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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, 16 Nov 2007 06:56:08 -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/Nov/16/t119522116200xlituqm1o85lv.htm/, Retrieved Fri, 16 Nov 2007 14:52:52 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

102,3 0 105,8 0 106,7 0 109,6 0 111,9 0 113,3 0 114,6 0 115,7 0 117,3 0 119,8 0 120,6 0 121,4 0 123,5 0 125,2 0 126 0 126,8 0 128,1 0 128,2 0 129,3 0 130,6 0 131,4 0 131,1 0 131,2 0 131,2 0 131,5 0 133,5 0 133,7 0 133,5 0 134 0 135,9 0 135,9 0 137,2 0 138,4 0 140,9 0 143 0 144,1 0 146,8 0 149,1 0 149,6 0 151,2 0 153,3 0 156,9 0 157,2 0 158,5 0 160 0 162,5 0 162,9 0 164,7 0 165 0 167,2 0 168,6 0 169,5 0 169,8 0 171,9 0 172 0 173,7 0 173,9 0 175,9 0 175,6 0 176,1 0 176,3 0 179,4 0 179,7 0 179,9 0 180,4 0 182,5 0 183,6 0 183,9 0 184,5 0 187,6 0 188 0 188,5 0 188,6 0 191,9 0 193,5 0 194,9 0 194,9 0 196,2 0 196,2 0 198 0 198,6 0 201,3 0 203,5 0 204,1 0 204,8 1 206,5 1 207,8 1 208,6 1 209,7 1 210 1 211,7 1 212,4 1 213,7 1 214,8 1 216,4 1 217,5 1 218,6 1 220,4 1 221,8 1 222,5 1 223,4 1 225,5 1 226,5 1 227,8 1 228,5 1 229,1 1 229,9 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] = + 155.132142857143 + 62.6026397515528X[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)	155.132142857143	2.815438	55.1005	0	0
X	62.6026397515528	6.072589	10.3091	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.709239800503977
R-squared	0.503021094618921
Adjusted R-squared	0.49828796218672
F-TEST (value)	106.276573035805
F-TEST (DF numerator)	1
F-TEST (DF denominator)	105
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	25.8039117352387
Sum Squared Residuals	69913.3953881989

