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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: Mon, 19 Nov 2007 16:01:19 -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/19/t1195512847yefglvh101me9d4.htm/, Retrieved Mon, 19 Nov 2007 23:54:17 +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 1 112.5 1 106.2 1 107.1 1 108.5 1 106.5 1 108.3 1 125.6 1 124 1 127.2 1 136.9 1 135.8 1 124.3 1 115.4 1 113.6 1 114.4 1 118.4 1 117 1 116.5 1 115.4 1 113.6 1 117.4 1 116.9 1 116.4 1 111.1 1 110.2 1 118.9 1 131.8 1 130.6 1 138.3 1 148.4 1 148.7 1 144.3 1 152.5 1 162.9 1 167.2 1 166.5 1 185.6 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

Y[t] = + 96.973721340388 + 32.970987654321x[t] + 1.42828483245152M1[t] + 3.24078483245151M2[t] + 8.5032848324515M3[t] + 8.8532848324515M4[t] + 11.5032848324515M5[t] + 12.3282848324515M6[t] + 10.7407848324515M7[t] + 3.8407848324515M8[t] + 5.3282848324515M9[t] -5.41428571428571M10[t] -1.11428571428571M11[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)	96.973721340388	7.589104	12.778	0	0
x	32.970987654321	3.981792	8.2804	0	0
M1	1.42828483245152	9.917845	0.144	0.885853	0.442927
M2	3.24078483245151	9.917845	0.3268	0.744701	0.37235
M3	8.5032848324515	9.917845	0.8574	0.3938	0.1969
M4	8.8532848324515	9.917845	0.8927	0.374715	0.187358
M5	11.5032848324515	9.917845	1.1599	0.249557	0.124778
M6	12.3282848324515	9.917845	1.243	0.217484	0.108742
M7	10.7407848324515	9.917845	1.083	0.282073	0.141036
M8	3.8407848324515	9.917845	0.3873	0.699592	0.349796
M9	5.3282848324515	9.917845	0.5372	0.592592	0.296296
M10	-5.41428571428571	10.238894	-0.5288	0.598411	0.299206
M11	-1.11428571428571	10.238894	-0.1088	0.913611	0.456805

Multiple Linear Regression - Regression Statistics
Multiple R	0.692865273240383
R-squared	0.480062286862471
Adjusted R-squared	0.402071629891841
F-TEST (value)	6.15538200996637
F-TEST (DF numerator)	12
F-TEST (DF denominator)	80
p-value	1.55241826504948e-07
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	19.1552161462791
Sum Squared Residuals	29353.7844488536

