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Author*The author of this computation has been verified*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationMon, 05 Nov 2012 17:19:11 -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/05/t1352153963dny1miutcgfqg77.htm/, Retrieved Fri, 03 Feb 2023 09:36:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=186334, Retrieved Fri, 03 Feb 2023 09:36:21 +0000
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Estimated Impact77
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Multiple Regression] [workshop 7] [2012-11-05 22:19:11] [eeec99d459a890eb36d32eb90406e4cb] [Current]
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Dataseries X:
   56	1911	 61	17	 21	 51
 73	2599	 74	19	 15	 48
 62	2145	 57	18	 17	 46
 42	1331	 50	15	 20	 42
 27	7375	  3	12	  4	 42
 59	1445	 48	15	 12	 39
 56	1595	 62	14	 12	 38
 59	1134	 41	15	  9	 36
 78	1235	 31	20	 11	 36
 47	1552	 12	12	  7	 35
 51	2110	 46	13	 14	 34
 51	1430	 27	13	 10	 34
 54	1726	 47	15	 14	 34
 47	1348	 31	17	 11	 34
 47	1569	 16	13	  4	 32
 55	1534	 60	15	 11	 32
 47	1515	 37	13	  8	 32
 35	 843	 49	10	 14	 31
 48	1075	 33	12	  9	 31
 42	1600	 28	12	 10	 30
 55	1233	 56	16	  9	 30
 60	 945	 41	15	 13	 30
 12	1149	 71	12	 10	 28
 47	1360	 30	12	 11	 28
 38	1758	 28	12	  7	 27
 52	1313	 40	15	 11	 27
 47	1318	 28	12	  9	 27
 48	1276	 56	12	 15	 26
 42	1553	 37	13	  8	 26
 47	1180	 36	12	 10	 26
 56	 868	 32	15	 11	 26
 27	1098	 19	 9	  4	 26
 32	1487	 25	 8	 10	 26
 46	1071	 58	13	 10	 26
 60	 968	 29	15	 10	 26
 32	1066	 26	 9	  5	 26
 48	1254	 54	12	  7	 26
 48	1508	 41	12	  8	 25
 41	1367	 39	12	  5	 25
 45	1428	 29	12	  6	 25
 47	1290	 19	14	  5	 25
 42	1216	 32	12	  9	 25
 46	 863	 26	12	 10	 25
 58	 903	 42	16	 13	 25
 41	 826	 10	12	  7	 24
 48	1470	 57	12	  9	 24
 60	1065	 48	15	 10	 24
 41	1218	 43	12	  8	 24
 39	 923	 37	12	 10	 24
 52	 874	 49	15	  5	 23
 39	1491	 28	13	 10	 23
 39	 853	 55	12	  8	 23
 36	1016	 13	 9	  5	 23
 49	 713	 17	15	  5	 23
 49	1218	 36	13	  5	 23
 50	 983	 22	13	  7	 23
 48	1672	 37	13	 13	 22
 52	1231	 29	14	  8	 22
 55	1107	  3	13	  2	 22
 45	1132	 15	13	  7	 22
 45	 804	 38	15	 10	 21
 48	 775	 19	12	  5	 21
 41	1206	 35	14	 10	 21
 51	1233	 38	15	  7	 20
 22	 988	 23	12	  6	 20
 52	 614	 27	14	  9	 20
 47	1172	 43	12	  9	 19
 54	1216	 32	16	  6	 19
 43	 619	 37	12	 10	 18
 27	 934	  7	 9	  6	 18
 41	 874	 62	12	  9	 18
 40	 713	 17	10	  5	 18
 45	 932	 39	12	 11	 18
 52	 706	 18	13	  6	 18
  9	 760	 30	13	  7	 17
 57	 828	 18	16	  3	 17
 46	 792	  0	12	  0	 16
 24	 844	 34	12	  7	 16
 31	 918	 37	10	  9	 16
 41	 796	 33	12	  6	 16
 30	1061	 35	15	 10	 16
 44	 847	 17	14	  3	 15
 45	 575	 25	12	  8	 15
 35	 707	 21	13	  0	 15
 32	 548	 26	15	  7	 15
 33	 835	 40	12	  5	 15
 21	 563	 29	 8	  3	 15
 37	 487	 40	12	 10	 15
 46	 504	 13	13	  5	 15
 64	 641	  9	16	  5	 15
 32	 862	 54	12	  8	 15
 20	 715	 29	12	  6	 14
 21	 872	 25	12	  4	 14
 21	 564	  9	 8	  3	 14
 26	 997	 32	13	  5	 14
 19	 476	  4	 8	  2	 13
 20	 646	 17	16	  5	 13
 13	 637	 28	12	  5	 13
 34	 598	  4	13	  0	 13
 33	 960	 18	11	  5	 13
 36	 959	 17	12	  6	 13
 31	 563	 15	 8	  5	 13
 58	 500	 16	15	  6	 13
 32	 694	 25	13	  4	 12
 15	 620	  1	 4	  1	 12
 40	 831	 10	12	  2	 12
 15	 791	 10	12	  8	 12
 24	 428	 10	11	  2	 12
 37	 573	  7	12	  2	 11
 31	 623	 25	12	  3	 11
 26	 590	 27	14	  8	 11
 47	 584	 16	16	  3	 11
 18	 533	 11	13	  4	 10
 28	 508	 16	 9	  2	 10
  9	 488	  0	 5	  1	 10
 32	 723	 15	10	  3	 10
 45	 476	 36	13	  4	  9
 35	 387	  5	13	  7	  9
 29	 511	 14	12	  3	  9
  1	 585	 43	13	  6	  9
 20	 581	 10	12	  1	  9
 11	 413	  8	12	  2	  8
 33	 496	 12	12	  2	  8
 10	 350	 39	 5	  5	  7
 41	 427	  0	12	  0	  7
 31	 267	  0	 9	  0	  6
 10	 350	 10	 9	  3	  6
  0	 335	  7	 6	  0	  6
 38	 229	  0	11	  1	  5
 28	 470	  8	15	  0	  5
 24	 310	  3	12	  2	  5
 25	 242	  1	 8	  0	  5
  0	 244	  8	 0	  4	  5
  4	 431	  8	 3	  3	  5
 40	 352	  0	12	  0	  5
 23	 285	  5	 9	  1	  5
  6	 291	  0	14	  2	  4
 13	 242	  0	 4	  0	  4
  3	 211	  3	 1	  3	  3
  0	 136	  0	 0	  1	  3
  0	 231	  0	 0	  0	  2
  7	 268	  0	 6	  0	  2
  2	 126	  0	 6	  0	  2
  0	  44	  0	 0	  0	  2
  0	 340	  0	 0	  0	  2
  5	 143	  2	 2	  0	  1
  0	 104	  0	 0	  0	  1
  0	  25	  0	 0	  0	  1
  0	  11	  0	 0	  0	  0




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=186334&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=186334&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=186334&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net



Parameters (Session):
Parameters (R input):
par1 = ; 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')
}