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paper_multiple_regression_2dummies

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

Title produced by software: Multiple Regression

Date of computation: Fri, 14 Dec 2007 03:34:34 -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/14/t119762781024bwp9apk1pchom.htm/, Retrieved Fri, 14 Dec 2007 11:23:40 +0100

User-defined keywords:

s0650921, 0650125

Dataseries X:

» Textbox « » Textfile « » CSV «

102.7 0 0 103.2 0 0 105.6 0 0 103.9 0 0 107.2 0 0 100.7 0 0 92.1 0 0 90.3 0 0 93.4 0 0 98.5 0 0 100.8 0 0 102.3 0 0 104.7 0 0 101.1 0 0 101.4 0 0 99.5 0 0 98.4 0 0 96.3 0 0 100.7 0 0 101.2 0 0 100.3 0 0 97.8 0 0 97.4 0 0 98.6 0 0 99.7 0 0 99.0 0 0 98.1 0 0 97.0 0 0 98.5 0 0 103.8 0 0 114.4 0 0 124.5 0 0 134.2 0 0 131.8 0 0 125.6 0 0 119.9 0 0 114.9 0 0 115.5 0 0 112.5 0 0 111.4 0 0 115.3 0 0 110.8 0 0 103.7 0 0 111.1 0 1 113.0 0 1 111.2 0 1 117.6 0 1 121.7 0 1 127.3 0 1 129.8 0 1 137.1 0 1 141.4 0 1 137.4 0 1 130.7 0 1 117.2 0 1 110.8 0 0 111.4 0 0 108.2 0 0 108.8 0 0 110.2 0 0 109.5 1 0 109.5 1 0 116.0 1 0 111.2 1 0 112.1 1 0 114.0 1 0 119.1 1 0 114.1 1 2 115.1 1 2 115.4 1 2 110.8 1 2 116.0 1 2 119.2 2 2 126.5 2 2 127.8 2 2 131.3 2 2 140.3 2 2 137.3 2 2 143.0 2 2 134.5 2 0 139.9 2 0 159.3 2 0 170.4 2 0 175.0 2 0 175.8 2 0 180.9 2 0 180.3 2 0 169.6 2 0 172.3 2 0 184.8 2 0 177.7 2 0 184.6 2 0 211.4 2 0 215.3 2 0 215.9 2 0

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

graanprijs[t] = + 90.6785257984054 + 11.1582395826032ontkoppelde_bedrijfstoeslag[t] -11.2396111935848oogstomvang[t] + 0.625545648317884t + 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)	90.6785257984054	4.029015	22.5064	0	0
ontkoppelde_bedrijfstoeslag	11.1582395826032	3.606864	3.0936	0.002626	0.001313
oogstomvang	-11.2396111935848	2.475575	-4.5402	1.7e-05	9e-06
t	0.625545648317884	0.114217	5.4768	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.842616613280444
R-squared	0.710002756976206
Adjusted R-squared	0.700442408305092
F-TEST (value)	74.265362216488
F-TEST (DF numerator)	3
F-TEST (DF denominator)	91
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	15.8101839862357
Sum Squared Residuals	22746.5345087547

