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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: Wed, 14 Nov 2007 16:25:11 -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/15/t1195082382yufoomn3ghzbg8i.htm/, Retrieved Thu, 15 Nov 2007 00:19:52 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

128 0 123 0 118 0 112 0 105 0 102 0 131 0 149 0 145 0 132 0 122 0 119 0 116 0 111 0 104 0 100 0 93 0 91 0 119 0 139 0 134 0 124 0 113 0 109 0 109 0 106 0 101 0 98 0 93 0 91 0 122 0 139 0 140 1 132 1 117 1 114 1 113 1 110 1 107 1 103 1 98 1 98 1 137 1 148 1 147 1 139 1 130 1 128 1 127 1 123 1 118 1 114 1 108 1 111 1 151 1 159 1 158 1 148 1 138 1 137 1 136 1 133 1 126 1 120 1 114 1 116 1 153 1 162 1 161 1 149 0 139 0 135 0 130 0 127 0 122 0 117 0 112 0 113 0 149 0 157 0 157 0 147 0 137 0 132 0 125 0 123 0 117 0 114 0 111 0 112 0 144 0 150 0 149 0 134 0 123 0 116 0 117 0 111 0 105 0 102 0 95 0 93 0 124 0 130 0 124 0 115 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

y[t] = + 121.124348203940 + 7.00173812282735x[t] -1.12492757821549M1[t] -4.90270535599331M2[t] -10.3471498004377M3[t] -14.5693720226600M4[t] -20.2360386893266M5[t] -20.4582609115488M6[t] + 13.2084057551178M7[t] + 24.6528501995622M8[t] + 21.8748792970259M9[t] + 12.0972946440067M10[t] + 3.62500000000001M11[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)	121.124348203940	3.506878	34.5391	0	0
x	7.00173812282735	1.979944	3.5363	0.000635	0.000317
M1	-1.12492757821549	4.711203	-0.2388	0.811804	0.405902
M2	-4.90270535599331	4.711203	-1.0406	0.300737	0.150368
M3	-10.3471498004377	4.711203	-2.1963	0.030558	0.015279
M4	-14.5693720226600	4.711203	-3.0925	0.00262	0.00131
M5	-20.2360386893266	4.711203	-4.2953	4.3e-05	2.1e-05
M6	-20.4582609115488	4.711203	-4.3425	3.6e-05	1.8e-05
M7	13.2084057551178	4.711203	2.8036	0.006151	0.003076
M8	24.6528501995622	4.711203	5.2328	1e-06	1e-06
M9	21.8748792970259	4.712487	4.6419	1.1e-05	6e-06
M10	12.0972946440067	4.711203	2.5678	0.011829	0.005915
M11	3.62500000000001	4.847044	0.7479	0.45642	0.22821

Multiple Linear Regression - Regression Statistics
Multiple R	0.859946975859105
R-squared	0.73950880128922
Adjusted R-squared	0.705897033713636
F-TEST (value)	22.0014850342592
F-TEST (DF numerator)	12
F-TEST (DF denominator)	93
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	9.69408879906772
Sum Squared Residuals	8739.70826091156

