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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 04:02:03 -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/t1195469816naum8tspmu7vf1l.htm/, Retrieved Mon, 19 Nov 2007 11:57:10 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

106.54 107.89 1 106.44 107.26 1 106.57 107.76 1 106.12 107.32 1 106.13 107.15 1 106.26 108.04 1 105.78 106.52 1 105.77 106.62 0 105.2 106.47 0 105.15 105.46 0 105.01 106.13 0 104.75 105.15 0 104.96 105.39 0 105.26 104.57 0 105.13 104.29 0 104.77 104.09 0 104.79 104.51 0 104.4 103.39 0 103.89 102.71 0 103.93 102.62 0 103.48 101.94 0 103.45 101.65 0 103.47 101.86 0 103.5 101.27 0 103.69 101.21 0 103.57 102.15 0 103.47 102.07 0 102.85 102.8 0 102.54 103.39 0 102.39 102.71 0 102.16 102.65 0 101.51 101.12 0 100.83 100.29 0 100.55 99.79 0 100.88 100.11 0 101 99.76 0 100.51 99.96 0 100.44 99.98 0 100.32 100.49 0 99.98 100.75 0 100.03 100.84 0 99.64 100.44 0 99.11 99.57 0 98.97 99.22 0 98.6 99.08 0 98.31 98.04 0 98.37 98.73 0 98.19 98.72 0 98.51 100.07 0 98.23 99.02 0 97.96 98.94 0 97.77 99 0 97.49 98.54 0 97.76 98.42 0 98.01 97.9 0 97.73 97.46 0 97.06 97 0 96.63 95.97 0 96.58 96.55 0 96.66 96.51 0 96.77 96.76 0 96.5 96.05 0 96.53 96.47 0 96.22 96.38 0 96.49 97.27 0 96.34 96.67 0 96.31 96.59 0 96.06 96.06 0 95.9 96.92 0 95.33 94.96 0 95.53 95.59 0 95.42 95.68 0 95.57 95.35 0 95.3 95.41 0 95.31 95.32 0 95.38 95.8 0 95.22 95.46 0 94.62 94.16 0 93.81 92.49 0 93.6 91.58 0 93.2 91.5 0 93.29 90.83 0 93.54 91.28 0 93.23 90.57 0 93.46 90.93 0 92.82 90.9 0 92.85 91.49 0 92.67 91.38 0 92.32 90.91 0 92.06 90.72 0 91.88 89.53 0 91.53 89.47 0 91.19 89.28 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

Y[t] = -7.25303327622183 + 1.06594187359589X[t] + 0.89571223355923D[t] + 0.240549460095881M1[t] + 0.156251424685183M2[t] + 0.398463373048969M3[t] + 0.801831080443743M4[t] + 0.97051313109336M5[t] + 0.735706941760564M6[t] + 0.247728631943272M7[t] + 0.129941719407226M8[t] + 0.406195271893356M9[t] -0.131051760722312M10[t] + 0.274065231376367M11[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)	-7.25303327622183	2.655996	-2.7308	0.007789	0.003894
X	1.06594187359589	0.026557	40.1373	0	0
D	0.89571223355923	0.458065	1.9554	0.054069	0.027034
M1	0.240549460095881	0.526977	0.4565	0.649304	0.324652
M2	0.156251424685183	0.526982	0.2965	0.767624	0.383812
M3	0.398463373048969	0.526991	0.7561	0.451832	0.225916
M4	0.801831080443743	0.527116	1.5212	0.13221	0.066105
M5	0.97051313109336	0.527179	1.841	0.069382	0.034691
M6	0.735706941760564	0.527347	1.3951	0.166892	0.083446
M7	0.247728631943272	0.527728	0.4694	0.640059	0.320029
M8	0.129941719407226	0.524554	0.2477	0.804995	0.402497
M9	0.406195271893356	0.524893	0.7739	0.441321	0.220661
M10	-0.131051760722312	0.541683	-0.2419	0.809458	0.404729
M11	0.274065231376367	0.541688	0.5059	0.614303	0.307151

Multiple Linear Regression - Regression Statistics
Multiple R	0.982169333137103
R-squared	0.964656598954982
Adjusted R-squared	0.958840596251372
F-TEST (value)	165.862474299768
F-TEST (DF numerator)	13
F-TEST (DF denominator)	79
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	1.01339534505927
Sum Squared Residuals	81.1306399056367

