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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationMon, 19 Nov 2012 18:31:02 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Nov/19/t1353367884tbme05bm088rfjr.htm/, Retrieved Sun, 28 Apr 2024 14:30:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=190867, Retrieved Sun, 28 Apr 2024 14:30:09 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact83

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [Competence to learn] [2010-11-17 07:43:53] [b98453cac15ba1066b407e146608df68]
- R PD    [Multiple Regression] [WS7.3] [2012-11-19 23:31:02] [6144fd9dab7e8876ce9100c6a2ac91c2] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
100,00	100,00	100,00	100,00
102,82	101,54	100,25	102,00
104,30	102,18	102,84	103,65
104,96	105,49	104,73	104,97
104,83	106,14	103,39	104,64
105,88	106,37	101,75	104,90
107,54	107,25	100,37	105,70
107,95	109,48	101,34	106,49
108,09	111,95	102,31	107,15
109,19	111,97	101,79	107,70
110,12	110,66	100,29	107,71
110,44	113,15	100,58	108,31
111,05	113,85	97,96	108,12
112,32	115,14	100,11	109,62
113,61	116,92	102,87	111,34
112,72	116,64	102,72	110,72
113,13	116,23	103,92	111,22
112,82	115,94	105,75	111,45
112,57	116,42	106,75	111,61
112,70	113,37	108,45	111,72
113,70	112,71	107,72	112,06
113,84	115,61	108,94	112,84
114,15	115,63	109,76	113,24
114,07	116,70	108,50	113,02
114,80	119,37	109,21	114,00
114,54	120,26	113,10	114,94
114,12	118,74	112,18	114,25
113,81	116,52	114,86	114,44
115,23	116,97	114,53	115,29
115,95	118,06	115,33	116,07
117,54	118,71	117,97	117,81
118,21	119,22	117,86	118,26
119,90	119,20	116,58	118,97
121,35	120,73	117,65	120,33
122,56	121,83	120,71	122,00
124,14	122,60	121,37	123,24
126,57	123,80	120,47	124,67
128,07	127,69	122,20	126,54
128,10	128,34	124,94	127,34
128,75	128,72	125,28	127,87
129,99	130,54	130,19	130,12
133,24	132,86	131,60	132,77
134,69	134,53	133,09	134,27
135,06	135,17	133,17	134,60
135,62	133,46	131,86	134,38
136,09	135,62	132,50	135,12
136,11	137,41	131,55	135,14
136,18	138,87	131,42	135,34
136,88	135,80	131,11	135,28
139,10	139,41	131,19	137,14
141,55	142,19	136,45	140,35
144,65	146,03	138,43	143,26
147,40	145,70	136,32	144,38
148,78	148,47	137,45	145,88
149,12	152,22	137,07	146,50
150,93	157,06	139,49	148,86
152,20	160,78	142,05	150,78
155,76	164,58	141,32	153,29
159,86	171,27	145,02	157,64
164,49	177,85	148,29	162,18
172,29	185,54	147,73	167,86
181,10	193,70	151,23	175,25
186,03	203,37	150,28	179,32
191,14	213,69	154,79	184,98
196,02	220,82	153,03	188,48
200,34	225,01	157,66	192,86
202,32	229,10	161,04	195,48
204,15	233,98	165,60	198,40
205,29	234,53	171,25	200,60
206,44	238,75	172,25	202,12
210,64	238,26	177,16	205,88
212,83	241,42	174,95	207,09
214,23	242,44	179,41	209,20
216,57	248,81	181,63	212,25
217,50	254,99	188,87	215,47
219,15	255,46	189,87	216,69
220,49	261,13	192,11	219,02
220,48	258,58	189,67	217,92
220,27	257,98	191,01	217,98
222,52	257,76	186,40	218,19
221,91	257,98	189,58	218,54
222,29	252,60	190,24	217,89
219,93	251,69	190,27	216,35
222,14	255,73	196,61	219,83
224,73	257,65	197,80	221,96
228,91	263,02	205,87	227,18
231,61	265,37	206,23	229,25
235,94	271,41	208,47	233,33
239,01	278,48	211,10	236,99
242,29	284,42	211,50	240,03
248,08	287,69	218,06	245,43
248,96	287,97	221,08	246,64
252,36	290,44	226,74	250,33
254,12	292,30	223,18	250,85
255,02	296,64	220,00	251,44
253,49	299,88	223,85	252,09
255,98	292,59	227,23	252,95
255,88	292,52	226,76	252,77
254,15	290,06	223,93	250,68
252,41	296,83	220,68	250,11
252,50	296,74	227,65	251,79
253,73	296,48	218,40	250,21
252,30	295,56	213,64	248,07
248,84	288,04	212,71	244,47
247,56	287,38	217,36	244,73
245,33	290,10	217,79	244,03
242,35	296,68	218,19	243,59
238,17	285,71	206,92	236,45
226,72	270,09	197,83	224,91
225,84	261,01	194,44	221,93
225,75	266,44	202,51	224,90
226,19	267,08	196,65	223,80
220,04	263,67	191,45	218,53
220,41	259,12	190,06	217,52
223,55	262,71	190,32	219,97
223,37	265,84	203,70	223,84
224,68	265,77	200,52	223,76
