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Fixed en linear

*The author of this computation has been verified*

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

Title produced by software: Multiple Regression

Date of computation: Mon, 24 Nov 2008 11:28:10 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/24/t1227551340f80ewyu5zm3nltx.htm/, Retrieved Mon, 24 Nov 2008 18:29:00 +0000

BibTeX entries for LaTeX users:

@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2008/Nov/24/t1227551340f80ewyu5zm3nltx.htm/},
    year = {2008},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2008},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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97.3 0 101 0 113.2 0 101 0 105.7 0 113.9 0 86.4 0 96.5 0 103.3 0 114.9 0 105.8 0 94.2 0 98.4 0 99.4 0 108.8 0 112.6 0 104.4 0 112.2 0 81.1 0 97.1 0 112.6 0 113.8 0 107.8 0 103.2 0 103.3 0 101.2 0 107.7 0 110.4 0 101.9 0 115.9 0 89.9 0 88.6 0 117.2 0 123.9 0 100 0 103.6 0 94.1 0 98.7 0 119.5 0 112.7 0 104.4 0 124.7 0 89.1 0 97 0 121.6 0 118.8 0 114 0 111.5 0 97.2 0 102.5 0 113.4 0 109.8 0 104.9 0 126.1 0 80 0 96.8 0 117.2 1 112.3 1 117.3 1 111.1 1 102.2 1 104.3 1 122.9 1 107.6 1 121.3 1 131.5 1 89 1 104.4 1 128.9 1 135.9 1 133.3 1 121.3 1 120.5 1 120.4 1 137.9 1 126.1 1 133.2 1 146.6 1 103.4 1 117.2 1

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 computational 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

y[t] = + 97.6646949404762 + 6.81015625x[t] -4.40325609410432M1[t] -2.51155576814059M2[t] + 11.0087159863946M3[t] + 4.65755916950114M4[t] + 3.84925949546486M5[t] + 17.2552455357143M6[t] -18.9244827097506M7[t] -7.86135381235827M8[t] + 9.85585140306122M9[t] + 12.8094564909297M10[t] + 5.72972824546486M11[t] + 0.179728245464853t + 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)	97.6646949404762	2.892524	33.7645	0	0
x	6.81015625	2.461431	2.7667	0.007338	0.003669
M1	-4.40325609410432	3.385008	-1.3008	0.197847	0.098923
M2	-2.51155576814059	3.383171	-0.7424	0.460499	0.230249
M3	11.0087159863946	3.382043	3.255	0.00179	0.000895
M4	4.65755916950114	3.381624	1.3773	0.173068	0.086534
M5	3.84925949546486	3.381914	1.1382	0.259156	0.129578
M6	17.2552455357143	3.382913	5.1007	3e-06	2e-06
M7	-18.9244827097506	3.384621	-5.5913	0	0
M8	-7.86135381235827	3.387037	-2.321	0.023385	0.011692
M9	9.85585140306122	3.511583	2.8067	0.006573	0.003287
M10	12.8094564909297	3.509875	3.6495	0.00052	0.00026
M11	5.72972824546486	3.508849	1.6329	0.107245	0.053622
t	0.179728245464853	0.048977	3.6696	0.000487	0.000244

Multiple Linear Regression - Regression Statistics
Multiple R	0.907219211715824
R-squared	0.823046698106281
Adjusted R-squared	0.788192259854488
F-TEST (value)	23.6138276612144
F-TEST (DF numerator)	13
F-TEST (DF denominator)	66
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	6.07691307608853
Sum Squared Residuals	2437.30558726616

