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Workshop 6 Q3

R Software Module: rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Sun, 18 Nov 2007 09:02:48 -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/18/t11954014147kb3e2i55bjtn7e.htm/, Retrieved Sun, 18 Nov 2007 16:56:54 +0100

User-defined keywords:

Multiple Regression line

Dataseries X:

» Textbox « » Textfile « » CSV «

100,6 115,9 59,7 96,1 112,9 58,2 110 126,3 75,3 108,2 116,8 69 106,9 112 66,1 117,2 129,7 77,5 105,2 113,6 69,3 106,3 115,7 70,2 95,9 119,5 70,2 107,5 125,8 78,2 113 129,6 85,4 111,4 128 82,4 95,5 112,8 61,2 90,3 101,6 52,2 110,8 123,9 85,3 107,1 118,8 79,9 101,4 109,1 72,2 112,9 130,6 85,7 98,5 112,4 75,5 100,1 111 69,2 93,4 116,2 77,6 104,4 119,8 85,3 101,8 117,2 77 107,9 127,3 89,9 91,3 107,7 60 86,6 97,5 54,3 111,4 120,1 84 98,4 110,6 69,9 102,2 111,3 75,1 103 119,8 81,7 95,8 105,5 69,9 96 108,7 68,3 95,7 128,7 77,3 106,4 119,5 77,4 112 121,1 85,3 116,2 128,4 91 93,9 108,8 60,6 100,5 107,5 57,6 112,5 125,6 93,8 101,2 102,9 78,7 107,8 107,5 80,3 114,3 120,4 89,8 99,6 104,3 77,5 98,6 100,6 71,7 93,6 121,9 83,2 99,6 112,7 86,2 113,1 124,9 100,7 110,7 123,9 100,8 88,1 102,2 57,1 93,1 104,9 62,5 107,4 109,8 79,7 99,5 98,9 80,3 105,6 107,3 92,4 108,3 112,6 91,8 99,2 104 85,8 99,3 110,6 84,2 107,1 100,8 93,1 106,9 103,8 101,2 115,4 117 100,6 99 108,4 106,7 100,1 95,5 64 96,2 96,9 67,5 96,9 103,9 101 96,2 101,1 95,5 91 100,6 97 99 104,3 103,8 99 98 95,2 107,2 99,5 86,7 110,8 97,4 93,5 111,1 105,6 102,5 104,6 117,5 112,3 94,3 107,4 105,5 90,7 97,8 75,4 88,8 91,5 70,4 90,9 107,7 108 90,5 100,1 100 95,5 96,6 93,3 103,1 106,8 111,1 100,6 98 101,1 103,1 98,6 98,1

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	6 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Multiple Linear Regression - Estimated Regression Equation

Int[t] = + 39.8313765615007 + 0.443260583766398Cons[t] + 0.157433989020551Duurzcons[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)	39.8313765615007	7.695576	5.1759	2e-06	1e-06
Cons	0.443260583766398	0.062715	7.0679	0	0
Duurzcons	0.157433989020551	0.042671	3.6895	0.000417	0.000209

Multiple Linear Regression - Regression Statistics
Multiple R	0.678910073141829
R-squared	0.460918887413444
Adjusted R-squared	0.446916780593014
F-TEST (value)	32.9178239621006
F-TEST (DF numerator)	2
F-TEST (DF denominator)	77
p-value	4.66319205472132e-11
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	5.60341382082505
Sum Squared Residuals	2417.66497645081

