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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: Thu, 15 Nov 2007 04:15:52 -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/15/t1195125097wxv5tq3eiddn2t1.htm/, Retrieved Thu, 15 Nov 2007 12:11:48 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

128 0 123 0 118 0 112 0 105 0 102 0 131 0 149 0 145 0 132 0 122 0 119 0 116 0 111 0 104 0 100 0 93 0 91 0 119 0 139 0 134 0 124 0 113 0 109 0 109 0 106 0 101 0 98 0 93 0 91 0 122 0 139 0 140 1 132 1 117 1 114 1 113 1 110 1 107 1 103 1 98 1 98 1 137 1 148 1 147 1 139 1 130 1 128 1 127 1 123 1 118 1 114 1 108 1 111 1 151 1 159 1 158 1 148 1 138 1 137 1 136 1 133 1 126 1 120 1 114 1 116 1 153 1 162 1 161 1 149 0 139 0 135 0 130 0 127 0 122 0 117 0 112 0 113 0 149 0 157 0 157 0 147 0 137 0 132 0 125 0 123 0 117 0 114 0 111 0 112 0 144 0 150 0 149 0 134 0 123 0 116 0 117 0 111 0 105 0 102 0 95 0 93 0 124 0 130 0 124 0 115 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] = + 116.117805975632 + 7.3629767954448x[t] -0.658850251479013M1[t] -4.52683317233233M2[t] -10.0614827598522M3[t] -14.3739101251499M4[t] -20.1307819348921M5[t] -20.4432093001898M6[t] + 13.1332522234014M7[t] + 24.4874915247703M8[t] + 21.5791778488676M9[t] + 11.7515256830638M10[t] + 3.71520514307549M11[t] + 0.0902051430754819t + 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)	116.117805975632	3.742523	31.0266	0	0
x	7.3629767954448	1.901293	3.8726	0.000201	0.000101
M1	-0.658850251479013	4.517819	-0.1458	0.884372	0.442186
M2	-4.52683317233233	4.51691	-1.0022	0.318877	0.159439
M3	-10.0614827598522	4.516196	-2.2279	0.028327	0.014164
M4	-14.3739101251499	4.515676	-3.1831	0.001988	0.000994
M5	-20.1307819348921	4.515352	-4.4583	2.3e-05	1.2e-05
M6	-20.4432093001898	4.515222	-4.5276	1.8e-05	9e-06
M7	13.1332522234014	4.515287	2.9086	0.004551	0.002275
M8	24.4874915247703	4.515546	5.4229	0	0
M9	21.5791778488676	4.517496	4.7768	7e-06	3e-06
M10	11.7515256830638	4.51665	2.6018	0.010807	0.005403
M11	3.71520514307549	4.645504	0.7997	0.42592	0.21296
t	0.0902051430754819	0.029662	3.0411	0.00307	0.001535

Multiple Linear Regression - Regression Statistics
Multiple R	0.873672379650808
R-squared	0.763303426964705
Adjusted R-squared	0.729857172079283
F-TEST (value)	22.8217906482976
F-TEST (DF numerator)	13
F-TEST (DF denominator)	92
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	9.29081927231896
Sum Squared Residuals	7941.37769308219

