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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, 14 Dec 2007 08:34:08 -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/14/t11976455445v6c927fur5kvjj.htm/, Retrieved Fri, 14 Dec 2007 16:19:15 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

0.96 0 1 0 1.05 0 1.03 0 1.07 0 1.12 0 1.1 0 1.06 0 1.11 0 1.08 0 1.07 0 1.02 0 1 0 1.04 0 1.02 0 1.07 0 1.12 0 1.08 0 1.02 0 1.01 0 1.04 0 0.98 0 0.95 0 0.94 0 0.94 0 0.96 0 0.97 0 1.03 0 1.01 0 0.99 0 1 0 1 0 1.02 0 1.01 0 0.99 0 0.98 0 1.01 0 1.03 0 1.03 1 1 1 0.96 1 0.97 1 0.98 1 1.02 1 1.04 1 1.01 1 1.01 1 1 1 1.01 1 1.02 1 1.03 1 1.06 1 1.12 1 1.12 1 1.13 1 1.13 1 1.13 1 1.17 1 1.14 1 1.08 1 1.07 1 1.12 1 1.14 1 1.21 1 1.2 1 1.23 1 1.29 1 1.31 1 1.37 1 1.35 1 1.26 1 1.26 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	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

Benz[t] = + 0.922969848316686 -0.0298612652608209Par1[t] -0.0170030213343189M1[t] + 0.0096963250709088M2[t] + 0.0230392156862744M3[t] + 0.0464052287581699M4[t] + 0.056437908496732M5[t] + 0.0581372549019607M6[t] + 0.0565032679738562M7[t] + 0.0548692810457517M8[t] + 0.0815686274509804M9[t] + 0.0599346405228758M10[t] + 0.0266339869281046M11[t] + 0.00330065359477123t + 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)	0.922969848316686	0.041335	22.3288	0	0
Par1	-0.0298612652608209	0.039193	-0.7619	0.449207	0.224604
M1	-0.0170030213343189	0.047219	-0.3601	0.720091	0.360046
M2	0.0096963250709088	0.047134	0.2057	0.837731	0.418865
M3	0.0230392156862744	0.04764	0.4836	0.630483	0.315241
M4	0.0464052287581699	0.04748	0.9774	0.332444	0.166222
M5	0.056437908496732	0.047338	1.1922	0.238021	0.119011
M6	0.0581372549019607	0.047214	1.2314	0.223161	0.111581
M7	0.0565032679738562	0.04711	1.1994	0.235249	0.117624
M8	0.0548692810457517	0.047024	1.1668	0.24805	0.124025
M9	0.0815686274509804	0.046957	1.7371	0.087679	0.043839
M10	0.0599346405228758	0.046909	1.2777	0.206454	0.103227
M11	0.0266339869281046	0.04688	0.5681	0.572142	0.286071
t	0.00330065359477123	0.000947	3.4842	0.000946	0.000473

Multiple Linear Regression - Regression Statistics
Multiple R	0.659569667619246
R-squared	0.435032146443363
Adjusted R-squared	0.308401420646186
F-TEST (value)	3.43543909824973
F-TEST (DF numerator)	13
F-TEST (DF denominator)	58
p-value	0.000583498928959258
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.0811826872403613
Sum Squared Residuals	0.382256465038847

