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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: Mon, 19 Nov 2007 03:22:35 -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/t119546743378pvz4yc6df7viu.htm/, Retrieved Mon, 19 Nov 2007 11:17:41 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

112.1 0 104.2 0 102.4 0 100.3 0 102.6 0 101.5 0 103.4 0 99.4 0 97.9 0 98 0 90.2 0 87.1 0 91.8 0 94.8 0 91.8 0 89.3 0 91.7 0 86.2 0 82.8 0 82.3 0 79.8 0 79.4 0 85.3 0 87.5 0 88.3 0 88.6 0 94.9 0 94.7 0 92.6 0 91.8 0 96.4 0 96.4 0 107.1 0 111.9 0 107.8 0 109.2 0 115.3 0 119.2 0 107.8 0 106.8 0 104.2 0 94.8 0 97.5 0 98.3 0 100.6 1 94.9 1 93.6 1 98 1 104.3 1 103.9 1 105.3 1 102.6 1 103.3 1 107.9 1 107.8 1 109.8 1 110.6 1 110.8 1 119.3 1 128.1 1 127.6 1 137.9 1 151.4 1 143.6 1 143.4 1 141.9 1 135.2 1 133.1 1 129.6 1 134.1 1 136.8 1 143.5 1 162.5 1 163.1 1 157.2 1 158.8 1 155.4 1 148.5 1 154.2 1 153.3 1 149.4 1 147.9 1 156 1 163 1 159.1 1 159.5 1 157.3 1 156.4 1 156.6 1 162.4 1 166.8 1 162.6 1 168.1 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	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

Suiker[t] = + 75.5132381823562 -4.9594561794693Fluctuatie[t] + 0.952340929269015t + 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)	75.5132381823562	2.986496	25.2849	0	0
Fluctuatie	-4.9594561794693	5.381921	-0.9215	0.359251	0.179626
t	0.952340929269015	0.100095	9.5144	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.877834062380164
R-squared	0.770592641074862
Adjusted R-squared	0.765494699765415
F-TEST (value)	151.157613299078
F-TEST (DF numerator)	2
F-TEST (DF denominator)	90
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	13.0103985336055
Sum Squared Residuals	15234.3423002919

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	112.1	76.4655791116255	35.6344208883745
2	104.2	77.4179200408942	26.7820799591058
3	102.4	78.3702609701633	24.0297390298367
4	100.3	79.3226018994323	20.9773981005677
5	102.6	80.2749428287013	22.3250571712987
6	101.5	81.2272837579703	20.2727162420297
7	103.4	82.1796246872394	21.2203753127607
8	99.4	83.1319656165084	16.2680343834916
9	97.9	84.0843065457774	13.8156934542226
10	98	85.0366474750464	12.9633525249536
11	90.2	85.9889884043154	4.21101159568459
12	87.1	86.9413293335844	0.158670666415566
13	91.8	87.8936702628534	3.90632973714655
14	94.8	88.8460111921225	5.95398880787754
15	91.8	89.7983521213915	2.00164787860852
16	89.3	90.7506930506605	-1.45069305066049
17	91.7	91.7030339799295	-0.00303397992949916
18	86.2	92.6553749091985	-6.45537490919851
19	82.8	93.6077158384675	-10.8077158384675
20	82.3	94.5600567677366	-12.2600567677366
21	79.8	95.5123976970056	-15.7123976970056
22	79.4	96.4647386262746	-17.0647386262746
23	85.3	97.4170795555436	-12.1170795555436
24	87.5	98.3694204848126	-10.8694204848126
25	88.3	99.3217614140816	-11.0217614140816
26	88.6	100.274102343351	-11.6741023433506
27	94.9	101.226443272620	-6.32644327261965
28	94.7	102.178784201889	-7.47878420188866
29	92.6	103.131125131158	-10.5311251311577
30	91.8	104.083466060427	-12.2834660604267
31	96.4	105.035806989696	-8.6358069896957
32	96.4	105.988147918965	-9.58814791896472
33	107.1	106.940488848234	0.159511151766253
34	111.9	107.892829777503	4.00717022249725
35	107.8	108.845170706772	-1.04517070677177
36	109.2	109.797511636041	-0.597511636040781
37	115.3	110.749852565310	4.5501474346902
38	119.2	111.702193494579	7.49780650542119
39	107.8	112.654534423848	-4.85453442384783
40	106.8	113.606875353117	-6.80687535311685
41	104.2	114.559216282386	-10.3592162823859
42	94.8	115.511557211655	-20.7115572116549
43	97.5	116.463898140924	-18.9638981409239
44	98.3	117.416239070193	-19.1162390701929
45	100.6	113.409123819993	-12.8091238199926
46	94.9	114.361464749262	-19.4614647492616
47	93.6	115.313805678531	-21.7138056785307
48	98	116.266146607800	-18.2661466077997
49	104.3	117.218487537069	-12.9184875370687
50	103.9	118.170828466338	-14.2708284663377
51	105.3	119.123169395607	-13.8231693956067
52	102.6	120.075510324876	-17.4755103248757
53	103.3	121.027851254145	-17.7278512541447
54	107.9	121.980192183414	-14.0801921834137
55	107.8	122.932533112683	-15.1325331126828
56	109.8	123.884874041952	-14.0848740419518
57	110.6	124.837214971221	-14.2372149712208
58	110.8	125.789555900490	-14.9895559004898
59	119.3	126.741896829759	-7.44189682975883
60	128.1	127.694237759028	0.405762240972151
61	127.6	128.646578688297	-1.04657868829686
62	137.9	129.598919617566	8.30108038243413
63	151.4	130.551260546835	20.8487394531651
64	143.6	131.503601476104	12.0963985238961
65	143.4	132.455942405373	10.9440575946271
66	141.9	133.408283334642	8.49171666535807
67	135.2	134.360624263911	0.839375736089042
68	133.1	135.31296519318	-2.21296519317997
69	129.6	136.265306122449	-6.66530612244898
70	134.1	137.217647051718	-3.117647051718
71	136.8	138.169987980987	-1.36998798098700
72	143.5	139.122328910256	4.37767108974398
73	162.5	140.074669839525	22.4253301604750
74	163.1	141.027010768794	22.0729892312059
75	157.2	141.979351698063	15.2206483019369
76	158.8	142.931692627332	15.8683073726679
77	155.4	143.884033556601	11.5159664433989
78	148.5	144.83637448587	3.66362551412989
79	154.2	145.788715415139	8.41128458486086
80	153.3	146.741056344408	6.55894365559187
81	149.4	147.693397273677	1.70660272632285
82	147.9	148.645738202946	-0.745738202946165
83	156	149.598079132215	6.40192086778482
84	163	150.550420061484	12.4495799385158
85	159.1	151.502760990753	7.59723900924678
86	159.5	152.455101920022	7.04489807997777
87	157.3	153.407442849291	3.89255715070877
88	156.4	154.359783778560	2.04021622143975
89	156.6	155.312124707829	1.28787529217072
90	162.4	156.264465637098	6.13553436290172
91	166.8	157.216806566367	9.5831934336327
92	162.6	158.169147495636	4.43085250436367
93	168.1	159.121488424905	8.97851157509466

Charts produced by software:

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/19/t119546743378pvz4yc6df7viu/7q2j51195467750.ps (open in new window)

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Parameters:

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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