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Paper - Regress.- Invoer België - Start euro

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

Title produced by software: Multiple Regression

Date of computation: Fri, 21 Dec 2007 07:32:45 -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/21/t119824651265f2zur9frgtbcx.htm/, Retrieved Fri, 21 Dec 2007 15:15:25 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

7272.2 0 6680.1 0 8427.6 0 8752.8 0 7952.7 0 8694.3 0 7787 0 8474.2 0 9154.7 0 8557.2 0 7951.1 0 9156.7 0 7865.7 0 7337.4 0 9131.7 0 8814.6 0 8598.8 0 8439.6 0 7451.8 0 8016.2 0 9544.1 0 8270.7 0 8102.2 0 9369 0 7657.7 0 7816.6 0 9391.3 0 9445.4 0 9533.1 0 10068.7 0 8955.5 0 10423.9 0 11617.2 0 9391.1 0 10872 0 10230.4 0 9221 0 9428.6 0 10934.5 0 10986 0 11724.6 0 11180.9 0 11163.2 0 11240.9 0 12107.1 0 10762.3 0 11340.4 0 11266.8 0 9542.7 0 9227.7 0 10571.9 0 10774.4 0 10392.8 0 9920.2 0 9884.9 1 10174.5 1 11395.4 1 10760.2 1 10570.1 1 10536 1 9902.6 1 8889 1 10837.3 1 11624.1 1 10509 1 10984.9 1 10649.1 1 10855.7 1 11677.4 1 10760.2 1 10046.2 1 10772.8 1 9987.7 1 8638.7 1 11063.7 1 11855.7 1 10684.5 1 11337.4 1 10478 1 11123.9 1 12909.3 1 11339.9 1 10462.2 1 12733.5 1 10519.2 1 10414.9 1 12476.8 1 12384.6 1 12266.7 1 12919.9 1 11497.3 1 12142 1 13919.4 1 12656.8 1 12034.1 1 13199.7 1 10881.3 1 11301.2 1 13643.9 1 12517 1 13981.1 1 14275.7 1 13435 1 13565.7 1 16216.3 1 12970 1 14079.9 1 14235 1 12213.4 1 12581 1 14130.4 1 14210.8 1 14378.5 1 13142.8 1 13714.7 1 13621.9 1 15379.8 1 13306.3 1 14391.2 1 14909.9 1 14552.7 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	4 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

Invoer[t] = + 7993.7491103842 -1443.30297607594X[t] -1412.68647481161M1[t] -1869.97019529526M2[t] -108.962205526499M3[t] -101.714215757733M4[t] -304.456225988966M5[t] -278.578236220198M6[t] -797.419948843835M7[t] -403.561959075068M8[t] + 956.236030693697M9[t] -626.745979537535M10[t] -587.657989768767M11[t] + 68.3820102312329t + 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)	7993.7491103842	220.327221	36.2813	0	0
X	-1443.30297607594	216.337578	-6.6715	0	0
M1	-1412.68647481161	261.758411	-5.3969	0	0
M2	-1869.97019529526	268.295016	-6.9698	0	0
M3	-108.962205526499	268.17348	-0.4063	0.685325	0.342662
M4	-101.714215757733	268.087192	-0.3794	0.705137	0.352569
M5	-304.456225988966	268.036186	-1.1359	0.258546	0.129273
M6	-278.578236220198	268.020482	-1.0394	0.300966	0.150483
M7	-797.419948843835	268.235931	-2.9728	0.003646	0.001823
M8	-403.561959075068	268.077119	-1.5054	0.135169	0.067584
M9	956.236030693697	267.953533	3.5687	0.000539	0.000269
M10	-626.745979537535	267.865223	-2.3398	0.021151	0.010575
M11	-587.657989768767	267.812223	-2.1943	0.030377	0.015188
t	68.3820102312329	3.076305	22.2286	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.960813246834253
R-squared	0.92316209529218
Adjusted R-squared	0.91382664892581
F-TEST (value)	98.887836645681
F-TEST (DF numerator)	13
F-TEST (DF denominator)	107
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	598.806826937201
Sum Squared Residuals	38366948.9105661

