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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: Sat, 15 Dec 2007 07:30:57 -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/15/t1197728111onmz5na4yi91dx2.htm/, Retrieved Sat, 15 Dec 2007 15:15:21 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

99.5 0 101.6 0 103.9 0 106.6 0 108.3 0 102 0 93.8 0 91.6 0 97.7 0 94.8 0 98 0 103.8 0 97.8 0 91.2 0 89.3 0 87.5 0 90.4 0 94.2 0 102.2 0 101.3 0 96 0 90.8 0 93.2 0 90.9 0 91.1 0 90.2 0 94.3 0 96 0 99 0 103.3 0 113.1 0 112.8 0 112.1 0 107.4 0 111 0 110.5 0 110.8 0 112.4 0 111.5 0 116.2 0 122.5 0 121.3 0 113.9 0 110.7 0 120.8 0 141.1 1 147.4 1 148 1 158.1 1 165 1 187 1 190.3 1 182.4 1 168.8 1 151.2 1 120.1 0 112.5 0 106.2 0 107.1 0 108.5 0 106.5 0 108.3 0 125.6 0 124 0 127.2 0 136.9 0 135.8 0 124.3 0 115.4 0 113.6 0 114.4 0 118.4 0 117 0 116.5 0 115.4 0 113.6 0 117.4 0 116.9 0 116.4 0 111.1 0 110.2 0 118.9 0 131.8 0 130.6 0 138.3 0 148.4 0 148.7 0 144.3 0 152.5 0 162.9 0 167.2 0 166.5 0 185.6 0

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

Oliezaden[t] = + 108.461953652097 + 51.4663244353184Fluctuatie[t] -0.0077442065121429M1[t] + 1.80475579348780M2[t] + 7.06725579348783M3[t] + 7.41725579348786M4[t] + 10.0672557934878M5[t] + 10.8922557934878M6[t] + 9.30475579348785M7[t] + 8.83804634790263M8[t] + 10.3255463479026M9[t] -5.41428571428569M10[t] -1.11428571428569M11[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)	108.461953652097	7.558603	14.3495	0	0
Fluctuatie	51.4663244353184	6.726389	7.6514	0	0
M1	-0.0077442065121429	10.266769	-8e-04	0.9994	0.4997
M2	1.80475579348780	10.266769	0.1758	0.860906	0.430453
M3	7.06725579348783	10.266769	0.6884	0.493216	0.246608
M4	7.41725579348786	10.266769	0.7225	0.472123	0.236061
M5	10.0672557934878	10.266769	0.9806	0.329762	0.164881
M6	10.8922557934878	10.266769	1.0609	0.291917	0.145959
M7	9.30475579348785	10.266769	0.9063	0.3675	0.18375
M8	8.83804634790263	10.310939	0.8572	0.393921	0.196961
M9	10.3255463479026	10.310939	1.0014	0.319645	0.159822
M10	-5.41428571428569	10.602748	-0.5106	0.611003	0.305501
M11	-1.11428571428569	10.602748	-0.1051	0.916564	0.458282

Multiple Linear Regression - Regression Statistics
Multiple R	0.665170802242955
R-squared	0.442452196156536
Adjusted R-squared	0.358820025580017
F-TEST (value)	5.29045453569465
F-TEST (DF numerator)	12
F-TEST (DF denominator)	80
p-value	1.72666663089682e-06
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	19.8359247378468
Sum Squared Residuals	31477.1128164418