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	0.96	0.909267480577132	0.0507325194228684
2	1	0.939267480577137	0.060732519422863
3	1.05	0.955911024787274	0.0940889752127264
4	1.03	0.98257769145394	0.0474223085460597
5	1.07	0.995911024787274	0.0740889752127264
6	1.12	1.00091102478727	0.119088975212726
7	1.1	1.00257769145394	0.0974223085460596
8	1.06	1.00424435812061	0.0557556418793932
9	1.11	1.03424435812061	0.075755641879393
10	1.08	1.01591102478727	0.0640889752127263
11	1.07	0.985911024787274	0.0840889752127265
12	1.02	0.96257769145394	0.0574223085460598
13	1	0.948875323714393	0.0511246762856074
14	1.04	0.978875323714392	0.0611246762856084
15	1.02	0.995518867924528	0.0244811320754717
16	1.07	1.02218553459120	0.0478144654088049
17	1.12	1.03551886792453	0.0844811320754717
18	1.08	1.04051886792453	0.0394811320754717
19	1.02	1.04218553459120	-0.0221855345911950
20	1.01	1.04385220125786	-0.0338522012578617
21	1.04	1.07385220125786	-0.0338522012578617
22	0.98	1.05551886792453	-0.0755188679245284
23	0.95	1.02551886792453	-0.0755188679245284
24	0.94	1.00218553459119	-0.0621855345911951
25	0.94	0.988483166851647	-0.0484831668516474
26	0.96	1.01848316685165	-0.0584831668516463
27	0.97	1.03512671106178	-0.0651267110617831
28	1.03	1.06179337772845	-0.0317933777284498
29	1.01	1.07512671106178	-0.0651267110617831
30	0.99	1.08012671106178	-0.0901267110617832
31	1	1.08179337772845	-0.0817933777284498
32	1	1.08346004439512	-0.0834600443951165
33	1.02	1.11346004439512	-0.0934600443951164
34	1.01	1.09512671106178	-0.0851267110617831
35	0.99	1.06512671106178	-0.075126711061783
36	0.98	1.04179337772845	-0.0617933777284497
37	1.01	1.02809100998890	-0.0180910099889020
38	1.03	1.0580910099889	-0.028091009988901
39	1.03	1.04487328893822	-0.0148732889382169
40	1	1.07153995560488	-0.0715399556048837
41	0.96	1.08487328893822	-0.124873288938217
42	0.97	1.08987328893822	-0.119873288938217
43	0.98	1.09153995560488	-0.111539955604884
44	1.02	1.09320662227155	-0.0732066222715502
45	1.04	1.12320662227155	-0.0832066222715502
46	1.01	1.10487328893822	-0.0948732889382169
47	1.01	1.07487328893822	-0.0648732889382169
48	1	1.05153995560488	-0.0515399556048835
49	1.01	1.03783758786534	-0.0278375878653359
50	1.02	1.06783758786533	-0.0478375878653348
51	1.03	1.08448113207547	-0.0544811320754716
52	1.06	1.11114779874214	-0.0511477987421383
53	1.12	1.12448113207547	-0.00448113207547159
54	1.12	1.12948113207547	-0.00948113207547157
55	1.13	1.13114779874214	-0.00114779874213842
56	1.13	1.13281446540881	-0.00281446540880512
57	1.13	1.16281446540881	-0.0328144654088051
58	1.17	1.14448113207547	0.0255188679245283
59	1.14	1.11448113207547	0.0255188679245283
60	1.08	1.09114779874214	-0.0111477987421382
61	1.07	1.07744543100259	-0.00744543100259053
62	1.12	1.10744543100259	0.0125545689974106
63	1.14	1.12408897521273	0.0159110247872735
64	1.21	1.15075564187939	0.0592443581206069
65	1.2	1.16408897521273	0.0359110247872736
66	1.23	1.16908897521273	0.0609110247872736
67	1.29	1.17075564187939	0.119244358120607
68	1.31	1.17242230854606	0.137577691453940
69	1.37	1.20242230854606	0.167577691453940
70	1.35	1.18408897521273	0.165911024787274
71	1.26	1.15408897521273	0.105911024787274
72	1.26	1.13075564187939	0.129244358120607

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/14/t11976455445v6c927fur5kvjj/185vs1197646443.png (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/14/t11976455445v6c927fur5kvjj/3qu2s1197646443.ps (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/14/t11976455445v6c927fur5kvjj/5w26e1197646443.ps (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/14/t11976455445v6c927fur5kvjj/6q2ai1197646443.ps (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/14/t11976455445v6c927fur5kvjj/7nguj1197646443.ps (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/14/t11976455445v6c927fur5kvjj/8dw8d1197646443.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/14/t11976455445v6c927fur5kvjj/9qh5a1197646443.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/14/t11976455445v6c927fur5kvjj/9qh5a1197646443.ps (open in new window)

Parameters (Session):

par1 = ward ; par2 = ALL ; par3 = FALSE ; par4 = FALSE ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ; par4 = FALSE ;

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 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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