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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 15:57:19 -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/t11955126157k5xwjvmkapa2yd.htm/, Retrieved Mon, 19 Nov 2007 23:50:15 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

99.5 0 101.6 0 103.9 0 106.6 0 108.3 0 102 0 93.8 0 91.6 0 97.7 0 94.8 0 98 0 103.8 0 97.8 0 91.2 0 89.3 0 87.5 0 90.4 0 94.2 0 102.2 0 101.3 0 96 0 90.8 0 93.2 0 90.9 0 91.1 0 90.2 0 94.3 0 96 0 99 0 103.3 0 113.1 0 112.8 0 112.1 0 107.4 0 111 0 110.5 0 110.8 0 112.4 0 111.5 0 116.2 0 122.5 0 121.3 0 113.9 0 110.7 0 120.8 0 141.1 1 147.4 1 148 1 158.1 1 165 1 187 1 190.3 1 182.4 1 168.8 1 151.2 1 120.1 1 112.5 1 106.2 1 107.1 1 108.5 1 106.5 1 108.3 1 125.6 1 124 1 127.2 1 136.9 1 135.8 1 124.3 1 115.4 1 113.6 1 114.4 1 118.4 1 117 1 116.5 1 115.4 1 113.6 1 117.4 1 116.9 1 116.4 1 111.1 1 110.2 1 118.9 1 131.8 1 130.6 1 138.3 1 148.4 1 148.7 1 144.3 1 152.5 1 162.9 1 167.2 1 166.5 1 185.6 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	5 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Multiple Linear Regression - Estimated Regression Equation

Y[t] = + 94.5481481481482 + 27.6650462962963x[t] + 1.61778273809523M1[t] + 3.31658399470900M2[t] + 8.46538525132275M3[t] + 8.7016865079365M4[t] + 11.2379877645503M5[t] + 11.9492890211640M6[t] + 10.2480902777778M7[t] + 3.23439153439153M8[t] + 4.60819279100529M9[t] -5.18688822751323M10[t] -1.00058697089947M11[t] + 0.113698743386243t + 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)	94.5481481481482	8.265588	11.4388	0	0
x	27.6650462962963	8.109128	3.4116	0.001021	0.00051
M1	1.61778273809523	9.948106	0.1626	0.871231	0.435616
M2	3.31658399470900	9.945423	0.3335	0.739657	0.369828
M3	8.46538525132275	9.945039	0.8512	0.397222	0.198611
M4	8.7016865079365	9.946956	0.8748	0.38433	0.192165
M5	11.2379877645503	9.951171	1.1293	0.262183	0.131092
M6	11.9492890211640	9.957682	1.2	0.233723	0.116861
M7	10.2480902777778	9.966484	1.0283	0.306968	0.153484
M8	3.23439153439153	9.977571	0.3242	0.746669	0.373334
M9	4.60819279100529	9.990936	0.4612	0.645896	0.322948
M10	-5.18688822751323	10.271291	-0.505	0.614972	0.307486
M11	-1.00058697089947	10.26795	-0.0974	0.922618	0.461309
t	0.113698743386243	0.151245	0.7518	0.454433	0.227217

Multiple Linear Regression - Regression Statistics
Multiple R	0.695525186305115
R-squared	0.483755284784765
Adjusted R-squared	0.398803622787321
F-TEST (value)	5.6944769932732
F-TEST (DF numerator)	13
F-TEST (DF denominator)	79
p-value	3.14955991953525e-07
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	19.2074917059669
Sum Squared Residuals	29145.2912731482

