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q3 dummie+trend

*The author of this computation has been verified*

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

Title produced by software: Multiple Regression

Date of computation: Wed, 19 Nov 2008 07:18:31 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/19/t1227104365gz3i5me0uw30w0h.htm/, Retrieved Wed, 19 Nov 2008 14:19:34 +0000

BibTeX entries for LaTeX users:

@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2008/Nov/19/t1227104365gz3i5me0uw30w0h.htm/},
    year = {2008},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2008},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

3.4 1 3 1 3.1 1 2.5 0 2.2 0 2.3 0 2.1 0 2.8 0 3.1 1 2.9 0 2.6 0 2.7 0 2.3 0 2.3 0 2.1 0 2.2 0 2.9 0 2.6 0 2.7 0 1.8 0 1.3 0 0.9 0 1.3 0 1.3 0 1.3 0 1.3 0 1.1 0 1.4 0 1.2 0 1.7 0 1.8 0 1.5 0 1 0 1.6 0 1.5 0 1.8 0 1.8 0 1.6 0 1.9 0 1.7 0 1.6 0 1.3 0 1.1 0 1.9 0 2.6 0 2.3 0 2.4 0 2.2 0 2 0 2.9 0 2.6 0 2.3 0 2.3 0 2.6 0 3.1 1 2.8 0 2.5 0 2.9 0 3.1 1 3.1 1 3.2 1 2.5 0 2.6 0 2.9 0 2.6 0 2.4 0 1.7 0 2 0 2.2 0 1.9 0 1.6 0 1.6 0 1.2 0 1.2 0 1.5 0 1.6 0 1.7 0 1.8 0 1.8 0 1.8 0 1.3 0 1.3 0 1.4 0 1.1 0 1.5 0 2.2 0 2.9 0 3.1 1 3.5 1 3.6 1 4.4 1 4.2 1 5.2 1 5.8 1

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 computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Multiple Linear Regression - Estimated Regression Equation

Consumptieprijsindex[t] = + 1.66897225848358 + 1.71692049618152Dumivariabele[t] -0.0619278850903809M1[t] + 0.188995886175069M2[t] + 0.287804595417827M3[t] + 0.274113304660584M4[t] + 0.310422013903342M5[t] + 0.3467307231461M6[t] + 0.180924370366167M7[t] + 0.406848141631615M8[t] + 0.241041788851683M9[t] + 0.50446556011713M10[t] + 0.0154770050429578M11[t] + 0.00119129075724229t + 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)	1.66897225848358	0.269648	6.1895	0	0
Dumivariabele	1.71692049618152	0.186074	9.2271	0	0
M1	-0.0619278850903809	0.333148	-0.1859	0.853004	0.426502
M2	0.188995886175069	0.332322	0.5687	0.571144	0.285572
M3	0.287804595417827	0.332261	0.8662	0.388971	0.194486
M4	0.274113304660584	0.332219	0.8251	0.41177	0.205885
M5	0.310422013903342	0.332196	0.9345	0.352881	0.176441
M6	0.3467307231461	0.332191	1.0438	0.299736	0.149868
M7	0.180924370366167	0.332753	0.5437	0.588147	0.294073
M8	0.406848141631615	0.332238	1.2246	0.224332	0.112166
M9	0.241041788851683	0.332772	0.7243	0.470966	0.235483
M10	0.50446556011713	0.33236	1.5178	0.133	0.0665
M11	0.0154770050429578	0.343077	0.0451	0.96413	0.482065
t	0.00119129075724229	0.002497	0.4772	0.634543	0.317271

Multiple Linear Regression - Regression Statistics
Multiple R	0.73697632247545
R-squared	0.543134099889437
Adjusted R-squared	0.468893391121471
F-TEST (value)	7.3158528373828
F-TEST (DF numerator)	13
F-TEST (DF denominator)	80
p-value	3.32162364280464e-09
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.641822164216338
Sum Squared Residuals	32.9548552383475

