Blog & Share Statistical Computations at FreeStatistics.org

Home » date » 2007 » Dec » 17 » attachments

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

Title produced by software: Multiple Regression

Date of computation: Mon, 17 Dec 2007 13:01:29 -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/17/t1197920702hpwx5e66cf0s4bm.htm/, Retrieved Mon, 17 Dec 2007 20:45:02 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

85,6 92,81 88 75,6 89 59,04 88,4 48,7 97,5 72,81 95 111,7 104 91,81 101,8 119,5 99,4 68,07 107,6 103,4 103,2 49,16 118,9 96,3 103 124,61 126,9 96,6 91,2 109,89 106,3 110,4 85,9 110,51 109,2 104,4 80,7 114,77 104,6 110,7 86,7 92,37 100,8 93,6 80,7 103,63 92,1 114,8 81,5 90,43 86,4 74,9 83,4 65,86 96 69,8 83,5 83,33 98,5 104,2 89,5 94,49 112 109,3 85,8 68,98 113,9 92,7 77,4 55,46 120 91,7 67,5 132,89 126,7 84,4 63,7 121,71 112,8 94,5 59,4 127,01 116,2 103,6 62 134,04 110,6 105,9 62,4 106,48 105 108 58,1 117,55 101,2 119,9 58 101,61 99,3 84,5 56,3 82,66 101,9 76,7 61,4 89,28 106,4 120,5 59,8 109,24 118,9 119,6 54,3 88,16 121,9 102,3 47 59,23 132 101,7 50,5 164,21 121,4 86,9 48,1 125,13 117 93,6 58,8 152,68 122,7 113,6 70,4 132,96 113 106,7 71,9 112,42 104 96,1 73,3 136,43 101,2 124,6 83,5 107,32 100,8 72,5 90,1 87,61 98,9 89 101,3 97,86 103 115,3 98,3 106,60 117,8 119,1 106,7 92,17 126,6 104,4 109,9 65,31 127,6 104,9 111,1 161,49 115,8 76,9 119 162,25 114,8 95,3 120,7 175,13 119,2 114,9 104,5 147,28 109,9 98,9 121,6 144,48 98,9 102,9 129,6 122,67 98,6 90 124,5 102,27 96,6 81 130,1 88,64 96,7 66,2 142,3 89,59 103,5 86,7 140 112,20 115,3 86,7 143,3 91,98 122,5 103,4 113,4 57,85 125,3 89,5 113,8 160,49 111,2 113,7 120,7 128,33 110,7 120,2 112,9 140,69 114,2 137,8 115,5 126,61 105,6 99,1 121,9 129,27 95,5 110,4 119,3 124,27 97,3 112,3 111 112,90 95,5 82,2 114,2 92,54 96,3 72,2 113,5 85,70 100,2 106,7 94 116,72 113,4 106,4 83,2 92,08 121,4 110 82,8 58,98 122,1 87,5 85,8 154,50 119,3 79,7 88,7 145,55 110,8 83,3 105,3 146,60 110,1 91,8 113,1 143,51 99,7 89,2 113,8 113,52 104,8 90,6 109,4 104,80 105,4 92,6

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	6 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Multiple Linear Regression - Estimated Regression Equation

olie[t] = + 131.058720667153 + 0.0777048133057692wagens[t] -0.365660000574707electric[t] -0.0686328689875479vervoers[t] + 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)	131.058720667153	32.037171	4.0908	0.000116	5.8e-05
wagens	0.0777048133057692	0.099594	0.7802	0.437971	0.218985
electric	-0.365660000574707	0.28047	-1.3037	0.196718	0.098359
vervoers	-0.0686328689875479	0.191959	-0.3575	0.721796	0.360898

Multiple Linear Regression - Regression Statistics
Multiple R	0.189440361235054
R-squared	0.0358876504648676
Adjusted R-squared	-0.00664671789697646
F-TEST (value)	0.843733005732395
F-TEST (DF numerator)	3
F-TEST (DF denominator)	68
p-value	0.474688991216682
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	24.6583433727325
Sum Squared Residuals	41346.3050563555

