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*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: Mon, 24 Nov 2008 17:12:13 -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/25/t12275719677ahdbkdxghil4rd.htm/, Retrieved Tue, 25 Nov 2008 00:12:55 +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/25/t12275719677ahdbkdxghil4rd.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 «

89.6 0 92.8 0 107.6 0 104.6 0 103.0 0 106.9 0 56.3 0 93.4 0 109.1 0 113.8 0 97.4 0 72.5 0 82.7 0 88.9 0 105.9 0 100.8 0 94.0 0 105.0 0 58.5 0 87.6 0 113.1 0 112.5 0 89.6 0 74.5 0 82.7 0 90.1 0 109.4 0 96.0 0 89.2 0 109.1 0 49.1 1 92.9 1 107.7 1 103.5 1 91.1 1 79.8 1 71.9 1 82.9 1 90.1 1 100.7 1 90.7 1 108.8 1 44.1 1 93.6 1 107.4 1 96.5 1 93.6 1 76.5 1 76.7 1 84.0 1 103.3 1 88.5 1 99.0 1 105.9 1 44.7 1 94.0 0 107.1 0 104.8 0 102.5 0 77.7 0 85.2 0 91.3 0 106.5 0 92.4 0 97.5 0 107.0 0 51.1 0 98.6 0 102.2 0 114.3 0 99.4 0 72.5 0 92.3 0 99.4 0 85.9 0 109.4 0 97.6 0 104.7 0 56.5 0

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] = + 77.6562368972747 -4.82405660377359x[t] + 7.14589198362787M1[t] + 14.0569606668664M2[t] + 25.3966007786762M3[t] + 23.0790980333433M4[t] + 20.0330238594390M5[t] + 30.9583782569632M6[t] -23.6414021164021M7[t] + 17.7223919337127M8[t] + 32.1501272836178M9[t] + 31.9611959668563M10[t] + 20.0055979834282M11[t] -0.0110686832384945t + 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)	77.6562368972747	2.443488	31.7809	0	0
x	-4.82405660377359	1.288105	-3.7451	0.000385	0.000192
M1	7.14589198362787	2.942881	2.4282	0.017951	0.008975
M2	14.0569606668664	2.941874	4.7782	1e-05	5e-06
M3	25.3966007786762	2.941102	8.6351	0	0
M4	23.0790980333433	2.940564	7.8485	0	0
M5	20.0330238594390	2.94026	6.8134	0	0
M6	30.9583782569632	2.94019	10.5294	0	0
M7	-23.6414021164021	2.942131	-8.0355	0	0
M8	17.7223919337127	3.052321	5.8062	0	0
M9	32.1501272836178	3.051531	10.5357	0	0
M10	31.9611959668563	3.050967	10.4758	0	0
M11	20.0055979834282	3.050628	6.5579	0	0
t	-0.0110686832384945	0.026249	-0.4217	0.674647	0.337323

Multiple Linear Regression - Regression Statistics
Multiple R	0.9569328575323
R-squared	0.915720493824934
Adjusted R-squared	0.898864592589921
F-TEST (value)	54.3264036171971
F-TEST (DF numerator)	13
F-TEST (DF denominator)	65
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	5.28364714189449
Sum Squared Residuals	1814.60026280323

