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Multiple regression

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 10:45:31 -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/t1198002379tm6rs7eb9k33dzl.htm/, Retrieved Tue, 18 Dec 2007 19:26:30 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

98,8 100,5 110,4 96,4 101,9 106,2 81,0 94,7 101,0 109,4 102,3 90,7 96,2 96,1 106,0 103,1 102,0 104,7 86,0 92,1 106,9 112,6 101,7 92,0 97,4 97,0 105,4 102,7 98,1 104,5 87,4 89,9 109,8 111,7 98,6 96,9 95,1 97,0 112,7 102,9 97,4 111,4 87,4 96,8 114,1 110,3 103,9 101,6 94,6 95,9 104,7 102,8 98,1 113,9 80,9 95,7 113,2 105,9 108,8 102,3 99,0 100,7 115,5 100,7 109,9 114,6 85,4 100,5 114,8 116,5 112,9 102,0 106,0 105,3 118,8 106,1 109,3 117,2 91,9 103,9 115,9

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

x[t] = + 92.4459770114943 + 1.18539956212370M1[t] + 1.83451012588942M2[t] + 13.2836206896552M3[t] + 4.76130268199233M4[t] + 4.92469896004379M5[t] + 12.7738095238095M6[t] -11.9913656267105M7[t] -1.59939792008757M8[t] + 12.8639983579639M9[t] + 13.727969348659M10[t] + 7.2389846743295M11[t] + 0.122318007662835t + 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)	92.4459770114943	1.557391	59.3595	0	0
M1	1.18539956212370	1.906635	0.6217	0.536203	0.268101
M2	1.83451012588942	1.906004	0.9625	0.339214	0.169607
M3	13.2836206896552	1.905513	6.9712	0	0
M4	4.76130268199233	1.905162	2.4992	0.014869	0.007434
M5	4.92469896004379	1.904952	2.5852	0.011881	0.00594
M6	12.7738095238095	1.904882	6.7058	0	0
M7	-11.9913656267105	1.904952	-6.2948	0	0
M8	-1.59939792008757	1.905162	-0.8395	0.404126	0.202063
M9	12.8639983579639	1.905513	6.7509	0	0
M10	13.727969348659	1.97706	6.9436	0	0
M11	7.2389846743295	1.976857	3.6619	0.000491	0.000245
t	0.122318007662835	0.016351	7.4807	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.929975605243166
R-squared	0.864854626347393
Adjusted R-squared	0.84100544276164
F-TEST (value)	36.2634898271318
F-TEST (DF numerator)	12
F-TEST (DF denominator)	68
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	3.42389921296394
Sum Squared Residuals	797.169835796388

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	98.8	93.7536945812808	5.04630541871923
2	100.5	94.5251231527094	5.97487684729063
3	110.4	106.096551724138	4.30344827586209
4	96.4	97.6965517241379	-1.29655172413792
5	101.9	97.9822660098522	3.9177339901478
6	106.2	105.953694581281	0.246305418719199
7	81	81.3108374384236	-0.310837438423637
8	94.7	91.8251231527094	2.87487684729065
9	101	106.410837438424	-5.41083743842365
10	109.4	107.397126436782	2.00287356321839
11	102.3	101.030459770115	1.26954022988505
12	90.7	93.9137931034483	-3.21379310344828
13	96.2	95.2215106732348	0.978489326765192
14	96.1	95.9929392446634	0.107060755336614
15	106	107.564367816092	-1.56436781609196
16	103.1	99.164367816092	3.93563218390804
17	102	99.4500821018062	2.54991789819376
18	104.7	107.421510673235	-2.72151067323481
19	86	82.7786535303777	3.22134646962232
20	92.1	93.2929392446634	-1.19293924466340
21	106.9	107.878653530378	-0.978653530377664
22	112.6	108.864942528736	3.73505747126436
23	101.7	102.498275862069	-0.798275862068966
24	92	95.3816091954023	-3.38160919540231
25	97.4	96.6893267651888	0.710673234811167
26	97	97.4607553366174	-0.460755336617403
27	105.4	109.032183908046	-3.63218390804598
28	102.7	100.632183908046	2.06781609195402
29	98.1	100.917898193760	-2.81789819376027
30	104.5	108.889326765189	-4.38932676518884
31	87.4	84.2464696223317	3.15353037766830
32	89.9	94.7607553366174	-4.8607553366174
33	109.8	109.346469622332	0.453530377668305
34	111.7	110.332758620690	1.36724137931035
35	98.6	103.966091954023	-5.366091954023
36	96.9	96.8494252873563	0.0505747126436779
37	95.1	98.1571428571429	-3.05714285714287
38	97	98.9285714285714	-1.92857142857143
39	112.7	110.5	2.20000000000000
40	102.9	102.1	0.800000000000003
41	97.4	102.385714285714	-4.98571428571428
42	111.4	110.357142857143	1.04285714285715
43	87.4	85.7142857142857	1.68571428571428
44	96.8	96.2285714285714	0.571428571428565
45	114.1	110.814285714286	3.28571428571428
46	110.3	111.800574712644	-1.50057471264368
47	103.9	105.433908045977	-1.53390804597701
48	101.6	98.3172413793103	3.28275862068964
49	94.6	99.6249589490969	-5.02495894909689
50	95.9	100.396387520525	-4.49638752052544
51	104.7	111.967816091954	-7.26781609195402
52	102.8	103.567816091954	-0.767816091954027
53	98.1	103.853530377668	-5.75353037766831
54	113.9	111.824958949097	2.07504105090312
55	80.9	87.1821018062397	-6.28210180623974
56	95.7	97.6963875205254	-1.99638752052545
57	113.2	112.282101806240	0.917898193760268
58	105.9	113.268390804598	-7.3683908045977
59	108.8	106.901724137931	1.89827586206896
60	102.3	99.7850574712644	2.51494252873563
61	99	101.092775041051	-2.09277504105091
62	100.7	101.864203612479	-1.16420361247947
63	115.5	113.435632183908	2.06436781609195
64	100.7	105.035632183908	-4.33563218390804
65	109.9	105.321346469622	4.57865353037767
66	114.6	113.292775041051	1.30722495894909
67	85.4	88.6499178981938	-3.24991789819376
68	100.5	99.1642036124795	1.33579638752052
69	114.8	113.749917898194	1.05008210180624
70	116.5	114.736206896552	1.76379310344828
71	112.9	108.369540229885	4.53045977011495
72	102	101.252873563218	0.747126436781606
73	106	102.560591133005	3.43940886699507
74	105.3	103.332019704433	1.96798029556651
75	118.8	114.903448275862	3.89655172413793
76	106.1	106.503448275862	-0.403448275862075
77	109.3	106.789162561576	2.51083743842364
78	117.2	114.760591133005	2.43940886699508
79	91.9	90.1177339901478	1.78226600985221
80	103.9	100.632019704434	3.26798029556651
81	115.9	115.217733990148	0.682266009852226

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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We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

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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