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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, 05 Dec 2007 15:01:56 -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/Dec/05/t1196891347n9ja58b9854epid.htm/, Retrieved Wed, 05 Dec 2007 22:49:18 +0100

User-defined keywords:

Dataseries X:

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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	5 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

Prod[t] = + 19.1968864455273 + 1.1337268515953Tot[t] -0.264635094351931Conjun[t] -0.264628251011800Mach[t] -0.0782681301598515`Elek `[t] + 0.0924904460551557t + 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)	19.1968864455273	6.173543	3.1095	0.00266	0.00133
Tot	1.1337268515953	0.135972	8.3379	0	0
Conjun	-0.264635094351931	2.274984	-0.1163	0.907711	0.453855
Mach	-0.264628251011800	0.12479	-2.1206	0.037307	0.018654
`Elek `	-0.0782681301598515	0.095623	-0.8185	0.415698	0.207849
t	0.0924904460551557	0.05528	1.6731	0.098528	0.049264

Multiple Linear Regression - Regression Statistics
Multiple R	0.922878188965104
R-squared	0.85170415166751
Adjusted R-squared	0.841684161915316
F-TEST (value)	85.0005012710633
F-TEST (DF numerator)	5
F-TEST (DF denominator)	74
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	5.25380915697527
Sum Squared Residuals	2042.58578868587

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	97.3	105.206921080818	-7.9069210808179
2	101	108.961831150456	-7.96183115045556
3	113.2	122.068574409798	-8.86857440979768
4	101	101.498627796619	-0.498627796619182
5	105.7	108.153292899398	-2.45329289939816
6	113.9	112.744150118673	1.15584988132733
7	86.4	88.4437087960664	-2.04370879606636
8	96.5	87.7189247031028	8.78107529689716
9	103.3	105.228070136834	-1.92807013683375
10	114.9	109.446480832286	5.45351916771417
11	105.8	107.474707960747	-1.67470796074669
12	94.2	96.5762310572258	-2.37623105722575
13	98.4	97.1306754111254	1.26932458887457
14	99.4	99.8705865544694	-0.470586554469342
15	108.8	109.258726197055	-0.458726197054978
16	112.6	107.478039987961	5.12196001203938
17	104.4	105.928961418175	-1.52896141817511
18	112.2	111.657095391925	0.542904608074616
19	81.1	86.8773175728138	-5.77731757281377
20	97.1	89.1084493659064	7.99155063409357
21	112.6	110.496244393415	2.10375560658479
22	113.8	116.552361493513	-2.75236149351288
23	107.8	105.27022125078	2.52977874922
24	103.2	99.0825951931535	4.11740480684653
25	103.3	97.0136551763242	6.28634482367584
26	101.2	99.9977978855862	1.20220211441385
27	107.7	106.048561070100	1.65143892990029
28	110.4	103.305539496348	7.09446050365188
29	101.9	103.282228109586	-1.38222810958605
30	115.9	108.840382091371	7.0596179086286
31	89.9	90.511399123977	-0.611399123977073
32	88.6	81.2921513944442	7.3078486055558
33	117.2	106.800251991758	10.3997480082421
34	123.9	108.118530329249	15.7814696707512
35	100	102.372461494373	-2.3724614943731
36	103.6	105.565880305903	-1.96588030590310
37	94.1	96.143831144909	-2.04383114490905
38	98.7	100.040513311392	-1.34051331139153
39	119.5	119.433470010324	0.0665299896765028
40	112.7	111.440694659944	1.25930534005560
41	104.4	103.163113626731	1.23688637326927
42	124.7	122.504290518272	2.19570948172791
43	89.1	91.7785097027512	-2.67850970275117
44	97	99.9151033159535	-2.9151033159535
45	121.6	118.422578636299	3.17742136370136
46	118.8	118.309184811417	0.490815188582529
47	114	110.393790777757	3.60620922224281
48	111.5	111.097303028903	0.402696971097087
49	97.2	105.143324922479	-7.9433249224791
50	102.5	108.871206384825	-6.37120638482532
51	113.4	122.771965236446	-9.37196523644642
52	109.8	113.413115938435	-3.61311593843453
53	104.9	104.999759700941	-0.0997597009410196
54	126.1	133.093957451903	-6.99395745190259
55	80	91.103217809565	-11.1032178095649
56	96.8	97.579435369419	-0.779435369419105
57	117.2	120.061599325869	-2.86159932586941
58	112.3	110.122037398811	2.17796260118940
59	117.3	117.705989107760	-0.405989107759516
60	111.1	114.773847339569	-3.67384733956903
61	102.2	107.571301497769	-5.37130149776945
62	104.3	113.965934966365	-9.66593496636503
63	122.9	129.924890995573	-7.02489099557296
64	107.6	108.724957878327	-1.12495787832671
65	121.3	123.390664435892	-2.09066443589201
66	131.5	131.401760621190	0.0982393788103453
67	89	96.1885477725295	-7.1885477725295
68	104.4	102.382883092917	2.01711690708265
69	128.9	127.486518604400	1.41348139559956
70	135.9	130.872085070755	5.02791492924512
71	133.3	130.129358433623	3.17064156637664
72	121.3	119.880802544012	1.41919745598785
73	120.5	121.851117667460	-1.35111766746044
74	120.4	119.274438178845	1.12556182115509
75	137.9	134.740711784208	3.15928821579202
76	126.1	120.236532501931	5.86346749806875
77	133.2	125.051106716660	8.14889328333979
78	146.6	139.703384735491	6.89661526450892
79	103.4	109.859123711361	-6.4591237113608
80	117.2	110.500405618681	6.69959438131872

Charts produced by software:

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Parameters:

par1 = 2 ; 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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