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Workshop 6, Q3

*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: Thu, 27 Nov 2008 08:06:29 -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/27/t1227798458zhnvwh2l4g2s5yv.htm/, Retrieved Thu, 27 Nov 2008 15:07:57 +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/27/t1227798458zhnvwh2l4g2s5yv.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)

Feedback Forum:

2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc] [reply] 
test

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

7,5 0 7,2 0 6,9 0 6,7 0 6,4 0 6,3 0 6,8 0 7,3 0 7,1 0 7,1 0 6,8 0 6,5 0 6,3 0 6,1 0 6,1 0 6,3 0 6,3 0 6 0 6,2 0 6,4 0 6,8 0 7,5 0 7,5 0 7,6 0 7,6 1 7,4 1 7,3 1 7,1 1 6,9 1 6,8 1 7,5 1 7,6 1 7,8 1 8 1 8,1 1 8,2 1 8,3 1 8,2 1 8 1 7,9 1 7,6 1 7,6 1 8,2 1 8,3 1 8,4 1 8,4 1 8,4 1 8,6 1 8,9 1 8,8 1 8,3 1 7,5 1 7,2 1 7,5 1 8,8 1 9,3 1 9,3 1 8,7 1 8,2 1 8,3 1 8,5 1 8,6 1 8,6 1 8,2 1 8,1 1 8 1 8,6 1 8,7 1 8,8 1 8,5 1 8,4 1 8,5 1 8,7 1 8,7 1 8,6 1 8,5 1 8,3 1 8,1 1 8,2 1 8,1 1 8,1 1 7,9 1 7,9 1 7,9 1 8 1 8 1 7,9 1 8 1 7,7 1 7,2 1 7,5 1 7,3 1 7 1 7 1 7 1 7,2 1 7,3 1 7,1 1 6,8 1 6,6 1 6,2 1 6,2 1 6,8 1 6,9 1 6,8 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	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

y[t] = + 7.10898437500001 + 1.66901041666666x[t] -0.0436523437499963M1[t] -0.145305266203702M2[t] -0.313624855324074M3[t] -0.493055555555555M4[t] -0.716930700231482M5[t] -0.818583622685185M6[t] -0.264680989583333M7[t] -0.110778356481481M8[t] -0.0790979456018516M9[t] + 0.0185836226851854M10[t] -0.0719581886574073M11[t] -0.0094581886574074t + 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)	7.10898437500001	0.23973	29.6541	0	0
x	1.66901041666666	0.203693	8.1937	0	0
M1	-0.0436523437499963	0.291677	-0.1497	0.881364	0.440682
M2	-0.145305266203702	0.291513	-0.4985	0.619368	0.309684
M3	-0.313624855324074	0.291377	-1.0764	0.284614	0.142307
M4	-0.493055555555555	0.291268	-1.6928	0.093917	0.046958
M5	-0.716930700231482	0.291187	-2.4621	0.015696	0.007848
M6	-0.818583622685185	0.291133	-2.8117	0.006035	0.003018
M7	-0.264680989583333	0.291106	-0.9092	0.365634	0.182817
M8	-0.110778356481481	0.291108	-0.3805	0.704431	0.352215
M9	-0.0790979456018516	0.291136	-0.2717	0.786478	0.393239
M10	0.0185836226851854	0.29957	0.062	0.950672	0.475336
M11	-0.0719581886574073	0.29953	-0.2402	0.810687	0.405343
t	-0.0094581886574074	0.002829	-3.3432	0.001204	0.000602

Multiple Linear Regression - Regression Statistics
Multiple R	0.727461330250513
R-squared	0.529199987009846
Adjusted R-squared	0.461942842296967
F-TEST (value)	7.8683088505913
F-TEST (DF numerator)	13
F-TEST (DF denominator)	91
p-value	2.91432322718777e-10
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.599033191292813
Sum Squared Residuals	32.6545095486112

