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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 02:50:12 -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/t1195465490v9xxcyhhwzvq5is.htm/, Retrieved Mon, 19 Nov 2007 10:45:25 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

106.54 107.89 106.44 107.26 106.57 107.76 106.12 107.32 106.13 107.15 106.26 108.04 105.78 106.52 105.77 106.62 105.2 106.47 105.15 105.46 105.01 106.13 104.75 105.15 104.96 105.39 105.26 104.57 105.13 104.29 104.77 104.09 104.79 104.51 104.4 103.39 103.89 102.71 103.93 102.62 103.48 101.94 103.45 101.65 103.47 101.86 103.5 101.27 103.69 101.21 103.57 102.15 103.47 102.07 102.85 102.8 102.54 103.39 102.39 102.71 102.16 102.65 101.51 101.12 100.83 100.29 100.55 99.79 100.88 100.11 101 99.76 100.51 99.96 100.44 99.98 100.32 100.49 99.98 100.75 100.03 100.84 99.64 100.44 99.11 99.57 98.97 99.22 98.6 99.08 98.31 98.04 98.37 98.73 98.19 98.72 98.51 100.07 98.23 99.02 97.96 98.94 97.77 99 97.49 98.54 97.76 98.42 98.01 97.9 97.73 97.46 97.06 97 96.63 95.97 96.58 96.55 96.66 96.51 96.77 96.76 96.5 96.05 96.53 96.47 96.22 96.38 96.49 97.27 96.34 96.67 96.31 96.59 96.06 96.06 95.9 96.92 95.33 94.96 95.53 95.59 95.42 95.68 95.57 95.35 95.3 95.41 95.31 95.32 95.38 95.8 95.22 95.46 94.62 94.16 93.81 92.49 93.6 91.58 93.2 91.5 93.29 90.83 93.54 91.28 93.23 90.57 93.46 90.93 92.82 90.9 92.85 91.49 92.67 91.38 92.32 90.91 92.06 90.72 91.88 89.53 91.53 89.47 91.19 89.28

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	4 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

y[t] = -9.34493940380609 + 1.09136281362709x[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)	-9.34493940380609	2.376769	-3.9318	0.000164	8.2e-05
x	1.09136281362709	0.023936	45.595	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.978806779791498
R-squared	0.958062712165803
Adjusted R-squared	0.957601862848944
F-TEST (value)	2078.90665585664
F-TEST (DF numerator)	1
F-TEST (DF denominator)	91
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	1.02853187503467
Sum Squared Residuals	96.2668814345723

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	107.89	106.928854760024	0.96114523997586
2	107.26	106.819718478661	0.440281521338944
3	107.76	106.961595644433	0.79840435556744
4	107.32	106.470482378300	0.849517621699604
5	107.15	106.481396006437	0.668603993563355
6	108.04	106.623273172208	1.41672682779182
7	106.52	106.099419021667	0.420580978332819
8	106.62	106.088505393531	0.531494606469105
9	106.47	105.466428589763	1.00357141023653
10	105.46	105.411860449082	0.0481395509178773
11	106.13	105.259069655174	0.870930344825672
12	105.15	104.975315323631	0.174684676368731
13	105.39	105.204501514493	0.185498485507044
14	104.57	105.531910358581	-0.961910358581102
15	104.29	105.390033192810	-1.10003319280956
16	104.09	104.997142579904	-0.90714257990381
17	104.51	105.018969836176	-0.50896983617636
18	103.39	104.593338338862	-1.2033383388618
19	102.71	104.036743303912	-1.32674330391199
20	102.62	104.080397816457	-1.46039781645707
21	101.94	103.589284550325	-1.64928455032488
22	101.65	103.556543665916	-1.90654366591606
23	101.86	103.578370922189	-1.71837092218860
24	101.27	103.611111806597	-2.34111180659742
25	101.21	103.818470741187	-2.60847074118657
26	102.15	103.687507203551	-1.5375072035513
27	102.07	103.578370922189	-1.50837092218861
28	102.8	102.901725977740	-0.101725977739807
29	103.39	102.563403505515	0.82659649448458
30	102.71	102.399699083471	0.310300916528643
31	102.65	102.148685636337	0.501314363662889
32	101.12	101.439299807480	-0.319299807479515
33	100.29	100.697173094213	-0.407173094213087
34	99.79	100.391591506398	-0.601591506397501
35	100.11	100.751741234894	-0.641741234894445
36	99.76	100.882704772530	-1.12270477252969
37	99.96	100.347936993852	-0.387936993852439
38	99.98	100.271541596899	-0.291541596898525
39	100.49	100.140578059263	0.349421940736722
40	100.75	99.76951470263	0.980485297369925
41	100.84	99.8240828433114	1.01591715668858
42	100.44	99.3984513459969	1.04154865400314
43	99.57	98.8200290547745	0.749970945225488
44	99.22	98.6672382608667	0.552761739133287
45	99.08	98.2634340198247	0.816565980175313
46	98.04	97.9469388038728	0.0930611961271679
47	98.73	98.0124205726905	0.717579427309538
48	98.72	97.8159752662376	0.904024733762416
49	100.07	98.1652113665983	1.90478863340173
50	99.02	97.8596297787827	1.16037022121732
51	98.94	97.5649618191033	1.37503818089665
52	99	97.3576028845142	1.64239711548580
53	98.54	97.0520212966986	1.48797870330139
54	98.42	97.346689256378	1.07331074362206
55	97.9	97.6195299597847	0.28047004021529
56	97.46	97.3139483719691	0.146051628030864
57	97	96.582735286839	0.41726471316102
58	95.97	96.1134492769793	-0.143449276979326
59	96.55	96.058881136298	0.491118863702023
60	96.51	96.1461901613881	0.363809838611866
61	96.76	96.2662400708871	0.493759929112887
62	96.05	95.9715721112078	0.0784278887921881
63	96.47	96.0043129956166	0.465687004383376
64	96.38	95.6659905233922	0.714009476607772
65	97.27	95.9606584830715	1.30934151692846
66	96.67	95.7969540610275	0.873045938972523
67	96.59	95.7642131766187	0.825786823381338
68	96.06	95.4913724732119	0.568627526788109
69	96.92	95.3167544230316	1.60324557696844
70	94.96	94.694677619264	0.265322380735878
71	95.59	94.9129501819895	0.677049818010468
72	95.68	94.7929002724906	0.88709972750945
73	95.35	94.9566046945346	0.393395305465384
74	95.41	94.6619367348553	0.748063265144695
75	95.32	94.6728503629916	0.647149637008415
76	95.8	94.7492457599455	1.05075424005453
77	95.46	94.5746277097651	0.885372290234858
78	94.16	93.919810021589	0.240189978411106
79	92.49	93.035806142551	-0.545806142550952
80	91.58	92.8066199516893	-1.22661995168925
81	91.5	92.3700748262384	-0.870074826238425
82	90.83	92.4682974794649	-1.63829747946487
83	91.28	92.7411381828716	-1.46113818287164
84	90.57	92.4028157106472	-1.83281571064725
85	90.93	92.6538291577815	-1.72382915778145
86	90.9	91.9553569570601	-1.05535695706012
87	91.49	91.988097841469	-0.49809784146894
88	91.38	91.7916525350161	-0.411652535016073
89	90.91	91.4096755502466	-0.499675550246581
90	90.72	91.1259212187036	-0.405921218703547
91	89.53	90.9294759122507	-1.39947591225066
92	89.47	90.5474989274812	-1.07749892748119
93	89.28	90.176435570848	-0.896435570847973

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

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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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