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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: Tue, 25 Nov 2008 00:27:34 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/25/t1227598107irqzvf9aze1p5mh.htm/, Retrieved Tue, 25 Nov 2008 07:28:35 +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/t1227598107irqzvf9aze1p5mh.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 «

106.7 0 110.2 0 125.9 0 100.1 0 106.4 0 114.8 0 81.3 0 87 0 104.2 0 108 0 105 0 94.5 0 92 0 95.9 0 108.8 0 103.4 0 102.1 0 110.1 0 83.2 0 82.7 0 106.8 0 113.7 0 102.5 0 96.6 0 92.1 0 95.6 0 102.3 0 98.6 0 98.2 0 104.5 0 84 0 73.8 0 103.9 0 106 0 97.2 0 102.6 0 89 0 93.8 0 116.7 1 106.8 1 98.5 1 118.7 1 90 1 91.9 1 113.3 1 113.1 1 104.1 1 108.7 1 96.7 1 101 1 116.9 1 105.8 1 99 1 129.4 1 83 1 88.9 1 115.9 1 104.2 1 113.4 1 112.2 1 100.8 1 107.3 1 126.6 1 102.9 1 117.9 1 128.8 1 87.5 1 93.8 1 122.7 1 126.2 1 124.6 1 116.7 1 115.2 1 111.1 1 129.9 1 113.3 1 118.5 1 133.5 1 102.1 1 102.4 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	16 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Multiple Linear Regression - Estimated Regression Equation

y[t] = + 97.545 + 5.53874999999998x[t] -5.30886408730163M1[t] -2.22558531746031M2[t] + 12.8950148809524M3[t] -0.964563492063498M4[t] + 0.304429563492081M5[t] + 14.3591369047619M6[t] -18.4290128968254M7[t] -17.2028769841270M8[t] + 6.26683035714287M9[t] + 6.88344246031746M10[t] + 2.70005456349207M11[t] + 0.116721230158731t + 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)	97.545	3.117271	31.2918	0	0
x	5.53874999999998	2.969448	1.8652	0.066593	0.033297
M1	-5.30886408730163	3.660279	-1.4504	0.151683	0.075842
M2	-2.22558531746031	3.658449	-0.6083	0.545049	0.272525
M3	12.8950148809524	3.677018	3.5069	0.000821	0.00041
M4	-0.964563492063498	3.671017	-0.2628	0.793561	0.39678
M5	0.304429563492081	3.666127	0.083	0.934072	0.467036
M6	14.3591369047619	3.662351	3.9207	0.000213	0.000106
M7	-18.4290128968254	3.659693	-5.0357	4e-06	2e-06
M8	-17.2028769841270	3.658156	-4.7026	1.4e-05	7e-06
M9	6.26683035714287	3.799089	1.6496	0.103785	0.051892
M10	6.88344246031746	3.796386	1.8132	0.074355	0.037177
M11	2.70005456349207	3.794763	0.7115	0.479269	0.239634
t	0.116721230158731	0.064078	1.8215	0.073057	0.036529

Multiple Linear Regression - Regression Statistics
Multiple R	0.881461940737189
R-squared	0.776975152968172
Adjusted R-squared	0.733046016431599
F-TEST (value)	17.6870117244694
F-TEST (DF numerator)	13
F-TEST (DF denominator)	66
p-value	1.11022302462516e-16
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	6.57178533306778
Sum Squared Residuals	2850.43192261904

