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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Wed, 12 Nov 2014 14:26:00 +0000

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Nov/12/t1415802367qo3ezu387abcmev.htm/, Retrieved Sun, 19 May 2024 14:14:07 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=253869, Retrieved Sun, 19 May 2024 14:14:07 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Multiple Regression] [] [2013-11-04 07:18:26] [0307e7a6407eb638caabc417e3a6b260]
-  MPD    [Multiple Regression] [kj] [2014-11-12 14:26:00] [ccc8d5d8fda28a28a4ef088d048ade85] [Current]

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Dataseries X:

Download CSV

Histogram

Boxplots

41	38	13	12	12	53
39	32	16	11	11	86
30	35	19	15	14	66
31	33	15	6	12	67
34	37	14	13	21	76
35	29	13	10	12	78
39	31	19	12	22	53
34	36	15	14	11	80
36	35	14	12	10	74
37	38	15	6	13	76
38	31	16	10	10	79
36	34	16	12	8	54
38	35	16	12	15	67
39	38	16	11	14	54
33	37	17	15	10	87
32	33	15	12	14	58
36	32	15	10	14	75
38	38	20	12	11	88
39	38	18	11	10	64
32	32	16	12	13	57
32	33	16	11	7	66
31	31	16	12	14	68
39	38	19	13	12	54
37	39	16	11	14	56
39	32	17	9	11	86
41	32	17	13	9	80
36	35	16	10	11	76
33	37	15	14	15	69
33	33	16	12	14	78
34	33	14	10	13	67
31	28	15	12	9	80
27	32	12	8	15	54
37	31	14	10	10	71
34	37	16	12	11	84
34	30	14	12	13	74
32	33	7	7	8	71
29	31	10	6	20	63
36	33	14	12	12	71
29	31	16	10	10	76
35	33	16	10	10	69
37	32	16	10	9	74
34	33	14	12	14	75
38	32	20	15	8	54
35	33	14	10	14	52
38	28	14	10	11	69
37	35	11	12	13	68
38	39	14	13	9	65
33	34	15	11	11	75
36	38	16	11	15	74
38	32	14	12	11	75
32	38	16	14	10	72
32	30	14	10	14	67
32	33	12	12	18	63
34	38	16	13	14	62
32	32	9	5	11	63
37	32	14	6	12	76
39	34	16	12	13	74
29	34	16	12	9	67
37	36	15	11	10	73
35	34	16	10	15	70
30	28	12	7	20	53
38	34	16	12	12	77
34	35	16	14	12	77
31	35	14	11	14	52
34	31	16	12	13	54
35	37	17	13	11	80
36	35	18	14	17	66
30	27	18	11	12	73
39	40	12	12	13	63
35	37	16	12	14	69
38	36	10	8	13	67
31	38	14	11	15	54
34	39	18	14	13	81
38	41	18	14	10	69
34	27	16	12	11	84
39	30	17	9	19	80
37	37	16	13	13	70
34	31	16	11	17	69
28	31	13	12	13	77
37	27	16	12	9	54
33	36	16	12	11	79
37	38	20	12	10	30
35	37	16	12	9	71
37	33	15	12	12	73
32	34	15	11	12	72
33	31	16	10	13	77
38	39	14	9	13	75
33	34	16	12	12	69
29	32	16	12	15	54
33	33	15	12	22	70
31	36	12	9	13	73
36	32	17	15	15	54
35	41	16	12	13	77
32	28	15	12	15	82
29	30	13	12	10	80
39	36	16	10	11	80
37	35	16	13	16	69
35	31	16	9	11	78
37	34	16	12	11	81
32	36	14	10	10	76
38	36	16	14	10	76
37	35	16	11	16	73
36	37	20	15	12	85
32	28	15	11	11	66
33	39	16	11	16	79
40	32	13	12	19	68
38	35	17	12	11	76
41	39	16	12	16	71
36	35	16	11	15	54
43	42	12	7	24	46
30	34	16	12	14	82
31	33	16	14	15	74
32	41	17	11	11	88
32	33	13	11	15	38
37	34	12	10	12	76
37	32	18	13	10	86
33	40	14	13	14	54
34	40	14	8	13	70
33	35	13	11	9	69
38	36	16	12	15	90
33	37	13	11	15	54
31	27	16	13	14	76
38	39	13	12	11	89
37	38	16	14	8	76
33	31	15	13	11	73
31	33	16	15	11	79
39	32	15	10	8	90
44	39	17	11	10	74
33	36	15	9	11	81
35	33	12	11	13	72
32	33	16	10	11	71
28	32	10	11	20	66
40	37	16	8	10	77
27	30	12	11	15	65
37	38	14	12	12	74
32	29	15	12	14	82
28	22	13	9	23	54
34	35	15	11	14	63
30	35	11	10	16	54
35	34	12	8	11	64
31	35	8	9	12	69
32	34	16	8	10	54
30	34	15	9	14	84
30	35	17	15	12	86
31	23	16	11	12	77
40	31	10	8	11	89
32	27	18	13	12	76
36	36	13	12	13	60
32	31	16	12	11	75
35	32	13	9	19	73
38	39	10	7	12	85
42	37	15	13	17	79
34	38	16	9	9	71
35	39	16	6	12	72
35	34	14	8	19	69
33	31	10	8	18	78
36	32	17	15	15	54
32	37	13	6	14	69
33	36	15	9	11	81
34	32	16	11	9	84
32	35	12	8	18	84
34	36	13	8	16	69