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	100.6	100.604087364553	-0.00408736455320509
2	96.1	99.0381546297231	-2.93815462972312
3	110	107.669967664444	2.33003233555573
4	108.2	102.467157987834	5.73284201216599
5	106.9	99.8829486175957	7.0170513824043
6	117.2	109.523408425095	7.67659157490478
7	105.2	101.095954316488	4.10404568351230
8	106.3	102.168492132516	4.13150786748436
9	95.9	103.852882350828	-7.95288235082795
10	107.5	107.904895940721	-0.404895940720662
11	113	110.722810879981	2.27718912001906
12	111.4	109.541291978893	1.85870802110695
13	95.5	99.4661305384081	-3.96613053840813
14	90.3	93.0847060990395	-2.78470609903952
15	110.8	108.180482153610	2.61951784638958
16	107.1	105.069709635691	2.03029036430918
17	101.4	99.5578402576985	1.84215974230149
18	112.9	111.213301660453	1.68669833954650
19	98.5	101.540132347895	-3.04013234789545
20	100.1	99.927733399793	0.172266600206973
21	93.4	103.555133943151	-10.1551339431509
22	104.4	106.363113760168	-1.96311376016818
23	101.8	103.903934133505	-2.10393413350499
24	107.9	110.411764487911	-2.51176448791070
25	91.3	97.0165807743748	-5.71658077437485
26	86.6	91.5979490825405	-4.99794908254045
27	111.4	106.291427749571	5.10857225042862
28	98.4	99.8606329586008	-1.46063295860084
29	102.2	100.989572110144	1.21042788985582
30	103	105.796351399694	-2.79635139969420
31	95.8	97.6000039813922	-1.80000398139222
32	96	98.7665434670118	-2.76654346701181
33	95.7	109.048661043525	-13.3486610435247
34	106.4	104.986407071776	1.41359292822409
35	112	106.939352519064	5.0606474809355
36	116.2	111.072528517976	5.12747148202365
37	93.9	97.5986278099302	-3.69862780993020
38	100.5	96.5500870839722	3.94991291602776
39	112.5	110.272214052688	2.22778594731203
40	101.2	97.8329455669804	3.36705443301957
41	107.8	100.123838634739	7.67616136526125
42	114.3	107.337523061021	6.96247693897949
43	99.6	98.2645895974287	1.33541040257127
44	98.6	95.7114083011739	2.88859169882613
45	93.6	106.963349609134	-13.3633496091345
46	99.6	103.357654205545	-3.75765420554527
47	113.1	111.048226168293	2.05177383170669
48	110.7	110.620708983429	0.079291016571046
49	88.1	94.1220889955	-6.02208899550006
50	93.1	96.1690361123803	-3.06903611238031
51	107.4	101.048877583989	6.35112241601088
52	99.5	96.3117976143477	3.18820238565228
53	105.6	101.940137785134	3.65986221486587
54	108.3	104.194958485684	4.10504151431630
55	99.2	99.4383135311694	-0.238313531169377
56	99.3	102.111939001595	-2.81193900159472
57	107.1	99.169147782967	7.93085221703307
58	106.9	101.774144845333	5.12585515466743
59	115.4	107.530724157637	7.8692758423633
60	99	104.679030470271	-5.67903047027104
61	100.1	92.238537608507	7.861462391493
62	96.2	93.4101213873519	2.78987861264812
63	96.9	101.786984105905	-4.88698410590511
64	96.2	99.6799675317462	-3.47996753174616
65	91	99.6944882233938	-8.6944882233938
66	99	102.405103508669	-3.40510350866921
67	99	98.2586295253642	0.741370474635829
68	107.2	97.585331494339	9.61466850566092
69	110.8	97.7250353937694	13.0749646062306
70	111.1	102.776678081839	8.32332191816118
71	104.6	109.594332121060	-4.99433212106035
72	94.3	104.04684909968	-9.74684909967999
73	90.7	95.052784426004	-4.35278442600398
74	88.8	91.473072803173	-2.67307280317293
75	90.9	104.573412247361	-13.6734122473613
76	90.5	99.9451598985722	-9.44515989857225
77	95.5	97.3389401289522	-1.83894012895216
78	103.1	104.662523087935	-1.56252308793523
79	100.6	99.1874900605854	1.41250993941458
80	103.1	98.9811444437836	4.11885555621639

Charts produced by software:

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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

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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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