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	106.7	92.3528571428574	14.3471428571426
2	110.2	95.5528571428571	14.6471428571429
3	125.9	110.790178571429	15.1098214285714
4	100.1	97.0473214285714	3.05267857142857
5	106.4	98.4330357142857	7.9669642857143
6	114.8	112.604464285714	2.19553571428574
7	81.3	79.9330357142857	1.36696428571428
8	87	81.2758928571428	5.72410714285718
9	104.2	104.862321428571	-0.662321428571399
10	108	105.595654761905	2.40434523809523
11	105	101.528988095238	3.47101190476192
12	94.5	98.9456547619047	-4.44565476190473
13	92	93.7535119047619	-1.75351190476185
14	95.9	96.9535119047619	-1.0535119047619
15	108.8	112.190833333333	-3.39083333333333
16	103.4	98.4479761904762	4.95202380952382
17	102.1	99.8336904761905	2.26630952380952
18	110.1	114.005119047619	-3.90511904761906
19	83.2	81.3336904761905	1.86630952380953
20	82.7	82.6765476190476	0.0234523809523808
21	106.8	106.262976190476	0.537023809523803
22	113.7	106.996309523810	6.70369047619048
23	102.5	102.929642857143	-0.429642857142853
24	96.6	100.346309523810	-3.74630952380952
25	92.1	95.1541666666666	-3.05416666666662
26	95.6	98.3541666666667	-2.75416666666667
27	102.3	113.591488095238	-11.2914880952381
28	98.6	99.848630952381	-1.24863095238096
29	98.2	101.234345238095	-3.03434523809524
30	104.5	115.405773809524	-10.9057738095238
31	84	82.7343452380952	1.26565476190476
32	73.8	84.0772023809524	-10.2772023809524
33	103.9	107.663630952381	-3.76363095238096
34	106	108.396964285714	-2.39696428571429
35	97.2	104.330297619048	-7.13029761904762
36	102.6	101.746964285714	0.85303571428571
37	89	96.5548214285714	-7.55482142857139
38	93.8	99.7548214285714	-5.95482142857143
39	116.7	120.530892857143	-3.83089285714285
40	106.8	106.788035714286	0.0119642857142910
41	98.5	108.17375	-9.67375
42	118.7	122.345178571429	-3.64517857142857
43	90	89.67375	0.326250000000014
44	91.9	91.0166071428571	0.883392857142863
45	113.3	114.603035714286	-1.30303571428572
46	113.1	115.336369047619	-2.23636904761905
47	104.1	111.269702380952	-7.16970238095238
48	108.7	108.686369047619	0.0136309523809659
49	96.7	103.494226190476	-6.79422619047614
50	101	106.694226190476	-5.69422619047618
51	116.9	121.931547619048	-5.03154761904762
52	105.8	108.188690476190	-2.38869047619048
53	99	109.574404761905	-10.5744047619048
54	129.4	123.745833333333	5.65416666666667
55	83	91.0744047619048	-8.07440476190475
56	88.9	92.4172619047619	-3.51726190476191
57	115.9	116.003690476190	-0.103690476190482
58	104.2	116.737023809524	-12.5370238095238
59	113.4	112.670357142857	0.72964285714286
60	112.2	110.087023809524	2.11297619047620
61	100.8	104.894880952381	-4.09488095238091
62	107.3	108.094880952381	-0.794880952380956
63	126.6	123.332202380952	3.2677976190476
64	102.9	109.589345238095	-6.68934523809524
65	117.9	110.975059523810	6.92494047619047
66	128.8	125.146488095238	3.6535119047619
67	87.5	92.4750595238095	-4.97505952380952
68	93.8	93.8179166666667	-0.0179166666666888
69	122.7	117.404345238095	5.29565476190475
70	126.2	118.137678571429	8.06232142857142
71	124.6	114.071011904762	10.5289880952381
72	116.7	111.487678571429	5.21232142857142
73	115.2	106.295535714286	8.90446428571433
74	111.1	109.495535714286	1.60446428571427
75	129.9	124.732857142857	5.16714285714284
76	113.3	110.99	2.30999999999998
77	118.5	112.375714285714	6.1242857142857
78	133.5	126.547142857143	6.95285714285712
79	102.1	93.8757142857143	8.2242857142857
80	102.4	95.2185714285715	7.18142857142855

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/25/t1227598107irqzvf9aze1p5mh/1d5om1227598036.png (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

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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