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	99.5	98.4020061728394	1.09799382716060
2	101.6	100.214506172840	1.38549382716049
3	103.9	105.477006172840	-1.57700617283952
4	106.6	105.827006172840	0.772993827160461
5	108.3	108.477006172840	-0.177006172839517
6	102	109.302006172840	-7.30200617283952
7	93.8	107.714506172840	-13.9145061728395
8	91.6	100.814506172840	-9.2145061728395
9	97.7	102.302006172839	-4.60200617283947
10	94.8	91.5594356261023	3.2405643738977
11	98	95.8594356261023	2.14056437389770
12	103.8	96.973721340388	6.826278659612
13	97.8	98.4020061728395	-0.602006172839525
14	91.2	100.214506172840	-9.0145061728395
15	89.3	105.477006172840	-16.1770061728395
16	87.5	105.827006172840	-18.3270061728395
17	90.4	108.477006172840	-18.0770061728395
18	94.2	109.302006172840	-15.1020061728395
19	102.2	107.714506172840	-5.5145061728395
20	101.3	100.814506172840	0.485493827160489
21	96	102.302006172839	-6.3020061728395
22	90.8	91.5594356261023	-0.7594356261023
23	93.2	95.8594356261023	-2.65943562610230
24	90.9	96.973721340388	-6.073721340388
25	91.1	98.4020061728395	-7.30200617283953
26	90.2	100.214506172840	-10.0145061728395
27	94.3	105.477006172840	-11.1770061728395
28	96	105.827006172840	-9.8270061728395
29	99	108.477006172840	-9.4770061728395
30	103.3	109.302006172840	-6.00200617283951
31	113.1	107.714506172840	5.38549382716049
32	112.8	100.814506172840	11.9854938271605
33	112.1	102.302006172840	9.79799382716049
34	107.4	91.5594356261023	15.8405643738977
35	111	95.8594356261023	15.1405643738977
36	110.5	96.973721340388	13.526278659612
37	110.8	98.4020061728395	12.3979938271605
38	112.4	100.214506172840	12.1854938271605
39	111.5	105.477006172840	6.0229938271605
40	116.2	105.827006172840	10.3729938271605
41	122.5	108.477006172840	14.0229938271605
42	121.3	109.302006172840	11.9979938271605
43	113.9	107.714506172840	6.1854938271605
44	110.7	100.814506172840	9.8854938271605
45	120.8	102.302006172840	18.4979938271605
46	141.1	124.530423280423	16.5695767195767
47	147.4	128.830423280423	18.5695767195767
48	148	129.944708994709	18.055291005291
49	158.1	131.372993827160	26.7270061728395
50	165	133.185493827160	31.8145061728395
51	187	138.447993827160	48.5520061728395
52	190.3	138.797993827160	51.5020061728395
53	182.4	141.447993827160	40.9520061728395
54	168.8	142.272993827160	26.5270061728395
55	151.2	140.685493827160	10.5145061728395
56	120.1	133.785493827161	-13.6854938271605
57	112.5	135.272993827160	-22.7729938271605
58	106.2	124.530423280423	-18.3304232804233
59	107.1	128.830423280423	-21.7304232804233
60	108.5	129.944708994709	-21.444708994709
61	106.5	131.372993827160	-24.8729938271605
62	108.3	133.185493827160	-24.8854938271605
63	125.6	138.447993827161	-12.8479938271605
64	124	138.797993827160	-14.7979938271605
65	127.2	141.447993827161	-14.2479938271605
66	136.9	142.272993827160	-5.37299382716049
67	135.8	140.685493827160	-4.88549382716048
68	124.3	133.785493827161	-9.4854938271605
69	115.4	135.272993827160	-19.8729938271605
70	113.6	124.530423280423	-10.9304232804233
71	114.4	128.830423280423	-14.4304232804233
72	118.4	129.944708994709	-11.544708994709
73	117	131.372993827161	-14.3729938271605
74	116.5	133.185493827160	-16.6854938271605
75	115.4	138.447993827161	-23.0479938271605
76	113.6	138.797993827160	-25.1979938271605
77	117.4	141.447993827161	-24.0479938271605
78	116.9	142.272993827160	-25.3729938271605
79	116.4	140.685493827160	-24.2854938271605
80	111.1	133.785493827161	-22.6854938271605
81	110.2	135.272993827160	-25.0729938271605
82	118.9	124.530423280423	-5.63042328042328
83	131.8	128.830423280423	2.96957671957673
84	130.6	129.944708994709	0.655291005291001
85	138.3	131.372993827161	6.92700617283950
86	148.4	133.185493827160	15.2145061728395
87	148.7	138.447993827161	10.2520061728395
88	144.3	138.797993827160	5.50200617283952
89	152.5	141.447993827161	11.0520061728395
90	162.9	142.272993827160	20.6270061728395
91	167.2	140.685493827160	26.5145061728395
92	166.5	133.785493827161	32.7145061728395
93	185.6	135.272993827161	50.3270061728395

Charts produced by software:

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/19/t1195512847yefglvh101me9d4/7gm061195513274.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/19/t1195512847yefglvh101me9d4/8v0en1195513274.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/19/t1195512847yefglvh101me9d4/8v0en1195513274.ps (open in new window)

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Parameters:

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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