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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: Sat, 22 Nov 2008 06:22:56 -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/22/t1227360215cu64emm6qf6gluk.htm/, Retrieved Sat, 22 Nov 2008 13:23:36 +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/22/t1227360215cu64emm6qf6gluk.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 «

15859.4 0 15258.9 0 15498.6 0 15106.5 0 15023.6 0 12083.0 0 15761.3 0 16942.6 0 15070.3 0 13659.6 0 14768.9 0 14725.1 0 15998.1 0 15370.6 0 14956.9 0 15469.7 0 15101.8 0 11703.7 0 16283.6 0 16726.5 0 14968.9 0 14861.0 0 14583.3 0 15305.8 0 17903.9 0 16379.4 0 15420.3 0 17870.5 0 15912.8 0 13866.5 0 17823.2 0 17872.0 0 17422.0 0 16704.5 0 15991.2 0 16583.6 0 19123.5 0 17838.7 0 17209.4 0 18586.5 0 16258.1 0 15141.6 1 19202.1 1 17746.5 1 19090.1 1 18040.3 1 17515.5 1 17751.8 1 21072.4 1 17170.0 1 19439.5 1 19795.4 1 17574.9 1 16165.4 1 19464.6 1 19932.1 1 19961.2 1 17343.4 1 18924.2 1 18574.1 1 21350.6 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	5 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001
R Framework error message	The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'.

Multiple Linear Regression - Estimated Regression Equation

x[t] = + 13685.7137142857 + 533.767678571428`y `[t] + 2372.27384722222M1[t] + 669.098873015874M2[t] + 695.828339285715M3[t] + 1481.91780555556M4[t] + 15.7472718253979M5[t] -2347.89679761905M6[t] + 1492.33266865079M7[t] + 1554.62213492064M8[t] + 938.491601190476M9[t] -316.938932539681M10[t] -156.769466269840M11[t] + 74.6905337301587t + 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)	13685.7137142857	365.566705	37.437	0	0
`y `	533.767678571428	316.963171	1.684	0.098812	0.049406
M1	2372.27384722222	403.195795	5.8837	0	0
M2	669.098873015874	423.004094	1.5818	0.120407	0.060204
M3	695.828339285715	422.438844	1.6472	0.106194	0.053097
M4	1481.91780555556	422.040557	3.5113	0.000996	0.000498
M5	15.7472718253979	421.809707	0.0373	0.970378	0.485189
M6	-2347.89679761905	423.145504	-5.5487	1e-06	1e-06
M7	1492.33266865079	422.224628	3.5345	0.000929	0.000465
M8	1554.62213492064	421.469687	3.6886	0.000584	0.000292
M9	938.491601190476	420.881575	2.2298	0.030574	0.015287
M10	-316.938932539681	420.460991	-0.7538	0.454736	0.227368
M11	-156.769466269840	420.208439	-0.3731	0.71077	0.355385
t	74.6905337301587	8.412551	8.8785	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.956265506678066
R-squared	0.914443719262259
Adjusted R-squared	0.890779216079479
F-TEST (value)	38.6419994622026
F-TEST (DF numerator)	13
F-TEST (DF denominator)	47
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	664.27471898456
Sum Squared Residuals	20739262.4072548

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	15859.4	16132.6780952381	-273.278095238091
2	15258.9	14504.1936547619	754.706345238096
3	15498.6	14605.6136547619	892.986345238096
4	15106.5	15466.3936547619	-359.893654761905
5	15023.6	14074.9136547619	948.686345238095
6	12083	11785.9601190476	297.03988095238
7	15761.3	15700.8801190476	60.4198809523805
8	16942.6	15837.8601190476	1104.73988095238
9	15070.3	15296.4201190476	-226.120119047619
10	13659.6	14115.6801190476	-456.080119047619
11	14768.9	14350.5401190476	418.359880952381
12	14725.1	14582.0001190476	143.099880952382
13	15998.1	17028.9645	-1030.86450000000
14	15370.6	15400.4800595238	-29.8800595238109
15	14956.9	15501.9000595238	-545.00005952381
16	15469.7	16362.6800595238	-892.98005952381
17	15101.8	14971.2000595238	130.599940476190
18	11703.7	12682.2465238095	-978.546523809523
19	16283.6	16597.1665238095	-313.566523809523
20	16726.5	16734.1465238095	-7.64652380952307
21	14968.9	16192.7065238095	-1223.80652380952
22	14861	15011.9665238095	-150.966523809524
23	14583.3	15246.8265238095	-663.526523809525
24	15305.8	15478.2865238095	-172.486523809524
25	17903.9	17925.2509047619	-21.3509047619045
26	16379.4	16296.7664642857	82.6335357142853
27	15420.3	16398.1864642857	-977.886464285715
28	17870.5	17258.9664642857	611.533535714286
29	15912.8	15867.4864642857	45.3135357142848
30	13866.5	13578.5329285714	287.967071428571
31	17823.2	17493.4529285714	329.747071428573
32	17872	17630.4329285714	241.567071428572
33	17422	17088.9929285714	333.007071428572
34	16704.5	15908.2529285714	796.247071428571
35	15991.2	16143.1129285714	-151.912928571428
36	16583.6	16374.5729285714	209.027071428571
37	19123.5	18821.5373095238	301.962690476189
38	17838.7	17193.0528690476	645.647130952382
39	17209.4	17294.4728690476	-85.072869047618
40	18586.5	18155.2528690476	431.24713095238
41	16258.1	16763.7728690476	-505.672869047618
42	15141.6	15008.5870119048	133.012988095239
43	19202.1	18923.5070119048	278.592988095237
44	17746.5	19060.4870119048	-1313.98701190476
45	19090.1	18519.0470119048	571.052988095237
46	18040.3	17338.3070119048	701.992988095237
47	17515.5	17573.1670119048	-57.667011904762
48	17751.8	17804.6270119048	-52.8270119047619
49	21072.4	20251.5913928571	820.808607142857
50	17170	18623.1069523810	-1453.10695238095
51	19439.5	18724.5269523810	714.973047619048
52	19795.4	19585.3069523810	210.093047619049
53	17574.9	18193.8269523810	-618.926952380951
54	16165.4	15904.8734166667	260.526583333333
55	19464.6	19819.7934166667	-355.193416666668
56	19932.1	19956.7734166667	-24.6734166666672
57	19961.2	19415.3334166667	545.866583333334
58	17343.4	18234.5934166667	-891.193416666665
59	18924.2	18469.4534166667	454.746583333334
60	18574.1	18700.9134166667	-126.813416666667
61	21350.6	21147.8777976191	202.72220238095

Charts produced by software:

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/22/t1227360215cu64emm6qf6gluk/7h39y1227360166.ps (open in new window)

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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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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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