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	128	119.999420625724	8.00057937427622
2	123	116.221642847946	6.77835715205356
3	118	110.777198403502	7.22280159649805
4	112	106.554976181280	5.44502381872025
5	105	100.888309514613	4.11169048538683
6	102	100.666087292391	1.33391270760911
7	131	134.332753959058	-3.33275395905761
8	149	145.777198403502	3.22280159649796
9	145	142.999227500966	2.00077249903436
10	132	133.221642847946	-1.22164284794641
11	122	124.749348203940	-2.7493482039397
12	119	121.124348203940	-2.12434820393975
13	116	119.999420625724	-3.99942062572427
14	111	116.221642847946	-5.22164284794644
15	104	110.777198403502	-6.777198403502
16	100	106.554976181280	-6.55497618127978
17	93	100.888309514613	-7.8883095146131
18	91	100.666087292391	-9.66608729239089
19	119	134.332753959058	-15.3327539590575
20	139	145.777198403502	-6.77719840350199
21	134	142.999227500966	-8.99922750096562
22	124	133.221642847946	-9.22164284794645
23	113	124.749348203940	-11.7493482039398
24	109	121.124348203940	-12.1243482039397
25	109	119.999420625724	-10.9994206257243
26	106	116.221642847946	-10.2216428479464
27	101	110.777198403502	-9.777198403502
28	98	106.554976181280	-8.55497618127978
29	93	100.888309514613	-7.8883095146131
30	91	100.666087292391	-9.66608729239089
31	122	134.332753959058	-12.3327539590575
32	139	145.777198403502	-6.77719840350199
33	140	150.000965623793	-10.0009656237930
34	132	140.223380970774	-8.22338097077379
35	117	131.751086326767	-14.7510863267671
36	114	128.126086326767	-14.1260863267671
37	113	127.001158748552	-14.0011587485516
38	110	123.223380970774	-13.2233809707738
39	107	117.778936526329	-10.7789365263293
40	103	113.556714304107	-10.5567143041071
41	98	107.890047637440	-9.89004763744044
42	98	107.667825415218	-9.66782541521823
43	137	141.334492081885	-4.33449208188489
44	148	152.778936526329	-4.77893652632933
45	147	150.000965623793	-3.00096562379297
46	139	140.223380970774	-1.22338097077378
47	130	131.751086326767	-1.75108632676710
48	128	128.126086326767	-0.126086326767089
49	127	127.001158748552	-0.00115874855161735
50	123	123.223380970774	-0.223380970773783
51	118	117.778936526329	0.221063473670653
52	114	113.556714304107	0.443285695892881
53	108	107.890047637440	0.109952362559556
54	111	107.667825415218	3.33217458478177
55	151	141.334492081885	9.66550791811512
56	159	152.778936526329	6.22106347367067
57	158	150.000965623793	7.99903437620703
58	148	140.223380970774	7.77661902922622
59	138	131.751086326767	6.2489136732329
60	137	128.126086326767	8.87391367323291
61	136	127.001158748552	8.99884125144838
62	133	123.223380970774	9.77661902922622
63	126	117.778936526329	8.22106347367065
64	120	113.556714304107	6.44328569589288
65	114	107.890047637440	6.10995236255956
66	116	107.667825415218	8.33217458478177
67	153	141.334492081885	11.6655079181151
68	162	152.778936526329	9.22106347367067
69	161	150.000965623793	10.9990343762070
70	149	133.221642847946	15.7783571520535
71	139	124.749348203940	14.2506517960602
72	135	121.124348203940	13.8756517960603
73	130	119.999420625724	10.0005793742757
74	127	116.221642847946	10.7783571520536
75	122	110.777198403502	11.222801596498
76	117	106.554976181280	10.4450238187202
77	112	100.888309514613	11.1116904853869
78	113	100.666087292391	12.3339127076091
79	149	134.332753959058	14.6672460409424
80	157	145.777198403502	11.222801596498
81	157	142.999227500966	14.0007724990344
82	147	133.221642847946	13.7783571520535
83	137	124.749348203940	12.2506517960602
84	132	121.124348203940	10.8756517960603
85	125	119.999420625724	5.00057937427573
86	123	116.221642847946	6.77835715205356
87	117	110.777198403502	6.222801596498
88	114	106.554976181280	7.44502381872022
89	111	100.888309514613	10.1116904853869
90	112	100.666087292391	11.3339127076091
91	144	134.332753959058	9.66724604094245
92	150	145.777198403502	4.222801596498
93	149	142.999227500966	6.00077249903437
94	134	133.221642847946	0.778357152053557
95	123	124.749348203940	-1.74934820393975
96	116	121.124348203940	-5.12434820393974
97	117	119.999420625724	-2.99942062572427
98	111	116.221642847946	-5.22164284794644
99	105	110.777198403502	-5.77719840350200
100	102	106.554976181280	-4.55497618127978
101	95	100.888309514613	-5.8883095146131
102	93	100.666087292391	-7.6660872923909
103	124	134.332753959058	-10.3327539590575
104	130	145.777198403502	-15.777198403502
105	124	142.999227500966	-18.9992275009656
106	115	133.221642847946	-18.2216428479464

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/15/t1195082382yufoomn3ghzbg8i/1gq921195082702.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/15/t1195082382yufoomn3ghzbg8i/1gq921195082702.ps (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/15/t1195082382yufoomn3ghzbg8i/2r8ck1195082702.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/15/t1195082382yufoomn3ghzbg8i/3xy481195082702.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/15/t1195082382yufoomn3ghzbg8i/3xy481195082702.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/15/t1195082382yufoomn3ghzbg8i/4q64b1195082702.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/15/t1195082382yufoomn3ghzbg8i/4q64b1195082702.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/15/t1195082382yufoomn3ghzbg8i/585ez1195082702.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/15/t1195082382yufoomn3ghzbg8i/585ez1195082702.ps (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/15/t1195082382yufoomn3ghzbg8i/67nga1195082702.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/15/t1195082382yufoomn3ghzbg8i/7dbr41195082702.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/15/t1195082382yufoomn3ghzbg8i/7dbr41195082702.ps (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/15/t1195082382yufoomn3ghzbg8i/8m8l41195082702.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/15/t1195082382yufoomn3ghzbg8i/90rxw1195082702.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/15/t1195082382yufoomn3ghzbg8i/90rxw1195082702.ps (open in new window)

Parameters:

par1 = 1 ; par2 = Include Monthly 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.

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