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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 computationWed, 01 Dec 2010 10:16:50 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/01/t1291198490bfzld2pr9ukln7c.htm/, Retrieved Sun, 05 May 2024 03:10:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=103908, Retrieved Sun, 05 May 2024 03:10:08 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact167

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]
-   PD    [Multiple Regression] [minitutorial work...] [2010-12-01 10:16:50] [0dfe009a651fec1e160584d659799586] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3	13	14	13	3	25	55	147
3	12	8	13	5	158	7	71
4	15	12	16	6	NA	NA	NA
3	12	7	12	6	143	10	NA
2	10	10	11	5	67	74	43
3	12	7	12	3	NA	NA	NA
4	15	16	18	8	148	138	8
2	9	11	11	4	28	NA	NA
3	12	14	14	4	114	113	34
4	11	6	9	4	NA	NA	NA
3	11	16	14	6	123	115	103
3	11	11	12	6	145	9	NA
4	15	16	11	5	113	114	73
2	7	12	12	4	152	59	159
2	11	7	13	6	NA	NA	NA
3	11	13	11	4	36	114	113
2	10	11	12	6	NA	NA	NA
4	14	15	16	6	8	102	44
2	10	7	9	4	108	NA	NA
1	6	9	11	4	112	86	NA
3	11	7	13	2	51	17	41
4	15	14	15	7	43	45	74
2	11	15	10	5	120	123	NA
3	12	7	11	4	13	24	NA
3	14	15	13	6	55	5	NA
4	15	17	16	6	103	123	32
3	9	15	15	7	127	136	126
3	13	14	14	5	14	4	154
4	13	14	14	6	135	76	129
4	16	8	14	4	38	99	98
4	13	8	8	4	11	98	82
3	12	14	13	7	43	67	45
4	14	14	15	7	141	92	8
3	11	8	13	4	62	13	NA
2	9	11	11	4	62	24	129
4	16	16	15	6	135	129	31
3	12	10	15	6	117	117	117
2	10	8	9	5	82	11	99
4	13	14	13	6	145	20	55
4	16	16	16	7	87	91	132
4	14	13	13	6	76	111	58
4	15	5	11	3	124	NA	NA
2	5	8	12	3	151	58	NA
2	8	10	12	4	131	NA	NA
3	11	8	12	6	127	146	101
4	16	13	14	7	76	129	31
5	17	15	14	5	25	48	147
2	9	6	8	4	NA	NA	NA
3	9	12	13	5	58	111	132
3	13	16	16	6	115	32	123
2	10	5	13	6	130	112	39
2	6	15	11	6	17	51	136
3	12	12	14	5	102	53	141
2	8	8	13	4	21	131	NA
4	14	13	13	5	NA	NA	NA
3	12	14	13	5	14	76	135
3	11	12	12	4	110	106	118
4	16	16	16	6	133	26	154
1	8	10	15	2	83	44	NA
4	15	15	15	8	56	63	116
2	7	8	12	3	NA	NA	NA
4	16	16	14	6	44	116	88
4	14	19	12	6	70	119	25
4	16	14	15	6	36	18	113
2	9	6	12	5	5	134	157
4	14	13	13	5	118	138	26
2	11	15	12	6	17	41	38
4	13	7	12	5	79	NA	NA
4	15	13	13	6	122	57	53
1	5	4	5	2	119	101	NA
4	15	14	13	5	36	114	106
4	13	13	13	5	36	113	106
3	11	11	14	5	141	122	102
3	11	14	17	6	NA	14	138
3	12	12	13	6	37	10	142
3	12	15	13	6	110	27	73
3	12	14	12	5	10	39	130
3	12	13	13	5	14	133	86
4	14	8	14	4	157	42	78
1	6	6	11	2	59	NA	NA
3	7	7	12	4	77	58	NA
4	14	13	12	6	129	133	4
3	14	13	16	6	125	151	91
3	10	11	12	5	87	111	132
4	13	5	12	3	61	139	NA
3	12	12	12	6	146	126	NA
2	9	8	10	4	96	139	NA
3	12	11	15	5	133	138	14
4	16	14	15	8	47	52	97
3	10	9	12	4	74	67	45
4	14	10	16	6	109	97	NA
3	10	13	15	6	30	137	149