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	'Gertrude Mary Cox' @ cox.wessa.net
R Engine error message	Error in lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) : 0 (non-NA) cases Calls: lm -> lm.fit In addition: Warning messages: 1: In model.matrix.default(mt, mf, contrasts) : the response appeared on the right-hand side and was dropped 2: In model.matrix.default(mt, mf, contrasts) : problem with term 1 in model.matrix: no columns are assigned 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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
R Engine error message & Error in lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) : 
  0 (non-NA) cases
Calls: lm -> lm.fit
In addition: Warning messages:
1: In model.matrix.default(mt, mf, contrasts) :
  the response appeared on the right-hand side and was dropped
2: In model.matrix.default(mt, mf, contrasts) :
  problem with term 1 in model.matrix: no columns are assigned
Execution halted
 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=253869&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]
[ROW][C]R Engine error message[/C][C]Error in lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) : 
  0 (non-NA) cases
Calls: lm -> lm.fit
In addition: Warning messages:
1: In model.matrix.default(mt, mf, contrasts) :
  the response appeared on the right-hand side and was dropped
2: In model.matrix.default(mt, mf, contrasts) :
  problem with term 1 in model.matrix: no columns are assigned
Execution halted
[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=253869&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=253869&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	'Gertrude Mary Cox' @ cox.wessa.net
R Engine error message	Error in lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) : 0 (non-NA) cases Calls: lm -> lm.fit In addition: Warning messages: 1: In model.matrix.default(mt, mf, contrasts) : the response appeared on the right-hand side and was dropped 2: In model.matrix.default(mt, mf, contrasts) : problem with term 1 in model.matrix: no columns are assigned Execution halted

Parameters (Session):

par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = ; par2 = Do not include Seasonal Dummies ; par3 = 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$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, signif(mysum$coefficients[i,1],6), 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,signif(mysum$coefficients[i,1],6))
a<-table.element(a, signif(mysum$coefficients[i,2],6))
a<-table.element(a, signif(mysum$coefficients[i,3],4))
a<-table.element(a, signif(mysum$coefficients[i,4],6))
a<-table.element(a, signif(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, signif(sqrt(mysum$r.squared),6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, signif(mysum$r.squared,6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, signif(mysum$adj.r.squared,6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, signif(mysum$fstatistic[1],6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, signif(mysum$fstatistic[2],6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, signif(mysum$fstatistic[3],6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, signif(1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]),6))
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, signif(mysum$sigma,6))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, signif(sum(myerror*myerror),6))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,signif(x[i],6))
a<-table.element(a,signif(x[i]-mysum$resid[i],6))
a<-table.element(a,signif(mysum$resid[i],6))
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,signif(gqarr[mypoint-kp3+1,1],6))
a<-table.element(a,signif(gqarr[mypoint-kp3+1,2],6))
a<-table.element(a,signif(gqarr[mypoint-kp3+1,3],6))
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,signif(numsignificant1,6))
a<-table.element(a,signif(numsignificant1/numgqtests,6))
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,signif(numsignificant5,6))
a<-table.element(a,signif(numsignificant5/numgqtests,6))
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,signif(numsignificant10,6))
a<-table.element(a,signif(numsignificant10/numgqtests,6))
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