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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Tue, 14 Dec 2010 11:20:15 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/14/t1292325517j4m1qycqavro2ck.htm/, Retrieved Thu, 02 May 2024 14:00:39 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=109415, Retrieved Thu, 02 May 2024 14:00:39 +0000

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Estimated Impact

130

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-       [Multiple Regression] [regression model 1] [2010-12-14 11:20:15] [0605ea080d54454c99180f574351b8e4] [Current]

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6654000,00	5712000,00	NA	NA	38,60	645,00	3,00	5,00	3,00	3,30
1000,00	6600,00	6,30	2,00	4,50	42,00	3,00	1,00	3,00	8,30
3385,00	44500,00	NA	NA	14,00	60,00	1,00	1,00	1,00	12,50
0,92	5700,00	NA	NA	NA	25,00	5,00	2,00	3,00	16,50
2547000,00	4603000,00	2,10	1,80	69,00	624,00	3,00	5,00	4,00	3,90
10550,00	179500,00	9,10	0,70	27,00	180,00	4,00	4,00	4,00	9,80
0,02	0,30	15,80	3,90	19,00	35,00	1,00	1,00	1,00	19,70
160000,00	169000,00	5,20	1,00	30,40	392,00	4,00	5,00	4,00	6,20
3300,00	25600,00	10,90	3,60	28,00	63,00	1,00	2,00	1,00	14,50
52160,00	440000,00	8,30	1,40	50,00	230,00	1,00	1,00	1,00	9,70
0,43	6400,00	11,00	1,50	7,00	112,00	5,00	4,00	4,00	12,50
465000,00	423000,00	3,20	0,70	30,00	281,00	5,00	5,00	5,00	3,90
0,55	2400,00	7,60	2,70	NA	NA	2,00	1,00	2,00	10,30
187100,00	419000,00	NA	NA	40,00	365,00	5,00	5,00	5,00	3,10
0,08	1200,00	6,30	2,10	3,50	42,00	1,00	1,00	1,00	8,40
3000,00	25000,00	8,60	0,00	50,00	28,00	2,00	2,00	2,00	8,60
0,79	3500,00	6,60	4,10	6,00	42,00	2,00	2,00	2,00	10,70
0,20	5000,00	9,50	1,20	10,40	120,00	2,00	2,00	2,00	10,70
1410,00	17500,00	4,80	1,30	34,00	NA	1,00	2,00	1,00	6,10
60000,00	81000,00	12,00	6,10	7,00	NA	1,00	1,00	1,00	18,10
529000,00	680000,00	NA	0,30	28,00	400,00	5,00	5,00	5,00	NA
27660,00	115000,00	3,30	0,50	20,00	148,00	5,00	5,00	5,00	3,80
0,12	1000,00	11,00	3,40	3,90	16,00	3,00	1,00	2,00	14,40
207000,00	406000,00	NA	NA	39,30	252,00	1,00	4,00	1,00	12,00
85000,00	325000,00	4,70	1,50	41,00	310,00	1,00	3,00	1,00	6,20
36330,00	119500,00	NA	NA	16,20	63,00	1,00	1,00	1,00	13,00
0,10	4000,00	10,40	3,40	9,00	28,00	5,00	1,00	3,00	13,80
1040,00	5500,00	7,40	0,80	7,60	68,00	5,00	3,00	4,00	8,20
521000,00	655000,00	2,10	0,80	46,00	336,00	5,00	5,00	5,00	2,90
100000,00	157000,00	NA	NA	22,40	100,00	1,00	1,00	1,00	10,80
35000,00	56000,00	NA	NA	16,30	33,00	3,00	5,00	4,00	NA
0,01	0,14	7,70	1,40	2,60	21,50	5,00	2,00	4,00	9,10
0,01	0,25	17,90	2,00	24,00	50,00	1,00	1,00	1,00	19,90
62000,00	1320000,00	6,10	1,90	100,00	267,00	1,00	1,00	1,00	8,00
0,12	3000,00	8,20	2,40	NA	30,00	2,00	1,00	1,00	10,60
1350,00	8100,00	8,40	2,80	NA	45,00	3,00	1,00	3,00	11,20
0,02	0,40	11,90	1,30	3,20	19,00	4,00	1,00	3,00	13,20
0,05	0,33	10,80	2,00	2,00	30,00	4,00	1,00	3,00	12,80
1700,00	6300,00	13,80	5,60	5,00	12,00	2,00	1,00	1,00	19,40
3500,00	10800,00	14,30	3,10	6,50	120,00	2,00	1,00	1,00	17,40
250000,00	490000,00	NA	1,00	23,60	440,00	5,00	5,00	5,00	NA
