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*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 11:37:50 -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/t12275520008e35gggr8yqwpbs.htm/, Retrieved Mon, 24 Nov 2008 18:40:00 +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/t12275520008e35gggr8yqwpbs.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:

» Textbox « » Textfile « » CSV «

56983 0 57942 0 34857 0 39421 0 45612 0 65410 0 50125 0 46879 0 53875 0 49652 0 54167 0 61558 0 56874 0 51966 0 45897 0 46832 0 47852 0 58236 0 54216 0 52687 0 47659 0 50089 0 51247 0 48658 0 47233 0 46988 0 51784 0 53620 0 51479 0 50007 0 52634 0 49566 0 48522 0 53864 0 51477 0 56214 0 60032 0 57862 0 55684 0 75894 1 80564 1 84562 1 87546 1 83654 1 89745 1 79565 1 78498 1 79468 1 82479 1 84675 1 85479 1 83547 1 89654 1 84523 1 87469 1 87985 1 88423 1 90475 1 86542 1 87963 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	5 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Multiple Linear Regression - Estimated Regression Equation

y[t] = + 50587.8084848485 + 29350.0787878788x[t] + 1176.01464646464M1[t] + 218.960202020203M2[t] -5050.89424242424M3[t] -5921.76444444444M4[t] -2875.81888888889M5[t] + 2516.12666666667M6[t] + 243.072222222224M7[t] -2124.18222222222M8[t] -757.036666666666M9[t] -1796.29111111111M10[t] -2262.54555555555M11[t] + 123.454444444445t + 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)	50587.8084848485	2826.585235	17.8971	0	0
x	29350.0787878788	2464.89946	11.9072	0	0
M1	1176.01464646464	3196.393216	0.3679	0.714621	0.357311
M2	218.960202020203	3189.852497	0.0686	0.945572	0.472786
M3	-5050.89424242424	3184.755984	-1.586	0.1196	0.0598
M4	-5921.76444444444	3212.785253	-1.8432	0.07175	0.035875
M5	-2875.81888888889	3201.93244	-0.8982	0.373782	0.186891
M6	2516.12666666667	3192.496825	0.7881	0.434659	0.21733
M7	243.072222222224	3184.491008	0.0763	0.939488	0.469744
M8	-2124.18222222222	3177.925792	-0.6684	0.507207	0.253604
M9	-757.036666666666	3172.810121	-0.2386	0.812475	0.406237
M10	-1796.29111111111	3169.151014	-0.5668	0.573602	0.286801
M11	-2262.54555555555	3166.953521	-0.7144	0.478575	0.239288
t	123.454444444445	68.126222	1.8121	0.076494	0.038247

Multiple Linear Regression - Regression Statistics
Multiple R	0.96435964366221
R-squared	0.929989522324306
Adjusted R-squared	0.910203952546393
F-TEST (value)	47.0034238469317
F-TEST (DF numerator)	13
F-TEST (DF denominator)	46
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	5006.23446900787
Sum Squared Residuals	1152869643.69939

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	56983	51887.2775757576	5095.72242424238
2	57942	51053.6775757576	6888.32242424243
3	34857	45907.2775757576	-11050.2775757576
4	39421	45159.8618181818	-5738.86181818182
5	45612	48329.2618181818	-2717.26181818182
6	65410	53844.6618181818	11565.3381818182
7	50125	51695.0618181818	-1570.06181818181
8	46879	49451.2618181818	-2572.26181818182
9	53875	50941.8618181818	2933.13818181818
10	49652	50026.0618181818	-374.061818181817
11	54167	49683.2618181818	4483.73818181818
12	61558	52069.2618181818	9488.73818181819
13	56874	53368.7309090909	3505.26909090910
14	51966	52535.1309090909	-569.130909090908
15	45897	47388.7309090909	-1491.73090909091
16	46832	46641.3151515152	190.684848484847
17	47852	49810.7151515151	-1958.71515151515
18	58236	55326.1151515152	2909.88484848485
19	54216	53176.5151515152	1039.48484848485
20	52687	50932.7151515151	1754.28484848485
21	47659	52423.3151515152	-4764.31515151515
22	50089	51507.5151515152	-1418.51515151515
23	51247	51164.7151515151	82.2848484848486
24	48658	53550.7151515151	-4892.71515151515
25	47233	54850.1842424242	-7617.18424242423
26	46988	54016.5842424242	-7028.58424242424
27	51784	48870.1842424242	2913.81575757576
28	53620	48122.7684848485	5497.23151515151
29	51479	51292.1684848485	186.831515151514
30	50007	56807.5684848485	-6800.56848484849
31	52634	54657.9684848485	-2023.96848484849
32	49566	52414.1684848485	-2848.16848484849
33	48522	53904.7684848485	-5382.76848484849
34	53864	52988.9684848485	875.031515151515
35	51477	52646.1684848485	-1169.16848484849
36	56214	55032.1684848485	1181.83151515151
37	60032	56331.6375757576	3700.36242424243
38	57862	55498.0375757576	2363.96242424242
39	55684	50351.6375757576	5332.36242424242
40	75894	78954.3006060606	-3060.30060606061
41	80564	82123.7006060606	-1559.70060606060
42	84562	87639.1006060606	-3077.10060606061
43	87546	85489.5006060606	2056.49939393939
44	83654	83245.7006060606	408.299393939395
45	89745	84736.3006060606	5008.6993939394
46	79565	83820.5006060606	-4255.50060606061
47	78498	83477.7006060606	-4979.7006060606
48	79468	85863.7006060606	-6395.7006060606
49	82479	87163.1696969697	-4684.16969696969
50	84675	86329.5696969697	-1654.56969696970
51	85479	81183.1696969697	4295.83030303031
52	83547	80435.753939394	3111.24606060606
53	89654	83605.153939394	6048.84606060606
54	84523	89120.553939394	-4597.55393939394
55	87469	86970.953939394	498.046060606059
56	87985	84727.153939394	3257.84606060606
57	88423	86217.753939394	2205.24606060606
58	90475	85301.953939394	5173.04606060606
59	86542	84959.153939394	1582.84606060606
60	87963	87345.153939394	617.846060606059

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')

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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