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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: Tue, 18 Dec 2007 03:31:59 -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/18/t1197973061f78vof8lv6cjddt.htm/, Retrieved Tue, 18 Dec 2007 11:17:42 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

88900 0 87280 0 85519 0 83647 0 81616 0 80100 0 94027 0 102327 0 104296 0 101593 0 94816 0 93535 0 93618 0 92330 0 90751 0 88576 0 86102 0 85494 0 103432 1 108870 1 109713 1 106960 1 103195 1 102348 1 102158 1 100431 1 97649 1 95611 1 93035 1 93579 1 111777 1 116065 1 116609 1 112934 1 107660 1 107965 1 107772 1 106201 1 102288 1 99217 1 96511 1 96456 1 113021 1 117836 1 118492 1 113922 1 109317 1 107496 1 105524 1 103824 1 101833 1 99436 1 96915 1 96072 1 111941 1 116008 1 117557 1 113445 1 108762 1 106661 1 102824 1 101912 1 99005 1 97894 1 96256 1 95606 1 108948 1 111223 1 113142 1 106078 1 100992 1 97413 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	6 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Multiple Linear Regression - Estimated Regression Equation

werkl50[t] = + 92451.0982905983 + 12142.2820512820premie[t] -413.28632478629M1[t] -1882.95299145299M2[t] -4371.78632478633M3[t] -6482.45299145299M4[t] -8806.78632478633M5[t] -9328.11965811966M6[t] + 4621.33333333333M7[t] + 9485.16666666667M8[t] + 10731.8333333333M9[t] + 6585.66666666666M10[t] + 1554M11[t] + 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)	92451.0982905983	1421.270844	65.0482	0	0
premie	12142.2820512820	840.251865	14.4508	0	0
M1	-413.28632478629	1754.720948	-0.2355	0.814614	0.407307
M2	-1882.95299145299	1754.720948	-1.0731	0.287605	0.143803
M3	-4371.78632478633	1754.720948	-2.4914	0.015554	0.007777
M4	-6482.45299145299	1754.720948	-3.6943	0.000484	0.000242
M5	-8806.78632478633	1754.720948	-5.0189	5e-06	3e-06
M6	-9328.11965811966	1754.720948	-5.316	2e-06	1e-06
M7	4621.33333333333	1749.123738	2.6421	0.010533	0.005267
M8	9485.16666666667	1749.123738	5.4228	1e-06	1e-06
M9	10731.8333333333	1749.123738	6.1355	0	0
M10	6585.66666666666	1749.123738	3.7651	0.000386	0.000193
M11	1554	1749.123738	0.8884	0.377909	0.188955

Multiple Linear Regression - Regression Statistics
Multiple R	0.956206137182481
R-squared	0.914330176785442
Adjusted R-squared	0.896905805962142
F-TEST (value)	52.4742147683632
F-TEST (DF numerator)	12
F-TEST (DF denominator)	59
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	3029.57118210534
Sum Squared Residuals	541519791.299144

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	88900	92037.8119658118	-3137.81196581178
2	87280	90568.1452991453	-3288.14529914531
3	85519	88079.311965812	-2560.31196581197
4	83647	85968.6452991453	-2321.64529914531
5	81616	83644.311965812	-2028.31196581197
6	80100	83122.9786324786	-3022.97863247864
7	94027	97072.4316239316	-3045.43162393164
8	102327	101936.264957265	390.735042735036
9	104296	103182.931623932	1113.06837606837
10	101593	99036.764957265	2556.23504273503
11	94816	94005.0982905983	810.90170940169
12	93535	92451.0982905983	1083.9017094017
13	93618	92037.811965812	1580.18803418799
14	92330	90568.1452991453	1761.85470085469
15	90751	88079.311965812	2671.68803418803
16	88576	85968.6452991453	2607.35470085469
17	86102	83644.311965812	2457.68803418803
18	85494	83122.9786324786	2371.02136752136
19	103432	109214.713675214	-5782.71367521367
20	108870	114078.547008547	-5208.54700854701
21	109713	115325.213675214	-5612.21367521367
22	106960	111179.047008547	-4219.04700854701
23	103195	106147.380341880	-2952.38034188034
24	102348	104593.380341880	-2245.38034188034
25	102158	104180.094017094	-2022.09401709405
26	100431	102710.427350427	-2279.42735042735
27	97649	100221.594017094	-2572.59401709401
28	95611	98110.9273504273	-2499.92735042735
29	93035	95786.594017094	-2751.59401709401
30	93579	95265.2606837607	-1686.26068376068
31	111777	109214.713675214	2562.28632478633
32	116065	114078.547008547	1986.45299145299
33	116609	115325.213675214	1283.78632478632
34	112934	111179.047008547	1754.95299145299
35	107660	106147.380341880	1512.61965811966
36	107965	104593.380341880	3371.61965811966
37	107772	104180.094017094	3591.90598290595
38	106201	102710.427350427	3490.57264957265
39	102288	100221.594017094	2066.40598290599
40	99217	98110.9273504273	1106.07264957265
41	96511	95786.594017094	724.405982905987
42	96456	95265.2606837607	1190.73931623932
43	113021	109214.713675214	3806.28632478633
44	117836	114078.547008547	3757.45299145299
45	118492	115325.213675214	3166.78632478632
46	113922	111179.047008547	2742.95299145299
47	109317	106147.380341880	3169.61965811966
48	107496	104593.380341880	2902.61965811966
49	105524	104180.094017094	1343.90598290595
50	103824	102710.427350427	1113.57264957265
51	101833	100221.594017094	1611.40598290599
52	99436	98110.9273504273	1325.07264957265
53	96915	95786.594017094	1128.40598290599
54	96072	95265.2606837607	806.73931623932
55	111941	109214.713675214	2726.28632478633
56	116008	114078.547008547	1929.45299145299
57	117557	115325.213675214	2231.78632478632
58	113445	111179.047008547	2265.95299145299
59	108762	106147.380341880	2614.61965811966
60	106661	104593.380341880	2067.61965811966
61	102824	104180.094017094	-1356.09401709405
62	101912	102710.427350427	-798.427350427346
63	99005	100221.594017094	-1216.59401709401
64	97894	98110.9273504273	-216.927350427346
65	96256	95786.594017094	469.405982905986
66	95606	95265.2606837607	340.739316239321
67	108948	109214.713675214	-266.713675213673
68	111223	114078.547008547	-2855.54700854701
69	113142	115325.213675214	-2183.21367521367
70	106078	111179.047008547	-5101.04700854701
71	100992	106147.380341880	-5155.38034188034
72	97413	104593.380341880	-7180.38034188034

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No 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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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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