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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 computationFri, 24 Dec 2010 13:34:32 +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/24/t12931976958beqxp0mzu54dat.htm/, Retrieved Tue, 30 Apr 2024 07:26:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=114937, Retrieved Tue, 30 Apr 2024 07:26:27 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact104

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Recursive Partitioning (Regression Trees)] [] [2010-12-05 18:59:57] [b98453cac15ba1066b407e146608df68]
- RMPD    [Multiple Regression] [MR fout] [2010-12-24 13:34:32] [4cd8ab5c565aadc5ce193fb2faa1c53a] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
4	1	27	5	26	49	35
4	1	36	4	25	45	34
5	1	25	4	17	54	13
2	1	27	3	37	36	35
3	2	25	3	35	36	28
5	2	44	3	15	53	32
4	1	50	4	27	46	35
4	1	41	4	36	42	36
4	1	48	5	25	41	27
4	2	43	4	30	45	29
5	2	47	2	27	47	27
4	2	41	3	33	42	28
3	1	44	2	29	45	29
4	2	47	5	30	40	28
3	2	40	3	25	45	30
3	2	46	3	23	40	25
4	1	28	3	26	42	15
3	1	56	3	24	45	33
4	2	49	4	35	47	31
2	2	25	4	39	31	37
4	2	41	4	23	46	37
3	2	26	3	32	34	34
4	1	50	5	29	43	32
4	1	47	4	26	45	21
3	1	52	2	21	42	25
3	2	37	5	35	51	32
2	2	41	3	23	44	28
4	1	45	4	21	47	22
5	2	26	4	28	47	25
4	1	NA	3	30	41	26
2	1	52	4	21	44	34
5	1	46	2	29	51	34
4	1	58	3	28	46	36
3	1	54	5	19	47	36
4	1	29	3	26	46	26
2	2	50	3	33	38	26
3	1	43	2	34	50	34
3	2	30	3	33	48	33
3	2	47	2	40	36	31
5	1	45	3	24	51	33
NA	2	48	1	35	35	22
4	2	48	3	35	49	29
4	2	26	4	32	38	24
4	1	46	5	20	47	37
2	2	NA	3	35	36	32
4	2	50	3	35	47	23
3	1	25	4	21	46	29
4	1	47	2	33	43	35
1	2	47	2	40	53	20
2	1	41	3	22	55	28
2	2	45	2	35	39	26
4	2	41	4	20	55	36
3	2	45	5	28	41	26
4	2	40	3	46	33	33
3	1	29	4	18	52	25
3	2	34	5	22	42	29
5	1	45	5	20	56	32
3	2	52	3	25	46	35
2	2	41	4	31	33	24
1	2	48	3	21	51	31
2	2	45	3	23	46	29
5	1	54	2	26	46	27
4	2	25	3	34	50	29
4	2	26	4	31	46	29
3	1	28	4	23	51	27
4	2	50	4	31	48	34
4	2	48	4	26	44	32
2	2	51	3	36	38	31
3	2	53	3	28	42	31
4	1	37	3	34	39	31
3	1	56	2	25	45	16
2	1	43	3	33	31	25
4	1	34	3	46	29	27
4	1	42	3	24	48	32
3	2	32	3	32	38	28
5	2	31	5	33	55	25
1	1	46	3	42	32	25
3	2	30	5	17	51	36
3	2	47	4	36	53	36
5	2	33	4	40	47	36
2	1	25	4	30	45	27
3	1	25	5	19	33	29
3	2	21	4	33	49	32
4	2	36	5	35	46	29
2	2	50	3	23	42	31
4	2	48	3	15	56	34
3	2	48	2	38	35	27
3	1	25	3	37	40	28
3	1	48	4	23	44	32
2	2	49	5	41	46	33
3	1	27	5	34	46	29
2	1	28	3	38	39	32
4	2	43	2	45	35	35
4	2	48	3	27	48	33
2	2	48	4	46	42	27
1	1	25	1	26	39	16
5	2	49	4	44	39	32
4	1	26	3	36	41	26
4	1	51	3	20	52	32
4	2	25	4	44	45	38
3	1	29	3	27	42	24
3	1	29	4	27	44	26
