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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: Mon, 19 Nov 2007 04:07:28 -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/19/t1195470082ujk9vofg49fmjz9.htm/, Retrieved Mon, 19 Nov 2007 12:01:52 +0100

User-defined keywords:

groep MENS

Dataseries X:

» Textbox « » Textfile « » CSV «

100,0 0 100,0 0 100,0 0 100,1 0 100,0 0 100,0 0 99,8 0 100,0 0 99,9 0 99,2 0 98,7 0 98,7 0 98,9 1 99,2 1 99,8 1 100,5 1 100,1 1 100,5 1 98,4 1 98,6 1 99,0 1 99,1 1 98,9 1 98,5 1 96,9 1 96,8 1 97,0 1 97,0 1 96,9 1 97,1 1 97,2 1 97,9 1 98,9 1 99,2 1 99,5 1 99,3 1 99,9 1 100,0 1 100,3 1 100,5 1 100,7 1 100,9 1 100,8 1 100,9 1 101,0 1 100,3 1 100,1 1 99,8 1 99,9 1 99,9 1 100,2 1 99,7 1 100,4 1 100,9 1 101,3 1 101,4 1 101,3 1 100,9 1 100,9 1 100,9 1 101,1 1 101,1 1 101,3 1 101,8 1 102,9 1 103,2 1 103,3 1 104,5 1 105,0 1 104,9 1 104,9 1 105,4 1 106,0 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	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

y[t] = + 98.7584114583333 -2.8036328125x[t] + 0.496667751736103M1[t] + 0.0217339409722206M2[t] + 0.192893880208329M3[t] + 0.264053819444441M4[t] + 0.401880425347222M5[t] + 0.573040364583331M6[t] + 0.177533637152775M7[t] + 0.498693576388888M8[t] + 0.703186848958332M9[t] + 0.357680121527777M10[t] + 0.162173394097222M11[t] + 0.0955067274305556t + 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)	98.7584114583333	0.666595	148.1536	0	0
x	-2.8036328125	0.560988	-4.9977	5e-06	3e-06
M1	0.496667751736103	0.754312	0.6584	0.512818	0.256409
M2	0.0217339409722206	0.786697	0.0276	0.978053	0.489027
M3	0.192893880208329	0.785496	0.2456	0.806868	0.403434
M4	0.264053819444441	0.784421	0.3366	0.737596	0.368798
M5	0.401880425347222	0.78347	0.5129	0.609902	0.304951
M6	0.573040364583331	0.782645	0.7322	0.466955	0.233477
M7	0.177533637152775	0.781947	0.227	0.821177	0.410589
M8	0.498693576388888	0.781375	0.6382	0.525796	0.262898
M9	0.703186848958332	0.78093	0.9004	0.371543	0.185771
M10	0.357680121527777	0.780612	0.4582	0.648488	0.324244
M11	0.162173394097222	0.780421	0.2078	0.836099	0.418049
t	0.0955067274305556	0.009967	9.5819	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.79267443661103
R-squared	0.628332762456614
Adjusted R-squared	0.546439981302987
F-TEST (value)	7.67262698378614
F-TEST (DF numerator)	13
F-TEST (DF denominator)	59
p-value	1.34614241975584e-08
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	1.35161819898456
Sum Squared Residuals	107.785433593750

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	100	99.3505859375	0.649414062499957
2	100	98.9711588541667	1.02884114583334
3	100	99.2378255208333	0.762174479166673
4	100.1	99.4044921875	0.695507812499998
5	100	99.6378255208333	0.362174479166669
6	100	99.9044921875	0.0955078125000025
7	99.8	99.6044921875	0.195507812500000
8	100	100.021158854167	-0.0211588541666628
9	99.9	100.321158854167	-0.42115885416666
10	99.2	100.071158854167	-0.87115885416666
11	98.7	99.9711588541667	-1.27115885416666
12	98.7	99.9044921875	-1.20449218749999
13	98.9	97.6930338541667	1.20696614583334
14	99.2	97.3136067708333	1.88639322916667
15	99.8	97.5802734375	2.2197265625
16	100.5	97.7469401041667	2.75305989583333
17	100.1	97.9802734375	2.11972656249999
18	100.5	98.2469401041667	2.25305989583333
19	98.4	97.9469401041667	0.45305989583334
20	98.6	98.3636067708333	0.236393229166659
21	99	98.6636067708333	0.336393229166666
22	99.1	98.4136067708333	0.68639322916666
23	98.9	98.3136067708333	0.58639322916667
24	98.5	98.2469401041667	0.253059895833330
25	96.9	98.8391145833333	-1.93911458333332
26	96.8	98.4596875	-1.65968750000000
27	97	98.7263541666667	-1.72635416666667
28	97	98.8930208333333	-1.89302083333333
29	96.9	99.1263541666667	-2.22635416666666
30	97.1	99.3930208333333	-2.29302083333334
31	97.2	99.0930208333333	-1.89302083333333
32	97.9	99.5096875	-1.60968750000000
33	98.9	99.8096875	-0.909687499999996
34	99.2	99.5596875	-0.359687499999999
35	99.5	99.4596875	0.0403124999999973
36	99.3	99.3930208333333	-0.0930208333333387
37	99.9	99.9851953125	-0.0851953124999897
38	100	99.6057682291667	0.394231770833332
39	100.3	99.8724348958333	0.427565104166664
40	100.5	100.0391015625	0.4608984375
41	100.7	100.272434895833	0.427565104166667
42	100.9	100.5391015625	0.360898437500003
43	100.8	100.2391015625	0.560898437499997
44	100.9	100.655768229167	0.244231770833336
45	101	100.955768229167	0.0442317708333315
46	100.3	100.705768229167	-0.405768229166672
47	100.1	100.605768229167	-0.505768229166676
48	99.8	100.5391015625	-0.739101562500006
49	99.9	101.131276041667	-1.23127604166666
50	99.9	100.751848958333	-0.851848958333329
51	100.2	101.018515625	-0.818515624999998
52	99.7	101.185182291667	-1.48518229166666
53	100.4	101.418515625	-1.01851562500000
54	100.9	101.685182291667	-0.785182291666664
55	101.3	101.385182291667	-0.0851822916666698
56	101.4	101.801848958333	-0.401848958333332
57	101.3	102.101848958333	-0.801848958333338
58	100.9	101.851848958333	-0.95184895833333
59	100.9	101.751848958333	-0.851848958333331
60	100.9	101.685182291667	-0.785182291666665
61	101.1	102.277356770833	-1.17735677083334
62	101.1	101.8979296875	-0.797929687500008
63	101.3	102.164596354167	-0.86459635416667
64	101.8	102.331263020833	-0.531263020833337
65	102.9	102.564596354167	0.335403645833335
66	103.2	102.831263020833	0.368736979166666
67	103.3	102.531263020833	0.768736979166662
68	104.5	102.9479296875	1.55207031250000
69	105	103.2479296875	1.75207031250000
70	104.9	102.9979296875	1.90207031250000
71	104.9	102.8979296875	2.00207031250000
72	105.4	102.831263020833	2.56873697916667
73	106	103.4234375	2.57656250000000

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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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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