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lineaire trend

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 12:15:19 -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/t119549932089f7xstp00lwhjv.htm/, Retrieved Mon, 19 Nov 2007 20:08:50 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

106.54 107.89 1 106.44 107.26 1 106.57 107.76 1 106.12 107.32 1 106.13 107.15 1 106.26 108.04 1 105.78 106.52 1 105.77 106.62 0 105.2 106.47 0 105.15 105.46 0 105.01 106.13 0 104.75 105.15 0 104.96 105.39 0 105.26 104.57 0 105.13 104.29 0 104.77 104.09 0 104.79 104.51 0 104.4 103.39 0 103.89 102.71 0 103.93 102.62 0 103.48 101.94 0 103.45 101.65 0 103.47 101.86 0 103.5 101.27 0 103.69 101.21 0 103.57 102.15 0 103.47 102.07 0 102.85 102.8 0 102.54 103.39 0 102.39 102.71 0 102.16 102.65 0 101.51 101.12 0 100.83 100.29 0 100.55 99.79 0 100.88 100.11 0 101 99.76 0 100.51 99.96 0 100.44 99.98 0 100.32 100.49 0 99.98 100.75 0 100.03 100.84 0 99.64 100.44 0 99.11 99.57 0 98.97 99.22 0 98.6 99.08 0 98.31 98.04 0 98.37 98.73 0 98.19 98.72 0 98.51 100.07 0 98.23 99.02 0 97.96 98.94 0 97.77 99 0 97.49 98.54 0 97.76 98.42 0 98.01 97.9 0 97.73 97.46 0 97.06 97 0 96.63 95.97 0 96.58 96.55 0 96.66 96.51 0 96.77 96.76 0 96.5 96.05 0 96.53 96.47 0 96.22 96.38 0 96.49 97.27 0 96.34 96.67 0 96.31 96.59 0 96.06 96.06 0 95.9 96.92 0 95.33 94.96 0 95.53 95.59 0 95.42 95.68 0 95.57 95.35 0 95.3 95.41 0 95.31 95.32 0 95.38 95.8 0 95.22 95.46 0 94.62 94.16 0 93.81 92.49 0 93.6 91.58 0 93.2 91.5 0 93.29 90.83 0 93.54 91.28 0 93.23 90.57 0 93.46 90.93 0 92.82 90.9 0 92.85 91.49 0 92.67 91.38 0 92.32 90.91 0 92.06 90.72 0 91.88 89.53 0 91.53 89.47 0 91.19 89.28 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	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

X[t] = + 103.956799581520 + 0.0277436224976786Y[t] -0.240428121994219D[t] + 0.22261655503733M1[t] + 0.209856411820287M2[t] + 0.312980163669945M3[t] + 0.173878277769374M4[t] + 0.23901190526251M5[t] + 0.219510100701345M6[t] + 0.0881549112736562M7[t] + 0.00085529777875065M8[t] -0.287562219485007M9[t] -0.323491449137164M10[t] -0.0810561418639918M11[t] -0.160791001539852t + 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)	103.956799581520	5.963318	17.4327	0	0
Y	0.0277436224976786	0.055805	0.4972	0.620477	0.310239
D	-0.240428121994219	0.209577	-1.1472	0.254802	0.127401
M1	0.22261655503733	0.238232	0.9345	0.352955	0.176477
M2	0.209856411820287	0.237681	0.8829	0.379985	0.189992
M3	0.312980163669945	0.240466	1.3016	0.196898	0.098449
M4	0.173878277769374	0.243562	0.7139	0.477421	0.23871
M5	0.23901190526251	0.247236	0.9667	0.336664	0.168332
M6	0.219510100701345	0.243537	0.9013	0.370182	0.185091
M7	0.0881549112736562	0.237904	0.3705	0.711978	0.355989
M8	0.00085529777875065	0.235664	0.0036	0.997113	0.498557
M9	-0.287562219485007	0.235656	-1.2203	0.226042	0.113021
M10	-0.323491449137164	0.244816	-1.3214	0.190243	0.095122
M11	-0.0810561418639918	0.24347	-0.3329	0.740087	0.370044
t	-0.160791001539852	0.010155	-15.8344	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.995616957055275
R-squared	0.991253125176006
Adjusted R-squared	0.98968317328452
F-TEST (value)	631.390764616169
F-TEST (DF numerator)	14
F-TEST (DF denominator)	78
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.455035471598093
Sum Squared Residuals	16.1504678721749