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	107.89	107.448675630340	0.441324369660214
2	107.26	107.257783407569	0.00221659243087586
3	107.76	107.638567799500	0.121432200499641
4	107.32	107.562261663777	-0.242261663777006
5	107.15	107.741603133163	-0.59160313316256
6	108.04	107.645369387397	0.394630612602762
7	106.52	106.645738978254	-0.125738978253926
8	106.62	105.621580413423	0.998419586577325
9	106.47	105.290247097959	1.17975290204084
10	105.46	104.699702971664	0.760297028336293
11	106.13	104.955588101459	1.17441189854104
12	105.15	104.404377982948	0.745622017052356
13	105.39	104.868775236499	0.521224763501339
14	104.57	105.104259763167	-0.534259763166749
15	104.29	105.207899267963	-0.917899267963046
16	104.09	105.227527900863	-1.13752790086330
17	104.51	105.417528788985	-0.907528788984849
18	103.39	104.767005268950	-1.37700526894966
19	102.71	103.735396603598	-1.02539660359846
20	102.62	103.660247366006	-1.04024736600625
21	101.94	103.456827075374	-1.51682707537423
22	101.65	102.887601786551	-1.23760178655068
23	101.86	103.314037616121	-1.45403761612128
24	101.27	103.071950640953	-1.80195064095279
25	101.21	103.515029057032	-2.30502905703189
26	102.15	103.302817996790	-1.15281799678967
27	102.07	103.438435757794	-1.36843575779389
28	102.8	103.180919503559	-0.380919503559199
29	103.39	103.019159573394	0.370840426605899
30	102.71	102.624462103022	0.085537896978079
31	102.65	101.891317162278	0.758682837722442
32	101.12	101.080668031904	0.0393319680958057
33	100.29	100.632081110345	-0.34208111034511
34	99.79	99.7963703531226	-0.00637035312259156
35	100.11	100.553248163508	-0.443248163507919
36	99.76	100.407095956963	-0.647095956963058
37	99.96	100.125333898997	-0.16533389899697
38	99.98	99.9664199324345	0.0135800675654582
39	100.49	100.080718855967	0.409281144033175
40	100.75	100.121666326339	0.628333673660997
41	100.84	100.343645470668	0.496354529331591
42	100.44	99.6931219506332	0.74687804936678
43	99.57	98.64019444781	0.92980555218989
44	99.22	98.3731756729706	0.846824327029367
45	99.08	98.2550307322263	0.82496926777372
46	98.04	97.4086605562678	0.631339443732197
47	98.73	97.8777340607822	0.85226593921776
48	98.72	97.4117992921586	1.30820070784139
49	100.07	97.9934501518052	2.07654984819481
50	99.02	97.6106883917876	1.40931160821236
51	98.94	97.5650960342805	1.37490396571948
52	99	97.765934785692	1.23406521430792
53	98.54	97.6361531117348	0.90384688826516
54	98.42	97.689151228273	0.730848771727053
55	97.9	97.4676583868546	0.432341613145376
56	97.46	97.0514077497117	0.40859225028826
57	97	96.6134802468886	0.386519753111384
58	95.97	95.6178782086267	0.352121791373291
59	96.55	95.9696981070456	0.580301892954402
60	96.51	95.780908225557	0.729091774443107
61	96.76	96.1387112917483	0.62128870825168
62	96.05	95.7666089504667	0.283391049533255
63	96.47	96.0407991550384	0.429200844961594
64	96.38	96.1137248816185	0.266275118381544
65	97.27	96.570211238139	0.69978876186104
66	96.67	96.1755137677668	0.494486232233218
67	96.59	95.6555572017416	0.93444279825839
68	96.06	95.2712848208066	0.788715179193406
69	96.92	95.3769876735174	1.54301232648261
70	94.96	94.232153772952	0.72784622704794
71	95.59	94.850459139770	0.73954086023009
72	95.68	94.459140302298	1.22085969770201
73	95.35	94.8595810434333	0.49041895656674
74	95.41	94.4874787021517	0.922521297848325
75	95.32	94.7403500692514	0.579649930748572
76	95.8	95.2183337077979	0.581666292202097
77	95.46	95.2164650586722	0.243534941327815
78	94.16	94.3420937451819	-0.182093745181858
79	92.49	92.9907025177519	-0.500702517751894
80	91.58	92.6490678117607	-1.0690678117607
81	91.5	92.4989446148085	-0.99894461480848
82	90.83	92.0576323508164	-1.22763235081645
83	91.28	92.7292348113141	-1.44923481131410
84	90.57	92.124727599123	-1.55472759912301
85	90.93	92.6104436901459	-1.68044369014592
86	90.9	91.8439428556339	-0.943942855633854
87	91.49	92.1181330602055	-0.628133060205528
88	91.38	92.329631230353	-0.94963123035305
89	90.91	92.125233625244	-1.21523362524409
90	90.72	91.6132825487764	-0.893282548776376
91	89.53	90.9334347017118	-1.40343470171181
92	89.47	90.4425681334172	-0.972568133417214
93	89.28	90.3564014488807	-1.07640144888073

Charts produced by software:

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/19/t1195469816naum8tspmu7vf1l/76o1n1195470118.ps (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/19/t1195469816naum8tspmu7vf1l/80hhe1195470118.ps (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/19/t1195469816naum8tspmu7vf1l/9su0h1195470118.ps (open in new window)

Parameters:

par1 = 2 ; 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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