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	89.6	84.7910601976639	4.80893980233612
2	92.8	91.691060197664	1.10893980233604
3	107.6	103.019631626235	4.58036837376456
4	104.6	100.691060197664	3.90893980233596
5	103	97.633917340521	5.36608265947891
6	106.9	108.548203054807	-1.64820305480682
7	56.3	53.937353998203	2.36264600179695
8	93.4	95.2900793650794	-1.89007936507938
9	109.1	109.706746031746	-0.606746031746072
10	113.8	109.506746031746	4.29325396825394
11	97.4	97.5400793650794	-0.140079365079344
12	72.5	77.5234126984127	-5.02341269841268
13	82.7	84.658235998802	-1.95823599880205
14	88.9	91.558235998802	-2.65823599880203
15	105.9	102.886807427373	3.01319257262654
16	100.8	100.558235998802	0.241764001197966
17	94	97.5010931416592	-3.50109314165918
18	105	108.415378855945	-3.41537885594489
19	58.5	53.8045297993411	4.69547020065889
20	87.6	95.1572551662174	-7.55725516621743
21	113.1	109.573921832884	3.52607816711591
22	112.5	109.373921832884	3.12607816711591
23	89.6	97.4072551662174	-7.80725516621744
24	74.5	77.3905884995508	-2.89058849955076
25	82.7	84.5254117999401	-1.82541179994012
26	90.1	91.4254117999401	-1.32541179994011
27	109.4	102.753983228512	6.64601677148848
28	96	100.42541179994	-4.42541179994009
29	89.2	97.3682689427972	-8.16826894279725
30	109.1	108.282554657083	0.817445342917033
31	49.1	48.8476489967056	0.252351003294395
32	92.9	90.2003743635819	2.6996256364181
33	107.7	104.617041030249	3.08295896975143
34	103.5	104.417041030249	-0.917041030248573
35	91.1	92.4503743635819	-1.35037436358192
36	79.8	72.4337076969152	7.36629230308475
37	71.9	79.5685309973046	-7.66853099730459
38	82.9	86.4685309973046	-3.56853099730458
39	90.1	97.797102425876	-7.69710242587601
40	100.7	95.4685309973046	5.23146900269543
41	90.7	92.4113881401617	-1.71138814016172
42	108.8	103.325673854447	5.47432614555256
43	44.1	48.7148247978437	-4.61482479784367
44	93.6	90.06755016472	3.53244983528002
45	107.4	104.484216831387	2.91578316861337
46	96.5	104.284216831387	-7.78421683138664
47	93.6	92.31755016472	1.28244983528002
48	76.5	72.3008834980533	4.19911650194669
49	76.7	79.4357067984427	-2.73570679844266
50	84	86.3357067984427	-2.33570679844265
51	103.3	97.664278227014	5.63572177298593
52	88.5	95.3357067984426	-6.83570679844264
53	99	92.2785639412998	6.7214360587002
54	105.9	103.192849655586	2.7071503444145
55	44.7	48.5820005989817	-3.88200059898174
56	94	94.7587825696316	-0.758782569631617
57	107.1	109.175449236298	-2.07544923629829
58	104.8	108.975449236298	-4.17544923629829
59	102.5	97.0087825696316	5.49121743036837
60	77.7	76.992115902965	0.707884097035043
61	85.2	84.1269392033543	1.07306079664569
62	91.3	91.0269392033543	0.273060796645696
63	106.5	102.355510631926	4.14448936807428
64	92.4	100.026939203354	-7.62693920335429
65	97.5	96.9697963462114	0.530203653788556
66	107	107.884082060497	-0.884082060497156
67	51.1	53.2732330038934	-2.17323300389338
68	98.6	94.6259583707697	3.97404162923031
69	102.2	109.042625037436	-6.84262503743635
70	114.3	108.842625037436	5.45737496256364
71	99.4	96.8759583707697	2.52404162923031
72	72.5	76.859291704103	-4.35929170410303
73	92.3	83.9941150044924	8.30588499550762
74	99.4	90.8941150044924	8.50588499550764
75	85.9	102.222686433064	-16.3226864330638
76	109.4	99.8941150044924	9.50588499550765
77	97.6	96.8369721473495	0.763027852650485
78	104.7	107.751257861635	-3.05125786163522
79	56.5	53.1404088050314	3.35959119496856

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/25/t12275719677ahdbkdxghil4rd/1bo4k1227571929.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/25/t12275719677ahdbkdxghil4rd/1bo4k1227571929.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/25/t12275719677ahdbkdxghil4rd/2tkk21227571929.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/25/t12275719677ahdbkdxghil4rd/2tkk21227571929.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/25/t12275719677ahdbkdxghil4rd/3vrgu1227571929.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/25/t12275719677ahdbkdxghil4rd/3vrgu1227571929.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/25/t12275719677ahdbkdxghil4rd/4kh081227571929.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/25/t12275719677ahdbkdxghil4rd/4kh081227571929.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/25/t12275719677ahdbkdxghil4rd/5jpap1227571929.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/25/t12275719677ahdbkdxghil4rd/5jpap1227571929.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/25/t12275719677ahdbkdxghil4rd/6h64j1227571929.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/25/t12275719677ahdbkdxghil4rd/6h64j1227571929.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/25/t12275719677ahdbkdxghil4rd/78b2h1227571929.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/25/t12275719677ahdbkdxghil4rd/78b2h1227571929.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/25/t12275719677ahdbkdxghil4rd/8e76t1227571929.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/25/t12275719677ahdbkdxghil4rd/8e76t1227571929.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/25/t12275719677ahdbkdxghil4rd/99lug1227571929.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/25/t12275719677ahdbkdxghil4rd/99lug1227571929.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

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

We may request personal information to be submitted to our servers in order to be able to:

personalize online software applications according to your needs
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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