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	102.7	91.3040714467235	11.3959285532766
2	103.2	91.9296170950413	11.2703829049588
3	105.6	92.555162743359	13.0448372566409
4	103.9	93.180708391677	10.7192916083231
5	107.2	93.8062540399949	13.3937459600052
6	100.7	94.4317996883127	6.26820031168726
7	92.1	95.0573453366306	-2.95734533663062
8	90.3	95.6828909849485	-5.3828909849485
9	93.4	96.3084366332664	-2.90843663326638
10	98.5	96.9339822815843	1.56601771841573
11	100.8	97.5595279299022	3.24047207009784
12	102.3	98.18507357822	4.11492642177996
13	104.7	98.810619226538	5.88938077346208
14	101.1	99.4361648748558	1.66383512514418
15	101.4	100.061710523174	1.33828947682631
16	99.5	100.687256171492	-1.18725617149158
17	98.4	101.312801819809	-2.91280181980946
18	96.3	101.938347468127	-5.63834746812735
19	100.7	102.563893116445	-1.86389311644523
20	101.2	103.189438764763	-1.98943876476311
21	100.3	103.814984413081	-3.514984413081
22	97.8	104.440530061399	-6.64053006139888
23	97.4	105.066075709717	-7.66607570971676
24	98.6	105.691621358035	-7.09162135803466
25	99.7	106.317167006353	-6.61716700635253
26	99	106.942712654670	-7.94271265467042
27	98.1	107.568258302988	-9.4682583029883
28	97	108.193803951306	-11.1938039513062
29	98.5	108.819349599624	-10.3193495996241
30	103.8	109.444895247942	-5.64489524794196
31	114.4	110.070440896260	4.32955910374017
32	124.5	110.695986544578	13.8040134554223
33	134.2	111.321532192896	22.8784678071044
34	131.8	111.947077841213	19.8529221587865
35	125.6	112.572623489531	13.0273765104686
36	119.9	113.198169137849	6.70183086215074
37	114.9	113.823714786167	1.07628521383286
38	115.5	114.449260434485	1.05073956551497
39	112.5	115.074806082803	-2.57480608280291
40	111.4	115.700351731121	-4.30035173112079
41	115.3	116.325897379439	-1.02589737943868
42	110.8	116.951443027757	-6.15144302775657
43	103.7	117.576988676074	-13.8769886760744
44	111.1	106.962923130808	4.13707686919245
45	113	107.588468779125	5.41153122087457
46	111.2	108.214014427443	2.98598557255669
47	117.6	108.839560075761	8.7604399242388
48	121.7	109.465105724079	12.2348942759209
49	127.3	110.090651372397	17.2093486276030
50	129.8	110.716197020715	19.0838029792852
51	137.1	111.341742669033	25.7582573309673
52	141.4	111.967288317351	29.4327116826494
53	137.4	112.592833965669	24.8071660343315
54	130.7	113.218379613986	17.4816203860136
55	117.2	113.843925262304	3.35607473769574
56	110.8	125.709082104207	-14.9090821042069
57	111.4	126.334627752525	-14.9346277525248
58	108.2	126.960173400843	-18.7601734008427
59	108.8	127.585719049161	-18.7857190491606
60	110.2	128.211264697478	-18.0112646974785
61	109.5	139.995049928400	-30.4950499283996
62	109.5	140.620595576717	-31.1205955767174
63	116	141.246141225035	-25.2461412250353
64	111.2	141.871686873353	-30.6716868733532
65	112.1	142.497232521671	-30.3972325216711
66	114	143.122778169989	-29.122778169989
67	119.1	143.748323818307	-24.6483238183069
68	114.1	121.894647079455	-7.79464707945516
69	115.1	122.520192727773	-7.42019272777305
70	115.4	123.145738376091	-7.74573837609092
71	110.8	123.771284024409	-12.9712840244088
72	116	124.396829672727	-8.39682967272669
73	119.2	136.180614903648	-16.9806149036478
74	126.5	136.806160551966	-10.3061605519657
75	127.8	137.431706200284	-9.63170620028354
76	131.3	138.057251848601	-6.75725184860141
77	140.3	138.682797496919	1.61720250308070
78	137.3	139.308343145237	-2.00834314523718
79	143	139.933888793555	3.06611120644492
80	134.5	163.038656829043	-28.5386568290425
81	139.9	163.664202477360	-23.7642024773604
82	159.3	164.289748125678	-4.98974812567829
83	170.4	164.915293773996	5.48470622600382
84	175	165.540839422314	9.45916057768593
85	175.8	166.166385070632	9.63361492936805
86	180.9	166.79193071895	14.1080692810502
87	180.3	167.417476367268	12.8825236327323
88	169.6	168.043022015586	1.55697798441439
89	172.3	168.668567663904	3.63143233609652
90	184.8	169.294113312221	15.5058866877786
91	177.7	169.919658960539	7.78034103946073
92	184.6	170.545204608857	14.0547953911429
93	211.4	171.170750257175	40.229249742825
94	215.3	171.796295905493	43.5037040945071
95	215.9	172.421841553811	43.4781584461892

Charts produced by software:

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Parameters (Session):

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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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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