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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: Thu, 13 Dec 2007 13:22:17 -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/13/t1197576468cptvivylpz9x2dw.htm/, Retrieved Thu, 13 Dec 2007 21:07:59 +0100

User-defined keywords:

wtc

Dataseries X:

» Textbox « » Textfile « » CSV «

98.6 0 98 0 106.8 0 96.6 0 100.1 0 107.7 0 91.5 0 97.8 0 107.4 1 117.5 1 105.6 1 97.4 1 99.5 1 98 1 104.3 1 100.6 1 101.1 1 103.9 1 96.9 1 95.5 1 108.4 1 117 1 103.8 1 100.8 1 110.6 1 104 1 112.6 1 107.3 1 98.9 1 109.8 1 104.9 1 102.2 1 123.9 1 124.9 1 112.7 1 121.9 1 100.6 1 104.3 1 120.4 1 107.5 1 102.9 1 125.6 1 107.5 1 108.8 1 128.4 1 121.1 1 119.5 1 128.7 1 108.7 1 105.5 1 119.8 1 111.3 1 110.6 1 120.1 1 97.5 1 107.7 1 127.3 1 117.2 1 119.8 1 116.2 1 111 1 112.4 1 130.6 1 109.1 1 118.8 1 123.9 1 101.6 1 112.8 1 128 1 129.6 1 125.8 1 119.5 1 115.7 1 113.6 1 129.7 1 112 1 116.8 1 126.3 1 112.9 1 115.9 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

Totaal[t] = + 103.887500000000 -2.05083333333325`WTC11-09`[t] -6.5326587301588M1[t] -8.09567460317459M2[t] + 4.24130952380952M3[t] -7.45027777777778M4[t] -7.05615079365079M5[t] + 2.38083333333334M6[t] -12.8393253968254M7[t] -9.1451984126984M8[t] + 7.35809523809524M9[t] + 7.71650793650794M10[t] + 0.741587301587295M11[t] + 0.291587301587302t + 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)	103.887500000000	2.598345	39.9822	0	0
`WTC11-09`	-2.05083333333325	2.100217	-0.9765	0.332389	0.166195
M1	-6.5326587301588	2.598482	-2.514	0.014383	0.007191
M2	-8.09567460317459	2.598894	-3.115	0.002721	0.001361
M3	4.24130952380952	2.599582	1.6315	0.10754	0.05377
M4	-7.45027777777778	2.600543	-2.8649	0.005589	0.002795
M5	-7.05615079365079	2.601779	-2.712	0.008517	0.004259
M6	2.38083333333334	2.603289	0.9145	0.363758	0.181879
M7	-12.8393253968254	2.605072	-4.9286	6e-06	3e-06
M8	-9.1451984126984	2.607128	-3.5078	0.000819	0.000409
M9	7.35809523809524	2.684756	2.7407	0.00788	0.00394
M10	7.71650793650794	2.684091	2.8749	0.005434	0.002717
M11	0.741587301587295	2.683692	0.2763	0.783157	0.391579
t	0.291587301587302	0.026729	10.9091	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.906469959176328
R-squared	0.821687786889133
Adjusted R-squared	0.78656568430669
F-TEST (value)	23.3951764408283
F-TEST (DF numerator)	13
F-TEST (DF denominator)	66
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	4.64805996085586
Sum Squared Residuals	1425.89445238095

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	98.6	97.646428571429	0.953571428571022
2	98	96.375	1.62500000000004
3	106.8	109.003571428571	-2.20357142857138
4	96.6	97.6035714285714	-1.00357142857139
5	100.1	98.2892857142857	1.81071428571434
6	107.7	108.017857142857	-0.317857142857068
7	91.5	93.0892857142857	-1.58928571428565
8	97.8	97.075	0.725000000000066
9	107.4	111.819047619048	-4.41904761904763
10	117.5	112.469047619048	5.03095238095239
11	105.6	105.785714285714	-0.185714285714298
12	97.4	105.335714285714	-7.93571428571427
13	99.5	99.0946428571428	0.405357142857214
14	98	97.8232142857143	0.176785714285718
15	104.3	110.451785714286	-6.15178571428572
16	100.6	99.0517857142857	1.54821428571428
17	101.1	99.7375	1.36249999999998
18	103.9	109.466071428571	-5.56607142857143
19	96.9	94.5375	2.36249999999999
20	95.5	98.5232142857143	-3.0232142857143
21	108.4	115.318095238095	-6.91809523809523
22	117	115.968095238095	1.03190476190476
23	103.8	109.284761904762	-5.4847619047619
24	100.8	108.834761904762	-8.03476190476191
25	110.6	102.593690476190	8.00630952380959
26	104	101.322261904762	2.67773809523809
27	112.6	113.950833333333	-1.35083333333334
28	107.3	102.550833333333	4.74916666666666
29	98.9	103.236547619048	-4.33654761904762
30	109.8	112.965119047619	-3.16511904761906
31	104.9	98.0365476190476	6.86345238095237
32	102.2	102.022261904762	0.177738095238085
33	123.9	118.817142857143	5.08285714285715
34	124.9	119.467142857143	5.43285714285715
35	112.7	112.783809523810	-0.083809523809515
36	121.9	112.333809523810	9.56619047619048
37	100.6	106.092738095238	-5.49273809523803
38	104.3	104.821309523810	-0.521309523809533
39	120.4	117.449880952381	2.95011904761905
40	107.5	106.049880952381	1.45011904761904
41	102.9	106.735595238095	-3.83559523809524
42	125.6	116.464166666667	9.13583333333332
43	107.5	101.535595238095	5.96440476190475
44	108.8	105.521309523810	3.27869047619046
45	128.4	122.316190476190	6.08380952380953
46	121.1	122.966190476190	-1.86619047619049
47	119.5	116.282857142857	3.21714285714286
48	128.7	115.832857142857	12.8671428571428
49	108.7	109.591785714286	-0.891785714285641
50	105.5	108.320357142857	-2.82035714285715
51	119.8	120.948928571429	-1.14892857142858
52	111.3	109.548928571429	1.75107142857142
53	110.6	110.234642857143	0.365357142857127
54	120.1	119.963214285714	0.136785714285695
55	97.5	105.034642857143	-7.53464285714287
56	107.7	109.020357142857	-1.32035714285715
57	127.3	125.815238095238	1.48476190476190
58	117.2	126.465238095238	-9.2652380952381
59	119.8	119.781904761905	0.0180952380952398
60	116.2	119.331904761905	-3.13190476190476
61	111	113.090833333333	-2.09083333333326
62	112.4	111.819404761905	0.580595238095237
63	130.6	124.447976190476	6.1520238095238
64	109.1	113.047976190476	-3.9479761904762
65	118.8	113.733690476190	5.06630952380951
66	123.9	123.462261904762	0.437738095238089
67	101.6	108.533690476190	-6.93369047619049
68	112.8	112.519404761905	0.280595238095223
69	128	129.314285714286	-1.31428571428571
70	129.6	129.964285714286	-0.364285714285725
71	125.8	123.280952380952	2.51904761904762
72	119.5	122.830952380952	-3.33095238095238
73	115.7	116.589880952381	-0.88988095238088
74	113.6	115.318452380952	-1.71845238095239
75	129.7	127.947023809524	1.75297619047618
76	112	116.547023809524	-4.54702380952381
77	116.8	117.232738095238	-0.432738095238105
78	126.3	126.961309523810	-0.661309523809538
79	112.9	112.032738095238	0.8672619047619
80	115.9	116.018452380952	-0.118452380952390

Charts produced by software:

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Parameters (Session):

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

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = 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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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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