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	7.5	7.05587384259257	0.444126157407434
2	7.2	6.94476273148147	0.255237268518531
3	6.9	6.76698495370371	0.133015046296294
4	6.7	6.57809606481482	0.121903935185183
5	6.4	6.34476273148148	0.0552372685185177
6	6.3	6.23365162037037	0.066348379629627
7	6.8	6.77809606481482	0.0219039351851845
8	7.3	6.92254050925926	0.377459490740739
9	7.1	6.94476273148148	0.155237268518516
10	7.1	7.03298611111111	0.0670138888888871
11	6.8	6.93298611111111	-0.132986111111113
12	6.5	6.99548611111111	-0.495486111111112
13	6.3	6.94237557870371	-0.642375578703709
14	6.1	6.8312644675926	-0.731264467592597
15	6.1	6.65348668981482	-0.553486689814817
16	6.3	6.46459780092593	-0.164597800925927
17	6.3	6.23126446759259	0.0687355324074054
18	6	6.12015335648148	-0.120153356481483
19	6.2	6.66459780092593	-0.464597800925928
20	6.4	6.80904224537037	-0.409042245370372
21	6.8	6.8312644675926	-0.0312644675925944
22	7.5	6.91948784722222	0.580512152777776
23	7.5	6.81948784722222	0.680512152777776
24	7.6	6.88198784722222	0.718012152777776
25	7.6	8.49788773148148	-0.897887731481484
26	7.4	8.38677662037037	-0.98677662037037
27	7.3	8.2089988425926	-0.908998842592592
28	7.1	8.0201099537037	-0.920109953703703
29	6.9	7.78677662037037	-0.88677662037037
30	6.8	7.67566550925926	-0.875665509259258
31	7.5	8.2201099537037	-0.720109953703703
32	7.6	8.36455439814815	-0.764554398148148
33	7.8	8.38677662037037	-0.58677662037037
34	8	8.475	-0.474999999999999
35	8.1	8.375	-0.275000000000000
36	8.2	8.4375	-0.2375
37	8.3	8.3843894675926	-0.0843894675925945
38	8.2	8.27327835648148	-0.073278356481483
39	8	8.0955005787037	-0.095500578703703
40	7.9	7.90661168981481	-0.00661168981481376
41	7.6	7.67327835648148	-0.0732783564814813
42	7.6	7.56216724537037	0.03783275462963
43	8.2	8.10661168981481	0.093388310185185
44	8.3	8.25105613425926	0.0489438657407421
45	8.4	8.27327835648148	0.126721643518519
46	8.4	8.36150173611111	0.0384982638888898
47	8.4	8.26150173611111	0.138498263888890
48	8.6	8.32400173611111	0.275998263888889
49	8.9	8.27089120370371	0.629108796296294
50	8.8	8.1597800925926	0.640219907407407
51	8.3	7.98200231481481	0.317997685185187
52	7.5	7.79311342592593	-0.293113425925925
53	7.2	7.55978009259259	-0.359780092592592
54	7.5	7.44866898148148	0.0513310185185192
55	8.8	7.99311342592593	0.806886574074075
56	9.3	8.13755787037037	1.16244212962963
57	9.3	8.1597800925926	1.14021990740741
58	8.7	8.24800347222222	0.451996527777777
59	8.2	8.14800347222222	0.0519965277777777
60	8.3	8.21050347222222	0.0894965277777792
61	8.5	8.15739293981482	0.342607060185183
62	8.6	8.0462818287037	0.553718171296295
63	8.6	7.86850405092593	0.731495949074074
64	8.2	7.67961516203704	0.520384837962963
65	8.1	7.4462818287037	0.653718171296296
66	8	7.33517071759259	0.664829282407408
67	8.6	7.87961516203704	0.720384837962963
68	8.7	8.02405960648148	0.675940393518518
69	8.8	8.0462818287037	0.753718171296297
70	8.5	8.13450520833333	0.365494791666667
71	8.4	8.03450520833333	0.365494791666668
72	8.5	8.09700520833333	0.402994791666667
73	8.7	8.04389467592593	0.65610532407407
74	8.7	7.93278356481482	0.767216435185183
75	8.6	7.75500578703704	0.844994212962963
76	8.5	7.56611689814815	0.933883101851852
77	8.3	7.33278356481481	0.967216435185186
78	8.1	7.2216724537037	0.878327546296297
79	8.2	7.76611689814815	0.433883101851852
80	8.1	7.9105613425926	0.189438657407407
81	8.1	7.93278356481481	0.167216435185185
82	7.9	8.02100694444444	-0.121006944444444
83	7.9	7.92100694444444	-0.0210069444444437
84	7.9	7.98350694444444	-0.0835069444444436
85	8	7.93039641203704	0.0696035879629601
86	8	7.81928530092593	0.180714699074073
87	7.9	7.64150752314815	0.258492476851853
88	8	7.45261863425926	0.547381365740741
89	7.7	7.21928530092593	0.480714699074074
90	7.2	7.10817418981481	0.0918258101851858
91	7.5	7.65261863425926	-0.152618634259259
92	7.3	7.7970630787037	-0.497063078703703
93	7	7.81928530092593	-0.819285300925926
94	7	7.90750868055556	-0.907508680555555
95	7	7.80750868055556	-0.807508680555555
96	7.2	7.87000868055556	-0.670008680555555
97	7.3	7.81689814814815	-0.516898148148151
98	7.1	7.70578703703704	-0.605787037037039
99	6.8	7.52800925925926	-0.728009259259259
100	6.6	7.33912037037037	-0.73912037037037
101	6.2	7.10578703703704	-0.905787037037037
102	6.2	6.99467592592593	-0.794675925925925
103	6.8	7.53912037037037	-0.73912037037037
104	6.9	7.68356481481481	-0.783564814814814
105	6.8	7.70578703703704	-0.905787037037037

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t1227798458zhnvwh2l4g2s5yv/1xzs01227798385.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t1227798458zhnvwh2l4g2s5yv/1xzs01227798385.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t1227798458zhnvwh2l4g2s5yv/2jei31227798385.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t1227798458zhnvwh2l4g2s5yv/2jei31227798385.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t1227798458zhnvwh2l4g2s5yv/3ulpf1227798385.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t1227798458zhnvwh2l4g2s5yv/3ulpf1227798385.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t1227798458zhnvwh2l4g2s5yv/4lcgp1227798385.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t1227798458zhnvwh2l4g2s5yv/4lcgp1227798385.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t1227798458zhnvwh2l4g2s5yv/5ylmm1227798385.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t1227798458zhnvwh2l4g2s5yv/5ylmm1227798385.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t1227798458zhnvwh2l4g2s5yv/6to461227798385.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t1227798458zhnvwh2l4g2s5yv/6to461227798385.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t1227798458zhnvwh2l4g2s5yv/7hhbg1227798385.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t1227798458zhnvwh2l4g2s5yv/7hhbg1227798385.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t1227798458zhnvwh2l4g2s5yv/8bdg11227798385.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t1227798458zhnvwh2l4g2s5yv/8bdg11227798385.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t1227798458zhnvwh2l4g2s5yv/9stsk1227798385.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/27/t1227798458zhnvwh2l4g2s5yv/9stsk1227798385.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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