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	106.54	106.771456444297	-0.231456444297298
2	106.44	106.580426817367	-0.140426817366874
3	106.57	106.536631378926	0.03336862107448
4	106.12	106.224531297586	-0.104531297586109
5	106.13	106.124157507715	0.00584249228520312
6	106.26	105.968556525637	0.291443474363295
7	105.78	105.634240028473	0.145759971527303
8	105.77	105.629351897682	0.140648102318069
9	105.2	105.175981835504	0.0240181644963368
10	105.15	104.951240545589	0.198759454411002
11	105.01	105.051473078396	-0.041473078395764
12	104.75	104.944549468672	-0.194549468672183
13	104.96	105.013033491569	-0.0530334915691116
14	105.26	104.816732576364	0.443267423635891
15	105.13	104.751297112375	0.378702887625423
16	104.77	104.445855500435	0.324144499565384
17	104.79	104.361850447837	0.428149552163084
18	104.4	104.150484784539	0.249515215461501
19	103.89	103.839472930273	0.050527069727458
20	103.93	103.588885389213	0.341114610787012
21	103.48	103.120811207111	0.359188792889041
22	103.45	102.916045325395	0.533954674605375
23	103.47	103.003515791852	0.466484208147537
24	103.5	102.907412194903	0.59258780509703
25	103.69	102.967573131051	0.722426868949408
26	103.57	102.820100991442	0.749899008558481
27	103.47	102.760214251952	0.709785748048495
28	102.85	102.480574208934	0.369425791065608
29	102.54	102.401285572161	0.138714427838704
30	102.39	102.202127102762	0.187872897238138
31	102.16	101.908316294444	0.251683705555534
32	101.51	101.617777936988	-0.107777936988252
33	100.83	101.145542211512	-0.315542211511576
34	100.55	100.934950169071	-0.384950169070729
35	100.88	101.025472434003	-0.145472434003309
36	101	100.936027306453	0.0639726935467434
37	100.51	101.003401584450	-0.493401584450265
38	100.44	100.830405312143	-0.390405312143332
39	100.32	100.786887309927	-0.466887309926958
40	99.98	100.494207764336	-0.514207764335922
41	100.03	100.401047316314	-0.371047316314000
42	99.64	100.209657061214	-0.569657061213912
43	99.11	99.8933739186734	-0.783373918673393
44	98.97	99.6355730357645	-0.665573035764449
45	98.6	99.1824804098112	-0.582480409811169
46	98.31	98.9569068112216	-0.646906811221567
47	98.37	99.0576942164783	-0.687694216478283
48	98.19	98.9776819205775	-0.787681920577453
49	98.51	99.0769613644468	-0.56696136444679
50	98.23	98.8742794160673	-0.644279416067335
51	97.96	98.8143926765773	-0.854392676577336
52	97.77	98.5161644064868	-0.746164406486772
53	97.49	98.4077449660911	-0.917744966091126
54	97.76	98.2241229252904	-0.464122925290377
55	98.01	97.917550050624	0.092449949375956
56	97.73	97.6572522416903	0.0727477583096912
57	97.06	97.1952816565378	-0.135281656537769
58	96.63	96.9699854941732	-0.339985494173159
59	96.58	97.0677211009551	-0.48772110095513
60	96.66	96.9868764963794	-0.326876496379365
61	96.77	97.0556379555013	-0.285637955501264
62	96.5	96.862388838771	-0.362388838771014
63	96.53	96.8163739105298	-0.286373910529843
64	96.22	96.5139840970646	-0.293984097064631
65	96.49	96.4430185470409	0.0469814529591465
66	96.34	96.2460795674412	0.0939204325587787
67	96.31	95.951713886674	0.358286113326132
68	96.06	95.6889191517153	0.371080848284658
69	95.9	95.2635701482597	0.636429851740269
70	95.33	95.0124724169723	0.31752758302772
71	95.53	95.1115952048791	0.418404795120864
72	95.42	95.034357271228	0.385642728771934
73	95.57	95.0870274293013	0.482972570698681
74	95.3	94.9151409018943	0.384859098105718
75	95.31	94.8549767261793	0.455023273820709
76	95.38	94.5684007775378	0.811599222462239
77	95.22	94.4633105718418	0.756689428158168
78	94.62	94.2469510564938	0.373048943506173
79	93.81	93.9084730159552	-0.098473015955166
80	93.6	93.6351357044475	-0.0351357044475297
81	93.2	93.1837076958441	0.0162923041559023
82	93.29	92.9683992375787	0.321600762421359
83	93.54	93.062528173436	0.477471826564084
84	93.23	92.9630953417867	0.266904658213293
85	93.46	93.0349085993834	0.42509140061664
86	92.82	92.8605251459515	-0.0405251459515358
87	92.85	92.819226633535	0.0307733664650291
88	92.67	92.5162819476198	0.153718052380204
89	92.32	92.4075850709992	-0.0875850709991806
90	92.06	92.2220209766236	-0.162020976623596
91	91.88	91.8968598748838	-0.016859874883824
92	91.53	91.6471046424992	-0.117104642499200
93	91.19	91.192624835421	-0.0026248354210355

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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