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

Title produced by software: Multiple Regression

Date of computation: Thu, 13 Dec 2007 02:11:20 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2007/Dec/13/t11975362015k4of08fba2bghj.htm/, Retrieved Thu, 13 Dec 2007 09:56:41 +0100

User-defined keywords:

bridome

Dataseries X:

» Textbox « » Textfile « » CSV «

540 0 522 0 526 0 527 0 516 0 503 0 489 0 479 0 475 0 524 0 552 0 532 0 511 0 492 0 492 0 493 0 481 0 462 0 457 0 442 0 439 0 488 0 521 0 501 0 485 0 464 0 460 0 467 0 460 0 448 0 443 0 436 0 431 0 484 0 510 0 513 0 503 0 471 0 471 0 476 0 475 0 470 0 461 0 455 0 456 0 517 0 525 0 523 0 519 0 509 0 512 0 519 0 517 0 510 0 509 0 501 0 507 0 569 0 580 0 578 0 565 0 547 0 555 0 562 1 561 1 555 1 544 1 537 1 543 1 594 1 611 1 613 1 611 1 594 1 595 1 591 1 589 1 584 1 573 1 567 1 569 1 621 1 629 1 628 1 612 1 595 1 597 1 593 1 590 1 580 1 574 1 573 1 573 1 620 1 626 1 620 1 588 1 566 1 557 1 561 1 549 1 532 1 526 1 511 1 499 1 555 1

Text written by user:

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 compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	7 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Multiple Linear Regression - Estimated Regression Equation

y[t] = + 525.754197271773 + 73.3752360965372x[t] -11.2732457930125M1[t] -30.7960252224943M2[t] -30.4299157630873M3[t] -36.1054992032956M4[t] -41.9616119661109M5[t] -52.595502506704M6[t] -60.3405041584082M7[t] -68.8632835878901M8[t] -70.0527296840387M9[t] -16.908842446854M10[t] + 5.93944609614861M11[t] + 0.189446096148616t + 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)	525.754197271773	10.653912	49.3485	0	0
x	73.3752360965372	9.693518	7.5695	0	0
M1	-11.2732457930125	12.441403	-0.9061	0.367246	0.183623
M2	-30.7960252224943	12.436965	-2.4762	0.015109	0.007554
M3	-30.4299157630873	12.434466	-2.4472	0.016295	0.008147
M4	-36.1054992032956	12.468438	-2.8958	0.004725	0.002363
M5	-41.9616119661109	12.458389	-3.3681	0.001107	0.000553
M6	-52.595502506704	12.45027	-4.2244	5.6e-05	2.8e-05
M7	-60.3405041584082	12.444087	-4.8489	5e-06	3e-06
M8	-68.8632835878901	12.439841	-5.5357	0	0
M9	-70.0527296840387	12.437535	-5.6324	0	0
M10	-16.908842446854	12.437169	-1.3595	0.177298	0.088649
M11	5.93944609614861	12.793426	0.4643	0.64356	0.32178
t	0.189446096148616	0.155375	1.2193	0.225853	0.112926

Multiple Linear Regression - Regression Statistics
Multiple R	0.889690607068077
R-squared	0.791549376305164
Adjusted R-squared	0.762094396870024
F-TEST (value)	26.8731939890898
F-TEST (DF numerator)	13
F-TEST (DF denominator)	92
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	25.5849656968537
Sum Squared Residuals	60222.3232132447