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	128	115.549160867228	12.4508391327719
2	123	111.771383089451	11.2286169105492
3	118	106.326938645006	11.6730613549937
4	112	102.104716422784	9.89528357721588
5	105	96.4380497561176	8.56195024388245
6	102	96.2158275338953	5.78417246610473
7	131	129.882494200562	1.11750579943800
8	149	141.326938645006	7.67306135499358
9	145	138.508830112179	6.4911698878208
10	132	128.771383089451	3.22861691054921
11	122	120.825267692538	1.17473230746208
12	119	117.200267692538	1.79973230746203
13	116	116.631622584134	-0.63162258413444
14	111	112.853844806357	-1.85384480635658
15	104	107.409400361912	-3.40940036191217
16	100	103.18717813969	-3.18717813968995
17	93	97.5205114730233	-4.52051147302327
18	91	97.298289250801	-6.29828925080105
19	119	130.964955917468	-11.9649559174677
20	139	142.409400361912	-3.40940036191216
21	134	139.591291829085	-5.59129182908495
22	124	129.853844806357	-5.85384480635661
23	113	121.907729409444	-8.90772940944374
24	109	118.282729409444	-9.28272940944374
25	109	117.714084301040	-8.71408430104023
26	106	113.936306523262	-7.9363065232624
27	101	108.491862078818	-7.49186207881795
28	98	104.269639856596	-6.26963985659573
29	93	98.602973189929	-5.60297318992905
30	91	98.3807509677068	-7.38075096770683
31	122	132.047417634373	-10.0474176343735
32	139	143.491862078818	-4.49186207881794
33	140	148.036730341436	-8.03673034143554
34	132	138.299283318707	-6.29928331870719
35	117	130.353167921794	-13.3531679217943
36	114	126.728167921794	-12.7281679217943
37	113	126.159522813391	-13.1595228133908
38	110	122.381745035613	-12.3817450356130
39	107	116.937300591169	-9.93730059116854
40	103	112.715078368946	-9.7150783689463
41	98	107.048411702280	-9.04841170227963
42	98	106.826189480057	-8.82618948005742
43	137	140.492856146724	-3.49285614672407
44	148	151.937300591169	-3.93730059116852
45	147	149.119192058341	-2.11919205834133
46	139	139.381745035613	-0.381745035612973
47	130	131.4356296387	-1.43562963870012
48	128	127.8106296387	0.189370361299889
49	127	127.241984530297	-0.241984530296595
50	123	123.464206752519	-0.464206752518757
51	118	118.019762308074	-0.0197623080743188
52	114	113.797540085852	0.202459914147909
53	108	108.130873419185	-0.130873419185412
54	111	107.908651196963	3.0913488030368
55	151	141.57531786363	9.42468213637015
56	159	153.019762308074	5.9802376919257
57	158	150.201653775247	7.79834622475289
58	148	140.464206752519	7.53579324748124
59	138	132.518091355606	5.4819086443941
60	137	128.893091355606	8.1069086443941
61	136	128.324446247202	7.67555375279762
62	133	124.546668469425	8.45333153057546
63	126	119.10222402498	6.8977759750199
64	120	114.880001802758	5.11999819724213
65	114	109.213335136091	4.7866648639088
66	116	108.991112913869	7.00888708613102
67	153	142.657779580536	10.3422204194644
68	162	154.10222402498	7.89777597501991
69	161	151.284115492153	9.7158845078471
70	149	134.183691673980	14.8163083260203
71	139	126.237576277067	12.7624237229331
72	135	122.612576277067	12.3874237229331
73	130	122.043931168663	7.95606883133664
74	127	118.266153390886	8.73384660911448
75	122	112.821708946441	9.17829105355892
76	117	108.599486724219	8.40051327578114
77	112	102.932820057552	9.06717994244783
78	113	102.71059783533	10.2894021646700
79	149	136.377264501997	12.6227354980034
80	157	147.821708946441	9.17829105355893
81	157	145.003600413614	11.9963995863861
82	147	135.266153390886	11.7338466091145
83	137	127.320037993973	9.67996200602733
84	132	123.695037993973	8.30496200602734
85	125	123.126392885569	1.87360711443086
86	123	119.348615107791	3.65138489220869
87	117	113.904170663347	3.09582933665313
88	114	109.681948441125	4.31805155887535
89	111	104.015281774458	6.98471822554204
90	112	103.793059552236	8.20694044776425
91	144	137.459726218902	6.54027378109759
92	150	148.904170663347	1.09582933665314
93	149	146.086062130520	2.91393786948034
94	134	136.348615107791	-2.34861510779131
95	123	128.402499710878	-5.40249971087845
96	116	124.777499710878	-8.77749971087844
97	117	124.208854602475	-7.20885460247493
98	111	120.431076824697	-9.43107682469709
99	105	114.986632380253	-9.98663238025265
100	102	110.764410158030	-8.76441015803043
101	95	105.097743491364	-10.0977434913637
102	93	104.875521269142	-11.8755212691415
103	124	138.542187935808	-14.5421879358082
104	130	149.986632380253	-19.9866323802526
105	124	147.168523847425	-23.1685238474254
106	115	137.431076824697	-22.4310768246971

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/15/t1195125097wxv5tq3eiddn2t1/14xyy1195125347.png (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/15/t1195125097wxv5tq3eiddn2t1/28z051195125347.ps (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/15/t1195125097wxv5tq3eiddn2t1/31v821195125347.ps (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/15/t1195125097wxv5tq3eiddn2t1/4y96g1195125347.ps (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/15/t1195125097wxv5tq3eiddn2t1/6fvid1195125347.ps (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/15/t1195125097wxv5tq3eiddn2t1/7euh91195125348.ps (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/15/t1195125097wxv5tq3eiddn2t1/8smtk1195125348.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/15/t1195125097wxv5tq3eiddn2t1/9zbkf1195125348.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/15/t1195125097wxv5tq3eiddn2t1/9zbkf1195125348.ps (open in new window)

Parameters:

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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