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	7272.2	6649.44464580379	622.755354196211
2	6680.1	6260.5429355514	419.557064448606
3	8427.6	8089.9329355514	337.667064448595
4	8752.8	8165.5629355514	587.237064448597
5	7952.7	8031.2029355514	-78.5029355514001
6	8694.3	8125.4629355514	568.837064448604
7	7787	7675.00323315899	111.996766841012
8	8474.2	8137.24323315899	336.956766841012
9	9154.7	9565.4232331590	-410.723233158992
10	8557.2	8050.82323315899	506.376766841009
11	7951.1	8158.29323315899	-207.193233158988
12	9156.7	8814.33323315899	342.366766841013
13	7865.7	7470.02876857861	395.671231421387
14	7337.4	7081.1270583262	256.272941673806
15	9131.7	8910.51705832619	221.182941673811
16	8814.6	8986.14705832619	-171.54705832619
17	8598.8	8851.78705832619	-252.987058326191
18	8439.6	8946.04705832619	-506.447058326191
19	7451.8	8495.58735593379	-1043.78735593379
20	8016.2	8957.82735593378	-941.627355933786
21	9544.1	10386.0073559338	-841.907355933784
22	8270.7	8871.40735593378	-600.707355933784
23	8102.2	8978.87735593379	-876.677355933786
24	9369	9634.91735593379	-265.917355933785
25	7657.7	8290.6128913534	-632.912891353406
26	7816.6	7901.71118110099	-85.1111811009849
27	9391.3	9731.10118110098	-339.801181100985
28	9445.4	9806.73118110098	-361.331181100985
29	9533.1	9672.37118110099	-139.271181100985
30	10068.7	9766.63118110099	302.068818899015
31	8955.5	9316.17147870858	-360.67147870858
32	10423.9	9778.41147870858	645.48852129142
33	11617.2	11206.5914787086	410.608521291422
34	9391.1	9691.99147870858	-300.891478708579
35	10872	9799.46147870858	1072.53852129142
36	10230.4	10455.5014787086	-225.101478708580
37	9221	9111.1970141282	109.802985871800
38	9428.6	8722.29530387578	706.304696124221
39	10934.5	10551.6853038758	382.814696124222
40	10986	10627.3153038758	358.684696124221
41	11724.6	10492.9553038758	1231.64469612422
42	11180.9	10587.2153038758	593.68469612422
43	11163.2	10136.7556014834	1026.44439851663
44	11240.9	10598.9956014834	641.904398516626
45	12107.1	12027.1756014834	79.9243985166273
46	10762.3	10512.5756014834	249.724398516626
47	11340.4	10620.0456014834	720.354398516625
48	11266.8	11276.0856014834	-9.28560148337375
49	9542.7	9931.781136903	-389.081136902994
50	9227.7	9542.87942665057	-315.179426650573
51	10571.9	11372.2694266506	-800.369426650573
52	10774.4	11447.8994266506	-673.499426650573
53	10392.8	11313.5394266506	-920.739426650575
54	9920.2	11407.7994266506	-1487.59942665057
55	9884.9	9514.03674818223	370.863251817773
56	10174.5	9976.27674818223	198.223251817774
57	11395.4	11404.4567481822	-9.05674818222588
58	10760.2	9889.85674818223	870.343251817775
59	10570.1	9997.32674818223	572.773251817774
60	10536	10653.3667481822	-117.366748182226
61	9902.6	9309.06228360185	593.537716398154
62	8889	8920.16057334943	-31.160573349427
63	10837.3	10749.5505733494	87.7494266505743
64	11624.1	10825.1805733494	798.919426650575
65	10509	10690.8205733494	-181.820573349426
66	10984.9	10785.0805733494	199.819426650573
67	10649.1	10334.6208709570	314.47912904298
68	10855.7	10796.8608709570	58.83912904298
69	11677.4	12225.0408709570	-547.640870957020
70	10760.2	10710.4408709570	49.7591290429804
71	10046.2	10817.9108709570	-771.71087095702
72	10772.8	11473.9508709570	-701.150870957021
73	9987.7	10129.6464063766	-141.946406376641
74	8638.7	9740.74469612422	-1102.04469612422
75	11063.7	11570.1346961242	-506.434696124219
76	11855.7	11645.7646961242	209.935303875781
77	10684.5	11511.4046961242	-826.90469612422
78	11337.4	11605.6646961242	-268.264696124222
79	10478	11155.2049937318	-677.204993731815
80	11123.9	11617.4449937318	-493.544993731816
81	12909.3	13045.6249937318	-136.324993731815
82	11339.9	11531.0249937318	-191.124993731815
83	10462.2	11638.4949937318	-1176.29499373181
84	12733.5	12294.5349937318	438.965006268185
85	10519.2	10950.2305291514	-431.030529151435
86	10414.9	10561.3288188990	-146.428818899016
87	12476.8	12390.7188188990	86.0811811009855
88	12384.6	12466.3488188990	-81.7488188990137
89	12266.7	12331.9888188990	-65.288818899014
90	12919.9	12426.2488188990	493.651181100984
91	11497.3	11975.7891165066	-478.489116506611
92	12142	12438.0291165066	-296.029116506610
93	13919.4	13866.2091165066	53.1908834933911
94	12656.8	12351.6091165066	305.190883493390
95	12034.1	12459.0791165066	-424.979116506609
96	13199.7	13115.1191165066	84.5808834933917
97	10881.3	11770.8146519262	-889.51465192623
98	11301.2	11381.9129416738	-80.7129416738088
99	13643.9	13211.3029416738	432.597058326191
100	12517	13286.9329416738	-769.932941673809
101	13981.1	13152.5729416738	828.527058326191
102	14275.7	13246.8329416738	1028.86705832619
103	13435	12796.3732392814	638.626760718596
104	13565.7	13258.6132392814	307.086760718597
105	16216.3	14686.7932392814	1529.50676071860
106	12970	13172.1932392814	-202.193239281403
107	14079.9	13279.6632392814	800.236760718596
108	14235	13935.7032392814	299.296760718597
109	12213.4	12591.3987747010	-377.998774701024
110	12581	12202.4970644486	378.502935551396
111	14130.4	14031.8870644486	98.5129355513976
112	14210.8	14107.5170644486	103.282935551397
113	14378.5	13973.1570644486	405.342935551397
114	13142.8	14067.4170644486	-924.617064448604
115	13714.7	13616.9573620562	97.7426379438026
116	13621.9	14079.1973620562	-457.297362056198
117	15379.8	15507.3773620562	-127.577362056198
118	13306.3	13992.7773620562	-686.477362056198
119	14391.2	14100.2473620562	290.952637943803
120	14909.9	14756.2873620562	153.612637943802
121	14552.7	13411.9828974758	1140.71710252418

Charts produced by software:

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/21/t119824651265f2zur9frgtbcx/77yi21198247559.ps (open in new window)

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

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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