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	540	514.670397574911	25.3296024250892
2	522	495.337064241576	26.6629357584237
3	526	495.892619797132	30.1073802028682
4	527	490.406482453072	36.5935175469279
5	516	484.739815786405	31.2601842135945
6	503	474.295371341961	28.7046286580390
7	489	466.739815786405	22.2601842135946
8	479	458.406482453072	20.5935175469279
9	475	457.406482453072	17.5935175469279
10	524	510.739815786405	13.2601842135945
11	552	533.777550425557	18.2224495744433
12	532	528.027550425557	3.97244957444331
13	511	516.943750728693	-5.94375072869284
14	492	497.61041739536	-5.61041739535965
15	492	498.165972950915	-6.16597295091521
16	493	492.679835606856	0.320164393144487
17	481	487.013168940189	-6.01316894018885
18	462	476.568724495744	-14.5687244957444
19	457	469.013168940189	-12.0131689401889
20	442	460.679835606856	-18.6798356068555
21	439	459.679835606856	-20.6798356068555
22	488	513.013168940189	-25.0131689401889
23	521	536.05090357934	-15.0509035793401
24	501	530.30090357934	-29.3009035793401
25	485	519.217103882476	-34.2171038824762
26	464	499.883770549143	-35.8837705491431
27	460	500.439326104699	-40.4393261046986
28	467	494.953188760639	-27.9531887606389
29	460	489.286522093972	-29.2865220939723
30	448	478.842077649528	-30.8420776495278
31	443	471.286522093972	-28.2865220939723
32	436	462.953188760639	-26.9531887606389
33	431	461.953188760639	-30.9531887606389
34	484	515.286522093972	-31.2865220939722
35	510	538.324256733123	-28.3242567331235
36	513	532.574256733123	-19.5742567331235
37	503	521.49045703626	-18.4904570362596
38	471	502.157123702926	-31.1571237029264
39	471	502.712679258482	-31.712679258482
40	476	497.226541914422	-21.2265419144223
41	475	491.559875247756	-16.5598752477556
42	470	481.115430803311	-11.1154308033112
43	461	473.559875247756	-12.5598752477556
44	455	465.226541914422	-10.2265419144223
45	456	464.226541914422	-8.22654191442231
46	517	517.559875247756	-0.559875247755636
47	525	540.597609886907	-15.5976098869069
48	523	534.847609886907	-11.8476098869069
49	519	523.763810190043	-4.76381019004302
50	509	504.43047685671	4.56952314329018
51	512	504.986032412265	7.01396758773461
52	519	499.499895068206	19.5001049317943
53	517	493.833228401539	23.1667715984610
54	510	483.388783957095	26.6112160429054
55	509	475.833228401539	33.166771598461
56	501	467.499895068206	33.5001049317943
57	507	466.499895068206	40.5001049317943
58	569	519.833228401539	49.166771598461
59	580	542.87096304069	37.1290369593098
60	578	537.12096304069	40.8790369593098
61	565	526.037163343826	38.9628366561736
62	547	506.703830010493	40.2961699895068
63	555	507.259385566049	47.7406144339512
64	562	575.148484318526	-13.1484843185263
65	561	569.48181765186	-8.4818176518596
66	555	559.037373207415	-4.03737320741516
67	544	551.48181765186	-7.48181765185962
68	537	543.148484318526	-6.14848431852629
69	543	542.148484318526	0.851515681473718
70	594	595.48181765186	-1.48181765185961
71	611	618.519552291011	-7.51955229101084
72	613	612.769552291011	0.230447708989156
73	611	601.685752594147	9.31424740585302
74	594	582.352419260814	11.6475807391862
75	595	582.907974816369	12.0920251836306
76	591	577.42183747231	13.5781625276903
77	589	571.755170805643	17.244829194357
78	584	561.310726361199	22.6892736388014
79	573	553.755170805643	19.244829194357
80	567	545.42183747231	21.5781625276903
81	569	544.42183747231	24.5781625276903
82	621	597.755170805643	23.244829194357
83	629	620.792905444794	8.20709455520577
84	628	615.042905444794	12.9570945552058
85	612	603.95910574793	8.04089425206963
86	595	584.625772414597	10.3742275854028
87	597	585.181327970153	11.8186720298473
88	593	579.695190626093	13.3048093739069
89	590	574.028523959426	15.9714760405736
90	580	563.584079514982	16.4159204850181
91	574	556.028523959426	17.9714760405736
92	573	547.695190626093	25.3048093739069
93	573	546.695190626093	26.3048093739069
94	620	600.028523959426	19.9714760405736
95	626	623.066258598578	2.93374140142238
96	620	617.316258598578	2.68374140142237
97	588	606.232458901714	-18.2324589017138
98	566	586.89912556838	-20.8991255683806
99	557	587.454681123936	-30.4546811239361
100	561	581.968543779876	-20.9685437798764
101	549	576.30187711321	-27.3018771132098
102	532	565.857432668765	-33.8574326687653
103	526	558.30187711321	-32.3018771132098
104	511	549.968543779876	-38.9685437798764
105	499	548.968543779876	-49.9685437798764
106	555	602.30187711321	-47.3018771132098

Charts produced by software:

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Parameters:

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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