192399
31	89.9	91.4177044921338	-1.51770449213382
32	88.6	80.6813192510155	7.91868074898446
33	117.2	105.982941578798	11.2170584212020
34	123.9	107.231973750378	16.6680262496224
35	100	101.381103951572	-1.38110395157241
36	103.6	105.348181257825	-1.74818125782496
37	94.1	95.4719698775218	-1.37196987752176
38	98.7	99.5292303967753	-0.829230396775268
39	119.5	118.822234769932	0.677765230068165
40	112.7	111.235396035732	1.46460396426849
41	104.4	102.490240354279	1.90975964572106
42	124.7	121.443083662419	3.2569163375811
43	89.1	90.3361689881911	-1.23616898819112
44	97	99.74124194728	-2.74124194727991
45	121.6	117.432399932881	4.16760006711928
46	118.8	116.723677297319	2.07632270268065
47	114	108.857919700930	5.14208029906984
48	111.5	109.851217403047	1.64878259695332
49	97.2	103.675559639339	-6.47555963933909
50	102.5	107.782957244432	-5.2829572444315
51	113.4	121.974692544980	-8.57469254497952
52	109.8	112.519217481466	-2.71921748146627
53	104.9	103.360554187648	1.53944581235199
54	126.1	131.577217559836	-5.47721755983652
55	80	89.4735507741039	-9.47355077410387
56	96.8	95.3980913188463	1.40190868115373
57	117.2	119.458614197728	-2.25861419772842
58	112.3	109.843186766449	2.45681323355101
59	117.3	118.225205022543	-0.925205022543493
60	111.1	115.492851852398	-4.39285185239828
61	102.2	107.547126250036	-5.34712625003588
62	104.3	113.679501980572	-9.37950198057154
63	122.9	130.148339633859	-7.24833963385904
64	107.6	108.561661781891	-0.96166178189127
65	121.3	123.705467508250	-2.4054675082505
66	131.5	131.616312519392	-0.116312519392342
67	89	96.3390948509386	-7.33909485093855
68	104.4	101.555586555549	2.84441344445074
69	128.9	126.314969168267	2.58503083173323
70	135.9	130.338405968972	5.56159403102844
71	133.3	129.517871542453	3.78212845754731
72	121.3	120.478366391501	0.82163360849878
73	120.5	121.995461463921	-1.49546146392078
74	120.4	119.409626233793	0.990373766207122
75	137.9	135.900633490677	1.99936650932344
76	126.1	120.437521671443	5.66247832855652
77	133.2	125.418893216413	7.7811067835874
78	146.6	140.045348670635	6.55465132936528
79	103.4	110.684419368525	-7.28441936852521
80	117.2	109.085533893794	8.11446610620604

Charts produced by software:

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Parameters:

par1 = 2 ; par2 = Do not include Seasonal 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

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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