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	3.4	3.32515616033197	0.0748438396680255
2	3	3.57727122235465	-0.577271222354654
3	3.1	3.67727122235465	-0.577271222354654
4	2.5	1.94785072617313	0.552149273826867
5	2.2	1.98535072617313	0.214649273826866
6	2.3	2.02285072617313	0.277149273826866
7	2.1	1.85823566415044	0.241764335849557
8	2.8	2.08535072617313	0.714649273826866
9	3.1	3.63765616033196	-0.537656160331963
10	2.9	2.18535072617313	0.714649273826866
11	2.6	1.69755346185620	0.902446538143796
12	2.7	1.68326774757049	1.01673225242951
13	2.3	1.62253115323735	0.67746884676265
14	2.3	1.87464621526004	0.425353784739959
15	2.1	1.97464621526004	0.125353784739959
16	2.2	1.96214621526004	0.237853784739959
17	2.9	1.99964621526004	0.900353784739959
18	2.6	2.03714621526004	0.562853784739959
19	2.7	1.87253115323735	0.827468846762649
20	1.8	2.09964621526004	-0.299646215260041
21	1.3	1.93503115323735	-0.635031153237351
22	0.9	2.19964621526004	-1.29964621526004
23	1.3	1.71184895094311	-0.411848950943111
24	1.3	1.69756323665740	-0.397563236657395
25	1.3	1.63682664232426	-0.336826642324257
26	1.3	1.88894170434695	-0.588941704346949
27	1.1	1.98894170434695	-0.888941704346949
28	1.4	1.97644170434695	-0.576441704346949
29	1.2	2.01394170434695	-0.813941704346949
30	1.7	2.05144170434695	-0.351441704346949
31	1.8	1.88682664232426	-0.0868266423242587
32	1.5	2.11394170434695	-0.613941704346949
33	1	1.94932664232426	-0.949326642324259
34	1.6	2.21394170434695	-0.613941704346949
35	1.5	1.72614444003002	-0.226144440030018
36	1.8	1.71185872574430	0.0881412742556973
37	1.8	1.65112213141116	0.148877868588836
38	1.6	1.90323719343386	-0.303237193433857
39	1.9	2.00323719343386	-0.103237193433857
40	1.7	1.99073719343386	-0.290737193433856
41	1.6	2.02823719343386	-0.428237193433856
42	1.3	2.06573719343386	-0.765737193433856
43	1.1	1.90112213141117	-0.801122131411166
44	1.9	2.12823719343386	-0.228237193433856
45	2.6	1.96362213141117	0.636377868588834
46	2.3	2.22823719343386	0.0717628065661436
47	2.4	1.74043992911693	0.659560070883074
48	2.2	1.72615421483121	0.47384578516879
49	2	1.66541762049807	0.334582379501928
50	2.9	1.91753268252076	0.982467317479236
51	2.6	2.01753268252076	0.582467317479236
52	2.3	2.00503268252076	0.294967317479236
53	2.3	2.04253268252076	0.257467317479236
54	2.6	2.08003268252076	0.519967317479236
55	3.1	3.63233811667959	-0.532338116679594
56	2.8	2.14253268252076	0.657467317479237
57	2.5	1.97791762049807	0.522082379501926
58	2.9	2.24253268252076	0.657467317479236
59	3.1	3.47165591438535	-0.371655914385354
60	3.1	3.45737020009964	-0.357370200099638
61	3.2	3.3966336057665	-0.1966336057665
62	2.5	1.93182817160767	0.568171828392328
63	2.6	2.03182817160767	0.568171828392329
64	2.9	2.01932817160767	0.880671828392329
65	2.6	2.05682817160767	0.543171828392329
66	2.4	2.09432817160767	0.305671828392329
67	1.7	1.92971310958498	-0.229713109584982
68	2	2.15682817160767	-0.156828171607671
69	2.2	1.99221310958498	0.207786890415019
70	1.9	2.25682817160767	-0.356828171607671
71	1.6	1.76903090729074	-0.169030907290741
72	1.6	1.75474519300503	-0.154745193005025
73	1.2	1.69400859867189	-0.494008598671887
74	1.2	1.94612366069458	-0.74612366069458
75	1.5	2.04612366069458	-0.546123660694579
76	1.6	2.03362366069458	-0.433623660694579
77	1.7	2.07112366069458	-0.371123660694579
78	1.8	2.10862366069458	-0.308623660694579
79	1.8	1.94400859867189	-0.144008598671889
80	1.8	2.17112366069458	-0.371123660694579
81	1.3	2.00650859867189	-0.706508598671889
82	1.3	2.27112366069458	-0.971123660694578
83	1.4	1.78332639637765	-0.383326396377649
84	1.1	1.76904068209193	-0.669040682091933
85	1.5	1.70830408775879	-0.208304087758795
86	2.2	1.96041914978149	0.239580850218513
87	2.9	2.06041914978149	0.839580850218513
88	3.1	3.76483964596301	-0.664839645963007
89	3.5	3.80233964596301	-0.302339645963007
90	3.6	3.83983964596301	-0.239839645963007
91	4.4	3.67522458394032	0.724775416059683
92	4.2	3.90233964596301	0.297660354036993
93	5.2	3.73772458394032	1.46227541605968
94	5.8	4.00233964596301	1.79766035403699

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/19/t1227104365gz3i5me0uw30w0h/1dse11227104306.png (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/19/t1227104365gz3i5me0uw30w0h/21s871227104306.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/19/t1227104365gz3i5me0uw30w0h/21s871227104306.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/19/t1227104365gz3i5me0uw30w0h/33m5z1227104306.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/19/t1227104365gz3i5me0uw30w0h/33m5z1227104306.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/19/t1227104365gz3i5me0uw30w0h/46xx11227104306.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/19/t1227104365gz3i5me0uw30w0h/46xx11227104306.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/19/t1227104365gz3i5me0uw30w0h/57uq81227104306.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/19/t1227104365gz3i5me0uw30w0h/57uq81227104306.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/19/t1227104365gz3i5me0uw30w0h/6snc11227104306.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/19/t1227104365gz3i5me0uw30w0h/6snc11227104306.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/19/t1227104365gz3i5me0uw30w0h/709zy1227104306.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/19/t1227104365gz3i5me0uw30w0h/709zy1227104306.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/19/t1227104365gz3i5me0uw30w0h/8e11s1227104306.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/19/t1227104365gz3i5me0uw30w0h/8e11s1227104306.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/19/t1227104365gz3i5me0uw30w0h/9ba1z1227104306.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/19/t1227104365gz3i5me0uw30w0h/9ba1z1227104306.ps (open in new window)

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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