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	85.6	100.903779444029	-15.3037794440286
2	89	99.9796480742283	-10.9796480742283
3	97.5	94.3124166034401	3.18758339655989
4	104	92.7669836742388	11.2330163257612
5	99.4	89.9064325937261	9.4935674062739
6	103.2	84.7923699374314	18.4076300625686
7	103	87.7093282360578	15.2906717639422
8	91.2	93.1509758040077	-1.95097580400765
9	85.9	92.5505360005159	-6.65053600051587
10	80.7	94.1312074332206	-13.4312074332205
11	86.7	94.9537496770423	-8.25374967704227
12	80.7	97.5549310573292	-16.8549310573292
13	81.5	101.351940997572	-19.851940997572
14	83.4	96.2824253609686	-12.8824253609686
15	83.5	94.364807754812	-10.8648077548119
16	89.5	89.9455558317093	-0.445555831709287
17	85.8	88.4078576683805	-2.60785766838047
18	77.4	85.1953954579683	-7.7953954579683
19	67.5	89.2631770919926	-21.7631770919926
20	63.7	92.7839193104483	-29.0839193104483
21	59.4	91.3279517112282	-31.9279517112282
22	62	93.7640569533147	-31.7640569533147
23	62.4	93.5260792769522	-31.1260792769522
24	58.1	94.9590484214792	-36.8590484214792
25	58	96.8447912606363	-38.8447912606363
26	56.3	94.9569054251006	-38.6569054251006
27	61.4	90.819721624944	-29.4197216249440
28	59.8	87.8617292734322	-28.0617292734322
29	54.3	86.314080440707	-32.014080440707
30	47	80.4140939073591	-33.4140939073591
31	50.5	93.4633076753063	-42.9633076753063
32	48.1	91.575667351629	-43.475667351629
33	58.8	90.2595155751762	-31.4595155751762
34	70.4	92.7476454583751	-22.3476454583751
35	71.9	95.170037009515	-23.270037009515
36	73.3	96.1035408124506	-22.8035408124506
37	83.5	97.5635901716008	-14.0635901716008
38	90.1	95.5943399641415	-5.49433996414148
39	101.3	93.0865638437968	8.2134361562032
40	98.3	88.0931310014309	10.2068689985691
41	106.7	84.7629457144882	21.9370542855118
42	109.9	82.2758179940267	27.6241820059733
43	111.1	95.9859752762085	15.1140247237915
44	119	95.1478461455247	23.8521538544753
45	120.7	93.1945759062183	27.5054240937816
46	104.5	95.5292607647982	8.97073923520178
47	121.6	99.0594158179136	22.5405841820863
48	129.6	98.3597358498266	31.2402641501734
49	124.5	98.1235734804263	26.3764265195737
50	130.1	98.0436573360269	32.0563426639731
51	142.3	94.2240150905146	48.0759849094854
52	140	91.6661329125765	48.3338670874235
53	143.3	86.316020671304	56.9839793286961
54	113.4	83.5941042704958	29.8058957295043
55	113.8	95.0646168868046	18.7353831131954
56	120.7	92.3023464427594	28.3976535572406
57	112.9	90.7750294390264	22.1249705609737
58	115.5	95.4817137024417	20.0182862975583
59	121.9	98.6060230920803	23.2939769079197
60	119.3	97.4289085734406	21.8710914265594
61	111	99.2694422037137	11.7305577962863
62	114.2	98.081172894224	16.1188271057760
63	113.5	93.7557639889007	19.7442360110993
64	94	91.3600451507558	2.63995484924417
65	83.2	86.2730402179489	-3.07304021794885
66	82.8	84.9892884493454	-2.18928844934544
67	85.8	93.9708365960246	-8.17083659602456
68	88.7	96.1364101934678	-7.43641019346775
69	105.3	95.890582861447	9.40941713855305
70	113.1	99.6317844536767	13.4682155463233
71	113.8	95.3404650831231	18.4595349168769
72	109.4	94.3062173727769	15.0937826272231

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/17/t1197920702hpwx5e66cf0s4bm/141sx1197921679.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/17/t1197920702hpwx5e66cf0s4bm/141sx1197921679.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/17/t1197920702hpwx5e66cf0s4bm/26rr41197921679.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/17/t1197920702hpwx5e66cf0s4bm/26rr41197921679.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/17/t1197920702hpwx5e66cf0s4bm/355ib1197921680.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/17/t1197920702hpwx5e66cf0s4bm/355ib1197921680.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/17/t1197920702hpwx5e66cf0s4bm/4vy1m1197921680.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/17/t1197920702hpwx5e66cf0s4bm/4vy1m1197921680.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/17/t1197920702hpwx5e66cf0s4bm/5v2j91197921680.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/17/t1197920702hpwx5e66cf0s4bm/5v2j91197921680.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/17/t1197920702hpwx5e66cf0s4bm/6ouud1197921680.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/17/t1197920702hpwx5e66cf0s4bm/6ouud1197921680.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/17/t1197920702hpwx5e66cf0s4bm/7vqrx1197921680.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/17/t1197920702hpwx5e66cf0s4bm/7vqrx1197921680.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/17/t1197920702hpwx5e66cf0s4bm/8rh1t1197921680.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/17/t1197920702hpwx5e66cf0s4bm/8rh1t1197921680.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/17/t1197920702hpwx5e66cf0s4bm/9akhd1197921680.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/17/t1197920702hpwx5e66cf0s4bm/9akhd1197921680.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No 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.

FreeStatistics.org is powered by