4	16	16	16	7	116	56	57
4	15	16	13	6	149	3	105
3	12	11	12	5	19	78	NA
2	10	8	11	4	96	NA	NA
1	8	4	13	6	NA	NA	NA
2	8	7	10	3	21	NA	NA
2	11	14	15	5	26	118	128
3	13	11	13	6	156	39	29
4	16	17	16	7	53	63	148
4	16	15	15	7	72	78	93
3	14	17	18	6	27	26	4
3	11	5	13	3	66	50	NA
1	4	4	10	2	71	104	158
3	14	10	16	8	66	54	144
3	9	11	13	3	40	104	NA
4	14	15	15	8	57	148	122
2	8	10	14	3	3	30	149
2	8	9	15	4	12	38	17
3	11	12	14	5	107	132	91
3	12	15	13	7	80	132	111
3	11	7	13	6	98	84	99
4	14	13	15	6	155	71	40
4	15	12	16	7	111	125	132
4	16	14	14	6	81	25	123
4	16	14	14	6	50	66	54
2	11	8	16	6	49	86	90
3	14	15	14	6	96	61	86
4	14	12	12	4	2	60	152
3	12	12	13	4	1	144	152
4	14	16	12	5	22	120	123
2	8	9	12	4	64	139	100
4	13	15	14	6	56	131	116
4	16	15	14	6	144	159	59
3	12	6	14	5	NA	NA	NA
4	16	14	16	8	94	18	5
3	12	15	13	6	25	123	147
3	11	10	14	5	93	18	139
1	4	6	4	4	NA	NA	NA
4	16	14	16	8	48	123	81
4	15	12	13	6	30	105	3
2	10	8	16	4	19	NA	NA
3	13	11	15	6	NA	NA	NA
4	15	13	14	6	10	68	37
3	12	9	13	4	78	157	5
4	14	15	14	6	93	94	69
2	7	13	12	3	NA	NA	NA
5	19	15	15	6	95	87	NA
3	12	14	14	5	50	156	142
4	12	16	13	4	86	139	17
3	13	14	14	6	33	145	100
4	15	14	16	4	152	55	70
2	8	10	6	4	51	41	NA
3	12	10	13	4	48	25	123
3	10	4	13	6	97	47	109
2	8	8	14	5	77	NA	NA
	10	15	15	6	130	143	37
4	15	16	14	6	8	102	44
4	16	12	15	8	84	148	98
3	13	12	13	7	51	153	11
4	16	15	16	7	33	32	9
2	9	9	12	4	6	106	NA
4	14	12	15	6	116	63	57
4	14	14	12	6	88	56	63
3	12	11	14	2	142	39	66

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24
R Engine error message
Error in if (gqarr[mypoint - kp3 + 1, 2] < 0.01) numsignificant1 <- numsignificant1 +  : 
  missing value where TRUE/FALSE needed
Execution halted


\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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
R Engine error message & 
Error in if (gqarr[mypoint - kp3 + 1, 2] < 0.01) numsignificant1 <- numsignificant1 +  : 
  missing value where TRUE/FALSE needed
Execution halted

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=103908&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[ROW][C]R Engine error message[/C][C]
Error in if (gqarr[mypoint - kp3 + 1, 2] < 0.01) numsignificant1 <- numsignificant1 +  : 
  missing value where TRUE/FALSE needed
Execution halted

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=103908&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=103908&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24
R Engine error message
Error in if (gqarr[mypoint - kp3 + 1, 2] < 0.01) numsignificant1 <- numsignificant1 +  : 
  missing value where TRUE/FALSE needed
Execution halted


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
Parameters (R input):
par1 = 1 ; 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')
}