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	97.3	93.4411670918368	3.85883290816321
2	101	95.5125956632653	5.48740433673468
3	113.2	109.212595663265	3.98740433673469
4	101	103.041167091837	-2.04116709183673
5	105.7	102.412595663265	3.2874043367347
6	113.9	115.998309948980	-2.09830994897959
7	86.4	79.9983099489796	6.40169005102042
8	96.5	91.2411670918367	5.25883290816327
9	103.3	109.138100552721	-5.83810055272109
10	114.9	112.271433886054	2.62856611394559
11	105.8	105.371433886054	0.42856611394558
12	94.2	99.8214338860544	-5.62143388605442
13	98.4	95.597906037415	2.80209396258505
14	99.4	97.6693346088435	1.73066539115647
15	108.8	111.369334608844	-2.56933460884354
16	112.6	105.197906037415	7.40209396258503
17	104.4	104.569334608844	-0.169334608843534
18	112.2	118.155048894558	-5.95504889455782
19	81.1	82.1550488945578	-1.05504889455783
20	97.1	93.397906037415	3.70209396258503
21	112.6	111.294839498299	1.30516050170068
22	113.8	114.428172831633	-0.628172831632654
23	107.8	107.528172831633	0.271827168367342
24	103.2	101.978172831633	1.22182716836735
25	103.3	97.7546449829932	5.54535501700681
26	101.2	99.8260735544218	1.37392644557823
27	107.7	113.526073554422	-5.82607355442177
28	110.4	107.354644982993	3.04535501700681
29	101.9	106.726073554422	-4.82607355442176
30	115.9	120.311787840136	-4.41178784013605
31	89.9	84.311787840136	5.58821215986395
32	88.6	95.5546449829932	-6.9546449829932
33	117.2	113.451578443878	3.74842155612246
34	123.9	116.584911777211	7.31508822278912
35	100	109.684911777211	-9.68491177721089
36	103.6	104.134911777211	-0.534911777210889
37	94.1	99.9113839285714	-5.81138392857143
38	98.7	101.9828125	-3.2828125
39	119.5	115.6828125	3.8171875
40	112.7	109.511383928571	3.18861607142858
41	104.4	108.8828125	-4.4828125
42	124.7	122.468526785714	2.23147321428572
43	89.1	86.4685267857143	2.63147321428571
44	97	97.7113839285714	-0.711383928571429
45	121.6	115.608317389456	5.99168261054421
46	118.8	118.741650722789	0.0583492772108809
47	114	111.841650722789	2.15834927721088
48	111.5	106.291650722789	5.20834927721088
49	97.2	102.068122874150	-4.86812287414965
50	102.5	104.139551445578	-1.63955144557823
51	113.4	117.839551445578	-4.43955144557823
52	109.8	111.668122874150	-1.86812287414966
53	104.9	111.039551445578	-6.13955144557823
54	126.1	124.625265731293	1.47473426870748
55	80	88.6252657312925	-8.62526573129252
56	96.8	99.8681228741497	-3.06812287414966
57	117.2	124.575212585034	-7.37521258503401
58	112.3	127.708545918367	-15.4085459183674
59	117.3	120.808545918367	-3.50854591836735
60	111.1	115.258545918367	-4.15854591836735
61	102.2	111.035018069728	-8.83501806972788
62	104.3	113.106446641156	-8.80644664115647
63	122.9	126.806446641156	-3.90644664115646
64	107.6	120.635018069728	-13.0350180697279
65	121.3	120.006446641156	1.29355335884353
66	131.5	133.592160926871	-2.09216092687075
67	89	97.5921609268707	-8.59216092687075
68	104.4	108.835018069728	-4.43501806972789
69	128.9	126.731951530612	2.16804846938776
70	135.9	129.865284863946	6.03471513605442
71	133.3	122.965284863946	10.3347151360544
72	121.3	117.415284863946	3.88471513605442
73	120.5	113.191757015306	7.30824298469388
74	120.4	115.263185586735	5.13681441326531
75	137.9	128.963185586735	8.9368144132653
76	126.1	122.791757015306	3.30824298469387
77	133.2	122.163185586735	11.0368144132653
78	146.6	135.748899872449	10.851100127551
79	103.4	99.748899872449	3.65110012755103
80	117.2	110.991757015306	6.20824298469388

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly 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')

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Software written by Ed van Stee & Patrick Wessa

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