0,48	15500,00	15,20	1,80	12,00	140,00	2,00	2,00	2,00	17,00
10000,00	115000,00	10,00	0,90	20,20	170,00	4,00	4,00	4,00	10,90
1620,00	11400,00	11,90	1,80	13,00	17,00	2,00	1,00	2,00	13,70
192000,00	180000,00	6,50	1,90	27,00	115,00	4,00	4,00	4,00	8,40
2500,00	12100,00	7,50	0,90	18,00	31,00	5,00	5,00	5,00	8,40
4288,00	39200,00	NA	NA	13,70	63,00	2,00	2,00	2,00	12,50
0,28	1900,00	10,60	2,60	4,70	21,00	3,00	1,00	3,00	13,20
4235,00	50400,00	7,40	2,40	9,80	52,00	1,00	1,00	1,00	9,80
6800,00	179000,00	8,40	1,20	29,00	164,00	2,00	3,00	2,00	9,60
0,75	12300,00	5,70	0,90	7,00	225,00	2,00	2,00	2,00	6,60
3600,00	21000,00	4,90	0,50	6,00	225,00	3,00	2,00	3,00	5,40
14830,00	98200,00	NA	NA	17,00	150,00	5,00	5,00	5,00	2,60
55500,00	175000,00	3,20	0,60	20,00	151,00	5,00	5,00	5,00	3,80
1400,00	12500,00	NA	NA	12,70	90,00	2,00	2,00	2,00	11,00
0,06	1000,00	8,10	2,20	3,50	NA	3,00	1,00	2,00	10,30
0,90	2600,00	11,00	2,30	4,50	60,00	2,00	1,00	2,00	13,30
2000,00	12300,00	4,90	0,50	7,50	200,00	3,00	1,00	3,00	5,40
0,10	2500,00	13,20	2,60	2,30	46,00	3,00	2,00	2,00	15,80
4190,00	58000,00	9,70	0,60	24,00	210,00	4,00	3,00	4,00	10,30
3500,00	3900,00	12,80	6,60	3,00	14,00	2,00	1,00	1,00	19,40
4050,00	17000,00	NA	NA	13,00	38,00	3,00	1,00	1,00	NA

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135
R Framework error message	Warning: there are blank lines in the 'Data X' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.
R Engine error message	Error in dimnames(data) <- dimnames : length of 'dimnames' [1] not equal to array extent Calls: array 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
R Framework error message & Warning: there are blank lines in the 'Data X' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values. \tabularnewline
R Engine error message & Error in dimnames(data) <- dimnames : 
  length of 'dimnames' [1] not equal to array extent
Calls: array
Execution halted
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=109415&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[ROW][C]R Framework error message[/C][C]Warning: there are blank lines in the 'Data X' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.[/C][/ROW]
[ROW][C]R Engine error message[/C][C]Error in dimnames(data) <- dimnames : 
  length of 'dimnames' [1] not equal to array extent
Calls: array
Execution halted
[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=109415&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=109415&T=0

As an alternative you can also use a QR Code:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135
R Framework error message	Warning: there are blank lines in the 'Data X' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values.
R Engine error message	Error in dimnames(data) <- dimnames : length of 'dimnames' [1] not equal to array extent Calls: array Execution halted

Parameters (Session):

par1 = 10 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 10 ; 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')
}

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code