1	1	43	2	41	33	19
5	2	46	3	30	42	37
3	1	44	3	33	46	25
3	1	25	3	37	45	24
2	1	51	2	30	40	23
4	1	42	5	20	48	28
4	2	53	5	44	32	38
3	1	25	4	20	53	28
4	2	49	2	33	39	28
4	1	51	3	31	45	26
2	2	20	3	23	36	21
3	2	44	3	33	38	35
3	2	38	4	33	49	31
3	1	46	5	32	46	34
4	2	42	4	25	43	30
5	1	29	NA	22	37	30
3	2	46	4	16	48	24
3	2	49	2	36	45	27
2	2	51	3	35	32	26
3	1	38	3	25	46	30
1	1	41	1	27	20	15
4	2	47	3	32	42	28
4	2	44	3	36	45	34
4	2	47	3	51	29	29
3	2	46	3	30	51	26
5	1	44	4	20	55	31
2	2	28	3	29	50	28
2	2	47	4	26	44	33
3	2	28	4	20	41	32
3	1	41	5	40	40	33
2	2	45	4	29	47	31
1	2	46	4	32	42	37
3	1	46	4	33	40	27
5	2	22	3	32	51	19
4	2	33	3	34	43	27
4	1	41	4	24	45	31
4	2	47	5	25	41	38
3	1	25	3	41	41	22
5	2	42	3	39	37	35
3	2	47	3	21	46	35
3	2	50	3	38	38	30
3	1	55	5	28	39	41
3	1	21	3	37	45	25
4	1	NA	3	26	46	28
2	1	52	3	30	39	45
2	2	49	4	25	21	21
4	2	46	4	38	31	33
3	1	NA	4	31	35	25
3	2	45	3	31	49	29
2	2	52	3	27	40	31
3	1	NA	3	21	45	29
3	2	40	4	26	46	31
4	2	49	4	37	45	31
1	1	38	5	28	34	25
1	1	32	5	29	41	27
5	2	46	4	33	43	26
4	2	32	3	41	45	26
3	2	41	3	19	48	23
3	2	43	3	37	43	27
4	1	44	4	36	45	24
3	1	47	5	27	45	35
2	2	28	3	33	34	24
1	1	52	1	29	40	32
1	1	27	2	42	40	24
5	2	45	5	27	55	24
4	1	27	4	47	44	38
3	1	25	4	17	44	36
4	1	28	4	34	48	24
5	1	25	3	32	51	18
4	1	52	4	25	49	34
4	1	44	3	27	33	23
2	2	43	3	37	43	35
3	2	47	4	34	44	22
4	2	52	4	27	44	34
3	2	40	2	37	41	28
4	1	42	3	32	45	34
3	1	45	5	26	44	32
4	1	45	2	29	44	24
1	1	50	5	28	40	34
2	1	49	3	19	48	33
3	1	52	2	46	49	33
3	2	48	3	31	46	29
5	2	51	3	42	49	38
4	2	49	4	33	55	24
3	2	31	4	39	51	25
3	2	43	3	27	46	37
3	2	31	3	35	37	33
3	2	28	4	23	43	30
4	2	43	4	32	41	22
3	2	31	3	22	45	28
2	2	51	3	17	39	24
4	2	58	4	35	38	33
2	2	25	5	34	41	37

Tables (Output of Computation)





\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
In addition: Warning messages:
1: In pf(q, df1, df2, lower.tail, log.p) : NaNs produced
2: In pf(q, df1, df2, lower.tail, log.p) : NaNs produced
3: In pf(q, df1, df2, lower.tail, log.p) : NaNs produced
4: In pf(q, df1, df2, lower.tail, log.p) : NaNs produced
Execution halted

 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114937&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
In addition: Warning messages:
1: In pf(q, df1, df2, lower.tail, log.p) : NaNs produced
2: In pf(q, df1, df2, lower.tail, log.p) : NaNs produced
3: In pf(q, df1, df2, lower.tail, log.p) : NaNs produced
4: In pf(q, df1, df2, lower.tail, log.p) : NaNs produced
Execution halted

[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114937&T=0


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')
}