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Stat Opdr3 Q3-3

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

Title produced by software: Multiple Regression

Date of computation: Thu, 22 Nov 2007 13:02:35 -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/Nov/22/t1195761516oevr0i6sppbh2zr.htm/, Retrieved Thu, 22 Nov 2007 20:58:46 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

3804 0 3491 0 4151 0 4254 1 4717 1 4866 1 4001 1 3758 1 4780 1 5016 1 4296 0 4467 0 3891 0 3872 0 3867 0 3973 1 4640 1 4538 1 3836 1 3770 1 4374 1 4497 1 3945 0 3862 0 3608 0 3301 0 3882 0 3605 0 4305 1 4216 1 3971 1 3988 1 4317 1 4484 1 4247 0 3520 0 3686 0 3403 0 3990 0 4053 0 4548 1 4559 1 3922 1 4209 1 4517 1 4386 1 3221 0 3127 0 3777 0 3322 0 3899 0 4033 1 4463 1 4819 1 4246 1 4255 1 4760 1 4581 0 4309 0 4016 0 3601 0 3257 0 3823 0 3940 1 4534 1 4575 1 3953 1 4206 1 4649 1 4353 1 3835 0 3944 0

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	4 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

O[t] = + 3905.27517025584 + 106.659856432909T[t] -116.468893797163M1[t] -401.335357997423M2[t] + 94.9648444689857M3[t] + 66.8251426467886M4[t] + 591.405392968894M5[t] + 654.37226210197M6[t] + 49.005797901712M7[t] + 93.8060003681218M8[t] + 630.939536167863M9[t] + 637.349714706424M10[t] + 150.866464200258M11[t] -1.96686913307567t + 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)	3905.27517025584	118.306429	33.0098	0	0
T	106.659856432909	169.753175	0.6283	0.532259	0.266129
M1	-116.468893797163	144.770732	-0.8045	0.42439	0.212195
M2	-401.335357997423	144.620908	-2.7751	0.007415	0.003707
M3	94.9648444689857	144.48522	0.6573	0.513611	0.256806
M4	66.8251426467886	182.934671	0.3653	0.71622	0.35811
M5	591.405392968894	222.229422	2.6612	0.010054	0.005027
M6	654.37226210197	222.246216	2.9444	0.00465	0.002325
M7	49.005797901712	222.272298	0.2205	0.826274	0.413137
M8	93.8060003681218	222.307664	0.422	0.674611	0.337305
M9	630.939536167863	222.35231	2.8376	0.006254	0.003127
M10	637.349714706424	201.670609	3.1604	0.002504	0.001252
M11	150.866464200258	143.912497	1.0483	0.29884	0.14942
t	-1.96686913307567	1.436888	-1.3688	0.176328	0.088164

Multiple Linear Regression - Regression Statistics
Multiple R	0.853144229923228
R-squared	0.727855077051297
Adjusted R-squared	0.666857077080036
F-TEST (value)	11.9324416766816
F-TEST (DF numerator)	13
F-TEST (DF denominator)	58
p-value	5.19650988906051e-12
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	249.251332461467
Sum Squared Residuals	3603321.15056138

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	3804	3786.83940732559	17.1605926744128
2	3491	3500.00607399227	-9.00607399226925
3	4151	3994.3394073256	156.660592674397
4	4254	4070.89269280324	183.10730719676
5	4717	4593.50607399227	123.493926007730
6	4866	4654.50607399227	211.493926007729
7	4001	4047.17274065894	-46.1727406589373
8	3758	4090.00607399227	-332.00607399227
9	4780	4625.17274065894	154.827259341064
10	5016	4629.61605006442	386.383949935578
11	4296	4034.50607399227	261.49392600773
12	4467	3881.67274065894	585.327259341063
13	3891	3763.2369777287	127.763022271301
14	3872	3476.40364439536	395.596355604638
15	3867	3970.7369777287	-103.736977728695
16	3973	4047.29026320633	-74.2902632063318
17	4640	4569.90364439536	70.096355604638
18	4538	4630.90364439536	-92.903644395362
19	3836	4023.57031106203	-187.570311062028
20	3770	4066.40364439536	-296.403644395362
21	4374	4601.57031106203	-227.570311062029
22	4497	4606.01362046751	-109.013620467514
23	3945	4010.90364439536	-65.903644395362
24	3862	3858.07031106203	3.9296889379713
25	3608	3739.63454813179	-131.634548131790
26	3301	3452.80121479845	-151.801214798454
27	3882	3947.13454813179	-65.1345481317873
28	3605	3917.02797717651	-312.027977176514
29	4305	4546.30121479845	-241.301214798454
30	4216	4607.30121479845	-391.301214798454
31	3971	3999.96788146512	-28.9678814651206
32	3988	4042.80121479845	-54.8012147984541
33	4317	4577.96788146512	-260.967881465121
34	4484	4582.41119087061	-98.4111908706055
35	4247	3987.30121479845	259.698785201546
36	3520	3834.46788146512	-314.467881465121
37	3686	3716.03211853488	-30.0321185348824
38	3403	3429.19878520155	-26.1987852015461
39	3990	3923.53211853488	66.4678814651207
40	4053	3893.42554757961	159.574452420394
41	4548	4522.69878520155	25.3012147984541
42	4559	4583.69878520155	-24.698785201546
43	3922	3976.36545186821	-54.3654518682126
44	4209	4019.19878520155	189.801214798454
45	4517	4554.36545186821	-37.3654518682127
46	4386	4558.8087612737	-172.808761273697
47	3221	3963.69878520155	-742.698785201546
48	3127	3810.86545186821	-683.865451868213
49	3777	3692.42968893797	84.5703110620255
50	3322	3405.59635560464	-83.5963556046381
51	3899	3899.92968893797	-0.929688937971274
52	4033	3976.48297441561	56.5170255843923
53	4463	4499.09635560464	-36.0963556046379
54	4819	4560.09635560464	258.903644395362
55	4246	3952.76302227130	293.236977728695
56	4255	3995.59635560464	259.403644395362
57	4760	4530.76302227131	229.236977728695
58	4581	4428.54647524388	152.453524756120
59	4309	3940.09635560464	368.903644395362
60	4016	3787.26302227130	228.736977728695
61	3601	3668.82725934107	-67.8272593410664
62	3257	3381.99392600773	-124.99392600773
63	3823	3876.32725934106	-53.3272593410632
64	3940	3952.8805448187	-12.8805448186997
65	4534	4475.49392600773	58.5060739922701
66	4575	4536.49392600773	38.5060739922701
67	3953	3929.16059267440	23.8394073256035
68	4206	3971.99392600773	234.00607399227
69	4649	4507.16059267440	141.839407325603
70	4353	4511.60390207988	-158.603902079881
71	3835	3916.49392600773	-81.4939260077299
72	3944	3763.6605926744	180.339407325603

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

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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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