223,63	269,16	200,52	223,66
220,86	256,57	191,58	217,68
220,13	257,92	195,73	218,48
215,47	253,32	194,77	214,82
214,69	257,50	194,58	215,14
216,20	264,86	198,56	218,38
219,85	257,80	201,68	219,96
220,18	251,32	201,51	218,93
220,28	243,53	204,45	218,36
216,68	247,50	206,55	217,72
217,81	256,90	205,64	219,93
217,66	261,81	205,68	220,84
217,95	260,76	204,58	220,58
215,90	244,36	204,48	216,35
217,14	255,12	208,73	220,22
219,46	256,46	210,26	222,18
222,90	258,25	214,21	225,46
225,48	256,33	214,17	226,42
228,10	259,19	213,66	228,29
230,73	260,78	219,03	231,35
230,54	261,17	217,60	231,02
229,74	265,35	220,64	232,24
233,15	261,63	222,01	233,69
235,22	266,93	224,95	236,67
237,46	268,70	225,57	238,44
239,95	274,37	219,32	239,49
240,44	275,67	213,56	238,74
241,59	270,83	214,03	238,50
241,51	275,14	225,59	242,12
243,05	277,59	227,64	243,92
246,47	276,36	229,00	245,81
248,64	279,39	226,84	247,14
251,15	274,79	221,49	246,38

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=190867&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=190867&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=190867&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 4 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
Parameters (R input):
par1 = 4 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
R code (references can be found in the software module):
library(lattice)
library(lmtest)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
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))
if (n > n25) {
kp3 <- k + 3
nmkm3 <- n - k - 3
gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))
numgqtests <- 0
numsignificant1 <- 0
numsignificant5 <- 0
numsignificant10 <- 0
for (mypoint in kp3:nmkm3) {
j <- 0
numgqtests <- numgqtests + 1
for (myalt in c('greater', 'two.sided', 'less')) {
j <- j + 1
gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value
}
if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
}
gqarr
}
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$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')
qqline(mysum$resid)
grid()
dev.off()
(myerror <- as.ts(mysum$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()
if (n > n25) {
bitmap(file='test9.png')
plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
grid()
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$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT
H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$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$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable4.tab')
if (n > n25) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-values',header=TRUE)
a<-table.element(a,'Alternative Hypothesis',3,header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'breakpoint index',header=TRUE)
a<-table.element(a,'greater',header=TRUE)
a<-table.element(a,'2-sided',header=TRUE)
a<-table.element(a,'less',header=TRUE)
a<-table.row.end(a)
for (mypoint in kp3:nmkm3) {
a<-table.row.start(a)
a<-table.element(a,mypoint,header=TRUE)
a<-table.element(a,gqarr[mypoint-kp3+1,1])
a<-table.element(a,gqarr[mypoint-kp3+1,2])
a<-table.element(a,gqarr[mypoint-kp3+1,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable5.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Description',header=TRUE)
a<-table.element(a,'# significant tests',header=TRUE)
a<-table.element(a,'% significant tests',header=TRUE)
a<-table.element(a,'OK/NOK',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'1% type I error level',header=TRUE)
a<-table.element(a,numsignificant1)
a<-table.element(a,numsignificant1/numgqtests)
if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'5% type I error level',header=TRUE)
a<-table.element(a,numsignificant5)
a<-table.element(a,numsignificant5/numgqtests)
if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'10% type I error level',header=TRUE)
a<-table.element(a,numsignificant10)
a<-table.element(a,numsignificant10/numgqtests)
if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable6.tab')
}