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	99.5	96.2796296296297	3.22037037037033
2	101.6	98.0921296296296	3.50787037037038
3	103.9	103.354629629630	0.54537037037038
4	106.6	103.704629629630	2.89537037037037
5	108.3	106.354629629630	1.94537037037038
6	102	107.179629629630	-5.17962962962963
7	93.8	105.592129629630	-11.7921296296296
8	91.6	98.6921296296296	-7.09212962962964
9	97.7	100.179629629630	-2.47962962962962
10	94.8	90.4982473544974	4.30175264550264
11	98	94.7982473544973	3.20175264550265
12	103.8	95.912533068783	7.88746693121693
13	97.8	97.6440145502645	0.155985449735449
14	91.2	99.4565145502646	-8.25651455026456
15	89.3	104.719014550265	-15.4190145502646
16	87.5	105.069014550265	-17.5690145502646
17	90.4	107.719014550265	-17.3190145502646
18	94.2	108.544014550265	-14.3440145502646
19	102.2	106.956514550265	-4.75651455026454
20	101.3	100.056514550265	1.24348544973545
21	96	101.544014550265	-5.54401455026455
22	90.8	91.8626322751323	-1.06263227513227
23	93.2	96.1626322751323	-2.96263227513228
24	90.9	97.276917989418	-6.37691798941798
25	91.1	99.0083994708995	-7.90839947089947
26	90.2	100.820899470899	-10.6208994708995
27	94.3	106.083399470899	-11.7833994708995
28	96	106.433399470899	-10.4333994708995
29	99	109.083399470899	-10.0833994708995
30	103.3	109.908399470899	-6.60839947089947
31	113.1	108.320899470899	4.77910052910053
32	112.8	101.420899470899	11.3791005291005
33	112.1	102.908399470899	9.19160052910053
34	107.4	93.2270171957672	14.1729828042328
35	111	97.5270171957672	13.4729828042328
36	110.5	98.6413029100529	11.8586970899471
37	110.8	100.372784391534	10.4272156084656
38	112.4	102.185284391534	10.2147156084656
39	111.5	107.447784391534	4.05221560846561
40	116.2	107.797784391534	8.40221560846561
41	122.5	110.447784391534	12.0522156084656
42	121.3	111.272784391534	10.0272156084656
43	113.9	109.685284391534	4.21471560846562
44	110.7	102.785284391534	7.91471560846562
45	120.8	104.272784391534	16.5272156084656
46	141.1	122.256448412698	18.8435515873016
47	147.4	126.556448412698	20.8435515873016
48	148	127.670734126984	20.3292658730159
49	158.1	129.402215608466	28.6977843915344
50	165	131.214715608466	33.7852843915344
51	187	136.477215608466	50.5227843915344
52	190.3	136.827215608466	53.4727843915344
53	182.4	139.477215608466	42.9227843915344
54	168.8	140.302215608466	28.4977843915344
55	151.2	138.714715608466	12.4852843915344
56	120.1	131.814715608466	-11.7147156084656
57	112.5	133.302215608466	-20.8022156084656
58	106.2	123.620833333333	-17.4208333333333
59	107.1	127.920833333333	-20.8208333333334
60	108.5	129.035119047619	-20.5351190476191
61	106.5	130.766600529101	-24.2666005291005
62	108.3	132.579100529101	-24.2791005291005
63	125.6	137.841600529101	-12.2416005291005
64	124	138.191600529101	-14.1916005291005
65	127.2	140.841600529101	-13.6416005291005
66	136.9	141.666600529101	-4.76660052910053
67	135.8	140.079100529101	-4.27910052910052
68	124.3	133.179100529101	-8.87910052910053
69	115.4	134.666600529101	-19.2666005291005
70	113.6	124.985218253968	-11.3852182539683
71	114.4	129.285218253968	-14.8852182539683
72	118.4	130.399503968254	-11.9995039682540
73	117	132.130985449735	-15.1309854497354
74	116.5	133.943485449735	-17.4434854497355
75	115.4	139.205985449735	-23.8059854497354
76	113.6	139.555985449735	-25.9559854497355
77	117.4	142.205985449735	-24.8059854497355
78	116.9	143.030985449735	-26.1309854497355
79	116.4	141.443485449735	-25.0434854497354
80	111.1	134.543485449735	-23.4434854497355
81	110.2	136.030985449735	-25.8309854497354
82	118.9	126.349603174603	-7.44960317460317
83	131.8	130.649603174603	1.15039682539683
84	130.6	131.763888888889	-1.16388888888890
85	138.3	133.495370370370	4.80462962962964
86	148.4	135.307870370370	13.0921296296296
87	148.7	140.570370370370	8.12962962962961
88	144.3	140.920370370370	3.37962962962964
89	152.5	143.570370370370	8.92962962962963
90	162.9	144.395370370370	18.5046296296296
91	167.2	142.807870370370	24.3921296296296
92	166.5	135.907870370370	30.5921296296296
93	185.6	137.395370370370	48.2046296296296

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/19/t11955126157k5xwjvmkapa2yd/1c9gq1195513030.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/19/t11955126157k5xwjvmkapa2yd/1c9gq1195513030.ps (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/19/t11955126157k5xwjvmkapa2yd/28mn61195513030.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/19/t11955126157k5xwjvmkapa2yd/3kcdr1195513030.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/19/t11955126157k5xwjvmkapa2yd/3kcdr1195513030.ps (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/19/t11955126157k5xwjvmkapa2yd/55ijy1195513030.ps (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/19/t11955126157k5xwjvmkapa2yd/617py1195513030.ps (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/19/t11955126157k5xwjvmkapa2yd/7qmt11195513030.ps (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/19/t11955126157k5xwjvmkapa2yd/88yk51195513030.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/19/t11955126157k5xwjvmkapa2yd/9i0dj1195513030.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/19/t11955126157k5xwjvmkapa2yd/9i0dj1195513030.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')

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Software written by Ed van Stee & Patrick Wessa

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