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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: Sat, 15 Dec 2007 07:33:04 -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/15/t1197728218idhhl7efqfx2ruu.htm/, Retrieved Sat, 15 Dec 2007 15:17:08 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

99.5 0 101.6 0 103.9 0 106.6 0 108.3 0 102 0 93.8 0 91.6 0 97.7 0 94.8 0 98 0 103.8 0 97.8 0 91.2 0 89.3 0 87.5 0 90.4 0 94.2 0 102.2 0 101.3 0 96 0 90.8 0 93.2 0 90.9 0 91.1 0 90.2 0 94.3 0 96 0 99 0 103.3 0 113.1 0 112.8 0 112.1 0 107.4 0 111 0 110.5 0 110.8 0 112.4 0 111.5 0 116.2 0 122.5 0 121.3 0 113.9 0 110.7 0 120.8 0 141.1 1 147.4 1 148 1 158.1 1 165 1 187 1 190.3 1 182.4 1 168.8 1 151.2 1 120.1 0 112.5 0 106.2 0 107.1 0 108.5 0 106.5 0 108.3 0 125.6 0 124 0 127.2 0 136.9 0 135.8 0 124.3 0 115.4 0 113.6 0 114.4 0 118.4 0 117 0 116.5 0 115.4 0 113.6 0 117.4 0 116.9 0 116.4 0 111.1 0 110.2 0 118.9 0 131.8 0 130.6 0 138.3 0 148.4 0 148.7 0 144.3 0 152.5 0 162.9 0 167.2 0 166.5 0 185.6 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

Oliezaden[t] = + 88.7430371002373 + 48.0608092540424Fluctuatie[t] + 0.537151557341t + 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)	88.7430371002373	2.695218	32.9261	0	0
Fluctuatie	48.0608092540424	4.281874	11.2242	0	0
t	0.537151557341	0.049411	10.8711	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.860048319537762
R-squared	0.739683111939728
Adjusted R-squared	0.733898292205056
F-TEST (value)	127.866233671252
F-TEST (DF numerator)	2
F-TEST (DF denominator)	90
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	12.7786892091705
Sum Squared Residuals	14696.5408114113

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	99.5	89.2801886575782	10.2198113424219
2	101.6	89.8173402149196	11.7826597850804
3	103.9	90.3544917722602	13.5455082277398
4	106.6	90.8916433296013	15.7083566703987
5	108.3	91.4287948869423	16.8712051130577
6	102	91.9659464442832	10.0340535557168
7	93.8	92.5030980016243	1.29690199837574
8	91.6	93.0402495589653	-1.44024955896526
9	97.7	93.5774011163062	4.12259888369375
10	94.8	94.1145526736473	0.685447326352745
11	98	94.6517042309883	3.34829576901175
12	103.8	95.1888557883292	8.61114421167074
13	97.8	95.7260073456703	2.07399265432974
14	91.2	96.2631589030113	-5.06315890301125
15	89.3	96.8003104603523	-7.50031046035226
16	87.5	97.3374620176933	-9.83746201769326
17	90.4	97.8746135750343	-7.47461357503425
18	94.2	98.4117651323753	-4.21176513237525
19	102.2	98.9489166897163	3.25108331028375
20	101.3	99.4860682470573	1.81393175294274
21	96	100.023219804398	-4.02321980439826
22	90.8	100.560371361739	-9.76037136173926
23	93.2	101.097522919080	-7.89752291908026
24	90.9	101.634674476421	-10.7346744764213
25	91.1	102.171826033762	-11.0718260337623
26	90.2	102.708977591103	-12.5089775911033
27	94.3	103.246129148444	-8.94612914844427
28	96	103.783280705785	-7.78328070578526
29	99	104.320432263126	-5.32043226312626
30	103.3	104.857583820467	-1.55758382046727
31	113.1	105.394735377808	7.70526462219173
32	112.8	105.931886935149	6.86811306485073
33	112.1	106.469038492490	5.63096150750973
34	107.4	107.006190049831	0.393809950168739
35	111	107.543341607172	3.45665839282773
36	110.5	108.080493164513	2.41950683548673
37	110.8	108.617644721854	2.18235527814573
38	112.4	109.154796279195	3.24520372080474
39	111.5	109.691947836536	1.80805216346373
40	116.2	110.229099393877	5.97090060612273
41	122.5	110.766250951218	11.7337490487817
42	121.3	111.303402508559	9.99659749144073
43	113.9	111.840554065900	2.05944593409973
44	110.7	112.377705623241	-1.67770562324127
45	120.8	112.914857180582	7.88514281941772
46	141.1	161.512817991966	-20.4128179919655
47	147.4	162.049969549306	-14.6499695493065
48	148	162.587121106648	-14.5871211066475
49	158.1	163.124272663989	-5.02427266398852
50	165	163.661424221329	1.33857577867049
51	187	164.198575778671	22.8014242213295
52	190.3	164.735727336012	25.5642726639885
53	182.4	165.272878893353	17.1271211066475
54	168.8	165.810030450694	2.9899695493065
55	151.2	166.347182008035	-15.1471820080345
56	120.1	118.823524311333	1.27647568866672
57	112.5	119.360675868674	-6.86067586867428
58	106.2	119.897827426015	-13.6978274260153
59	107.1	120.434978983356	-13.3349789833563
60	108.5	120.972130540697	-12.4721305406973
61	106.5	121.509282098038	-15.0092820980383
62	108.3	122.046433655379	-13.7464336553793
63	125.6	122.583585212720	3.01641478727971
64	124	123.120736770061	0.879263229938719
65	127.2	123.657888327402	3.54211167259772
66	136.9	124.195039884743	12.7049601152567
67	135.8	124.732191442084	11.0678085579157
68	124.3	125.269342999425	-0.969342999425287
69	115.4	125.806494556766	-10.4064945567663
70	113.6	126.343646114107	-12.7436461141073
71	114.4	126.880797671448	-12.4807976714483
72	118.4	127.417949228789	-9.01794922878928
73	117	127.955100786130	-10.9551007861303
74	116.5	128.492252343471	-11.9922523434713
75	115.4	129.029403900812	-13.6294039008123
76	113.6	129.566555458153	-15.9665554581533
77	117.4	130.103707015494	-12.7037070154943
78	116.9	130.640858572835	-13.7408585728353
79	116.4	131.178010130176	-14.7780101301763
80	111.1	131.715161687517	-20.6151616875173
81	110.2	132.252313244858	-22.0523132448583
82	118.9	132.789464802199	-13.8894648021993
83	131.8	133.326616359540	-1.52661635954028
84	130.6	133.863767916881	-3.2637679168813
85	138.3	134.400919474222	3.89908052577772
86	148.4	134.938071031563	13.4619289684367
87	148.7	135.475222588904	13.2247774110957
88	144.3	136.012374146245	8.28762585375472
89	152.5	136.549525703586	15.9504742964137
90	162.9	137.086677260927	25.8133227390727
91	167.2	137.623828818268	29.5761711817317
92	166.5	138.160980375609	28.3390196243907
93	185.6	138.698131932950	46.9018680670497

Charts produced by software:

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/15/t1197728218idhhl7efqfx2ruu/6gck41197729179.ps (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/15/t1197728218idhhl7efqfx2ruu/7ut971197729179.ps (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/15/t1197728218idhhl7efqfx2ruu/892301197729179.ps (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/15/t1197728218idhhl7efqfx2ruu/9l64h1197729179.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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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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