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	99.5	108.454209445585	-8.95420944558508
2	101.6	110.266709445586	-8.66670944558562
3	103.9	115.529209445585	-11.6292094455852
4	106.6	115.879209445585	-9.27920944558523
5	108.3	118.529209445585	-10.2292094455852
6	102	119.354209445585	-17.3542094455853
7	93.8	117.766709445585	-23.9667094455852
8	91.6	117.3	-25.7
9	97.7	118.7875	-21.0875000000000
10	94.8	103.047667937812	-8.24766793781169
11	98	107.347667937812	-9.34766793781168
12	103.8	108.461953652097	-4.66195365209737
13	97.8	108.454209445585	-10.6542094455852
14	91.2	110.266709445585	-19.0667094455852
15	89.3	115.529209445585	-26.2292094455852
16	87.5	115.879209445585	-28.3792094455852
17	90.4	118.529209445585	-28.1292094455852
18	94.2	119.354209445585	-25.1542094455852
19	102.2	117.766709445585	-15.5667094455852
20	101.3	117.3	-16
21	96	118.7875	-22.7875
22	90.8	103.047667937812	-12.2476679378117
23	93.2	107.347667937812	-14.1476679378117
24	90.9	108.461953652097	-17.5619536520974
25	91.1	108.454209445585	-17.3542094455852
26	90.2	110.266709445585	-20.0667094455852
27	94.3	115.529209445585	-21.2292094455852
28	96	115.879209445585	-19.8792094455852
29	99	118.529209445585	-19.5292094455852
30	103.3	119.354209445585	-16.0542094455852
31	113.1	117.766709445585	-4.66670944558523
32	112.8	117.3	-4.5
33	112.1	118.7875	-6.6875
34	107.4	103.047667937812	4.35233206218833
35	111	107.347667937812	3.65233206218832
36	110.5	108.461953652097	2.03804634790263
37	110.8	108.454209445585	2.34579055441477
38	112.4	110.266709445585	2.13329055441485
39	111.5	115.529209445585	-4.02920944558522
40	116.2	115.879209445585	0.320790554414797
41	122.5	118.529209445585	3.97079055441477
42	121.3	119.354209445585	1.94579055441478
43	113.9	117.766709445585	-3.86670944558522
44	110.7	117.3	-6.59999999999999
45	120.8	118.7875	2.01250000000000
46	141.1	154.51399237313	-13.4139923731299
47	147.4	158.81399237313	-11.4139923731299
48	148	159.928278087416	-11.9282780874156
49	158.1	159.920533880904	-1.82053388090351
50	165	161.733033880903	3.26696611909656
51	187	166.995533880904	20.0044661190965
52	190.3	167.345533880903	22.9544661190965
53	182.4	169.995533880904	12.4044661190965
54	168.8	170.820533880903	-2.02053388090348
55	151.2	169.233033880904	-18.0330338809035
56	120.1	117.3	2.80000000000000
57	112.5	118.7875	-6.2875
58	106.2	103.047667937812	3.15233206218833
59	107.1	107.347667937812	-0.247667937811685
60	108.5	108.461953652097	0.0380463479026356
61	106.5	108.454209445585	-1.95420944558523
62	108.3	110.266709445585	-1.96670944558516
63	125.6	115.529209445585	10.0707905544148
64	124	115.879209445585	8.1207905544148
65	127.2	118.529209445585	8.67079055441478
66	136.9	119.354209445585	17.5457905544148
67	135.8	117.766709445585	18.0332905544148
68	124.3	117.3	7
69	115.4	118.7875	-3.38749999999999
70	113.6	103.047667937812	10.5523320621883
71	114.4	107.347667937812	7.05233206218833
72	118.4	108.461953652097	9.93804634790264
73	117	108.454209445585	8.54579055441477
74	116.5	110.266709445585	6.23329055441484
75	115.4	115.529209445585	-0.129209445585217
76	113.6	115.879209445585	-2.27920944558521
77	117.4	118.529209445585	-1.12920944558522
78	116.9	119.354209445585	-2.45420944558521
79	116.4	117.766709445585	-1.36670944558522
80	111.1	117.3	-6.2
81	110.2	118.7875	-8.5875
82	118.9	103.047667937812	15.8523320621883
83	131.8	107.347667937812	24.4523320621883
84	130.6	108.461953652097	22.1380463479026
85	138.3	108.454209445585	29.8457905544148
86	148.4	110.266709445585	38.1332905544148
87	148.7	115.529209445585	33.1707905544148
88	144.3	115.879209445585	28.4207905544148
89	152.5	118.529209445585	33.9707905544148
90	162.9	119.354209445585	43.5457905544148
91	167.2	117.766709445585	49.4332905544148
92	166.5	117.3	49.2
93	185.6	118.7875	66.8125

Charts produced by software:

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/15/t1197728111onmz5na4yi91dx2/2h1js1197729052.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/15/t1197728111onmz5na4yi91dx2/3arsz1197729052.png (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/15/t1197728111onmz5na4yi91dx2/68rmi1197729052.ps (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/15/t1197728111onmz5na4yi91dx2/7r02i1197729052.ps (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/15/t1197728111onmz5na4yi91dx2/8n6dk1197729052.ps (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/15/t1197728111onmz5na4yi91dx2/90jng1197729052.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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