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	102.3	155.132142857144	-52.8321428571437
2	105.8	155.132142857143	-49.332142857143
3	106.7	155.132142857143	-48.4321428571428
4	109.6	155.132142857143	-45.5321428571429
5	111.9	155.132142857143	-43.2321428571428
6	113.3	155.132142857143	-41.8321428571429
7	114.6	155.132142857143	-40.5321428571429
8	115.7	155.132142857143	-39.4321428571428
9	117.3	155.132142857143	-37.8321428571429
10	119.8	155.132142857143	-35.3321428571428
11	120.6	155.132142857143	-34.5321428571429
12	121.4	155.132142857143	-33.7321428571428
13	123.5	155.132142857143	-31.6321428571428
14	125.2	155.132142857143	-29.9321428571428
15	126	155.132142857143	-29.1321428571428
16	126.8	155.132142857143	-28.3321428571429
17	128.1	155.132142857143	-27.0321428571429
18	128.2	155.132142857143	-26.9321428571429
19	129.3	155.132142857143	-25.8321428571428
20	130.6	155.132142857143	-24.5321428571429
21	131.4	155.132142857143	-23.7321428571428
22	131.1	155.132142857143	-24.0321428571429
23	131.2	155.132142857143	-23.9321428571429
24	131.2	155.132142857143	-23.9321428571429
25	131.5	155.132142857143	-23.6321428571428
26	133.5	155.132142857143	-21.6321428571429
27	133.7	155.132142857143	-21.4321428571429
28	133.5	155.132142857143	-21.6321428571429
29	134	155.132142857143	-21.1321428571429
30	135.9	155.132142857143	-19.2321428571428
31	135.9	155.132142857143	-19.2321428571428
32	137.2	155.132142857143	-17.9321428571429
33	138.4	155.132142857143	-16.7321428571428
34	140.9	155.132142857143	-14.2321428571428
35	143	155.132142857143	-12.1321428571428
36	144.1	155.132142857143	-11.0321428571429
37	146.8	155.132142857143	-8.33214285714284
38	149.1	155.132142857143	-6.03214285714286
39	149.6	155.132142857143	-5.53214285714286
40	151.2	155.132142857143	-3.93214285714286
41	153.3	155.132142857143	-1.83214285714284
42	156.9	155.132142857143	1.76785714285716
43	157.2	155.132142857143	2.06785714285714
44	158.5	155.132142857143	3.36785714285715
45	160	155.132142857143	4.86785714285715
46	162.5	155.132142857143	7.36785714285715
47	162.9	155.132142857143	7.76785714285716
48	164.7	155.132142857143	9.56785714285714
49	165	155.132142857143	9.86785714285715
50	167.2	155.132142857143	12.0678571428571
51	168.6	155.132142857143	13.4678571428571
52	169.5	155.132142857143	14.3678571428572
53	169.8	155.132142857143	14.6678571428572
54	171.9	155.132142857143	16.7678571428572
55	172	155.132142857143	16.8678571428572
56	173.7	155.132142857143	18.5678571428571
57	173.9	155.132142857143	18.7678571428572
58	175.9	155.132142857143	20.7678571428572
59	175.6	155.132142857143	20.4678571428571
60	176.1	155.132142857143	20.9678571428571
61	176.3	155.132142857143	21.1678571428572
62	179.4	155.132142857143	24.2678571428572
63	179.7	155.132142857143	24.5678571428571
64	179.9	155.132142857143	24.7678571428572
65	180.4	155.132142857143	25.2678571428572
66	182.5	155.132142857143	27.3678571428571
67	183.6	155.132142857143	28.4678571428571
68	183.9	155.132142857143	28.7678571428572
69	184.5	155.132142857143	29.3678571428571
70	187.6	155.132142857143	32.4678571428571
71	188	155.132142857143	32.8678571428571
72	188.5	155.132142857143	33.3678571428571
73	188.6	155.132142857143	33.4678571428571
74	191.9	155.132142857143	36.7678571428572
75	193.5	155.132142857143	38.3678571428571
76	194.9	155.132142857143	39.7678571428572
77	194.9	155.132142857143	39.7678571428572
78	196.2	155.132142857143	41.0678571428571
79	196.2	155.132142857143	41.0678571428571
80	198	155.132142857143	42.8678571428571
81	198.6	155.132142857143	43.4678571428571
82	201.3	155.132142857143	46.1678571428572
83	203.5	155.132142857143	48.3678571428571
84	204.1	155.132142857143	48.9678571428571
85	204.8	217.734782608696	-12.9347826086956
86	206.5	217.734782608696	-11.2347826086957
87	207.8	217.734782608696	-9.93478260869565
88	208.6	217.734782608696	-9.13478260869566
89	209.7	217.734782608696	-8.03478260869567
90	210	217.734782608696	-7.73478260869566
91	211.7	217.734782608696	-6.03478260869567
92	212.4	217.734782608696	-5.33478260869565
93	213.7	217.734782608696	-4.03478260869567
94	214.8	217.734782608696	-2.93478260869565
95	216.4	217.734782608696	-1.33478260869565
96	217.5	217.734782608696	-0.234782608695657
97	218.6	217.734782608696	0.865217391304337
98	220.4	217.734782608696	2.66521739130435
99	221.8	217.734782608696	4.06521739130435
100	222.5	217.734782608696	4.76521739130434
101	223.4	217.734782608696	5.66521739130435
102	225.5	217.734782608696	7.76521739130434
103	226.5	217.734782608696	8.76521739130434
104	227.8	217.734782608696	10.0652173913044
105	228.5	217.734782608696	10.7652173913043
106	229.1	217.734782608696	11.3652173913043
107	229.9	217.734782608696	12.1652173913043

Charts produced by software:

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/16/t119522116200xlituqm1o85lv/3ml4g1195221363.png (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/16/t119522116200xlituqm1o85lv/4tmzu1195221363.png (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/16/t119522116200xlituqm1o85lv/58g901195221363.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/16/t119522116200xlituqm1o85lv/58g901195221363.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/16/t119522116200xlituqm1o85lv/63ro71195221363.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/16/t119522116200xlituqm1o85lv/63ro71195221363.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/16/t119522116200xlituqm1o85lv/7npvh1195221363.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/16/t119522116200xlituqm1o85lv/7npvh1195221363.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/16/t119522116200xlituqm1o85lv/8c2ke1195221363.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/16/t119522116200xlituqm1o85lv/8c2ke1195221363.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/16/t119522116200xlituqm1o85lv/9e0jv1195221363.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/16/t119522116200xlituqm1o85lv/9e0jv1195221363.ps (open in new window)

Parameters:

par1 = 1 ; 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

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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