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Author

*The author of this computation has been verified*

R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Tue, 20 Dec 2011 03:47:52 -0500

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/2011/Dec/20/t1324370895qss822qsc31q4p4.htm/, Retrieved Mon, 06 May 2024 06:12:47 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=157801, Retrieved Mon, 06 May 2024 06:12:47 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

139

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

-     [Multiple Regression] [] [2010-11-17 09:55:05] [b98453cac15ba1066b407e146608df68]
-   PD    [Multiple Regression] [] [2011-12-20 08:47:52] [d519577d845e738b812f706f10c86f64] [Current]

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Dataseries X:

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Histogram

Boxplots

1	1	1	41	41	13	14	14	12	12
1	2	2	39	39	16	18	18	11	11
1	3	3	30	30	19	11	11	14	14
1	4	4	31	31	15	12	12	12	12
1	5	5	34	34	14	16	16	21	21
1	6	6	35	35	13	18	18	12	12
1	7	7	39	39	19	14	14	22	22
1	8	8	34	34	15	14	14	11	11
1	9	9	36	36	14	15	15	10	10
1	10	10	37	37	15	15	15	13	13
1	11	11	38	38	16	17	17	10	10
1	12	12	36	36	16	19	19	8	8
1	13	13	38	38	16	10	10	15	15
1	14	14	39	39	16	16	16	14	14
1	15	15	33	33	17	18	18	10	10
1	16	16	32	32	15	14	14	14	14
1	17	17	36	36	15	14	14	14	14
1	18	18	38	38	20	17	17	11	11
1	19	19	39	39	18	14	14	10	10
1	20	20	32	32	16	16	16	13	13
1	21	21	32	32	16	18	18	7	7
1	22	22	31	31	16	11	11	14	14
1	23	23	39	39	19	14	14	12	12
1	24	24	37	37	16	12	12	14	14
1	25	25	39	39	17	17	17	11	11
1	26	26	41	41	17	9	9	9	9
1	27	27	36	36	16	16	16	11	11
1	28	28	33	33	15	14	14	15	15
1	29	29	33	33	16	15	15	14	14
1	30	30	34	34	14	11	11	13	13
1	31	31	31	31	15	16	16	9	9
1	32	32	27	27	12	13	13	15	15
1	33	33	37	37	14	17	17	10	10
1	34	34	34	34	16	15	15	11	11
1	35	35	34	34	14	14	14	13	13
1	36	36	32	32	7	16	16	8	8
1	37	37	29	29	10	9	9	20	20
1	38	38	36	36	14	15	15	12	12
1	39	39	29	29	16	17	17	10	10
1	40	40	35	35	16	13	13	10	10
1	41	41	37	37	16	15	15	9	9
1	42	42	34	34	14	16	16	14	14
1	43	43	38	38	20	16	16	8	8
1	44	44	35	35	14	12	12	14	14
1	45	45	38	38	14	12	12	11	11
1	46	46	37	37	11	11	11	13	13
1	47	47	38	38	14	15	15	9	9
1	48	48	33	33	15	15	15	11	11
1	49	49	36	36	16	17	17	15	15
1	50	50	38	38	14	13	13	11	11
1	51	51	32	32	16	16	16	10	10
1	52	52	32	32	14	14	14	14	14
1	53	53	32	32	12	11	11	18	18
1	54	54	34	34	16	12	12	14	14
1	55	55	32	32	9	12	12	11	11
1	56	56	37	37	14	15	15	12	12
1	57	57	39	39	16	16	16	13	13
1	58	58	29	29	16	15	15	9	9
1	59	59	37	37	15	12	12	10	10
1	60	60	35	35	16	12	12	15	15
1	61	61	30	30	12	8	8	20	20
1	62	62	38	38	16	13	13	12	12
1	63	63	34	34	16	11	11	12	12
1	64	64	31	31	14	14	14	14	14
1	65	65	34	34	16	15	15	13	13
1	66	66	35	35	17	10	10	11	11
1	67	67	36	36	18	11	11	17	17
1	68	68	30	30	18	12	12	12	12
1	69	69	39	39	12	15	15	13	13
1	70	70	35	35	16	15	15	14	14
1	71	71	38	38	10	14	14	13	13
1	72	72	31	31	14	16	16	15	15
1	73	73	34	34	18	15	15	13	13
1	74	74	38	38	18	15	15	10	10
1	75	75	34	34	16	13	13	11	11
1	76	76	39	39	17	12	12	19	19
1	77	77	37	37	16	17	17	13	13
1	78	78	34	34	16	13	13	17	17
1	79	79	28	28	13	15	15	13	13
1	80	80	37	37	16	13	13	9	9
0	81	81	33	33	16	15	15	11	11
0	82	82	37	37	20	16	16	10	10
0	83	83	35	35	16	15	15	9	9
0	84	84	37	37	15	16	16	12	12
0	85	85	32	32	15	15	15	12	12
0	86	86	33	33	16	14	14	13	13
0	87	87	38	38	14	15	15	13	13
0	88	88	33	33	16	14	14	12	12
0	89	89	29	29	16	13	13	15	15
0	90	90	33	33	15	7	7	22	22
0	91	91	31	31	12	17	17	13	13
0	92	92	36	36	17	13	13	15	15
0	93	93	35	35	16	15	15	13	13
0	94	94	32	32	15	14	14	15	15
0	95	95	29	29	13	13	13	10	10
0	96	96	39	39	16	16	16	11	11
0	97	97	37	37	16	12	12	16	16
0	98	98	35	35	16	14	14	11	11
0	99	99	37	37	16	17	17	11	11
0	100	100	32	32	14	15	15	10	10
0	101	101	38	38	16	17	17	10	10
0	102	102	37	37	16	12	12	16	16
0	103	103	36	36	20	16	16	12	12
0	104	104	32	32	15	11	11	11	11
0	105	105	33	33	16	15	15	16	16
0	106	106	40	40	13	9	9	19	19
0	107	107	38	38	17	16	16	11	11
0	108	108	41	41	16	15	15	16	16
0	109	109	36	36	16	10	10	15	15
0	110	110	43	43	12	10	10	24	24
0	111	111	30	30	16	15	15	14	14
0	112	112	31	31	16	11	11	15	15
0	113	113	32	32	17	13	13	11	11
0	114	114	32	32	13	14	14	15	15
0	115	115	37	37	12	18	18	12	12
0	116	116	37	37	18	16	16	10	10
0	117	117	33	33	14	14	14	14	14
0	118	118	34	34	14	14	14	13	13
0	119	119	33	33	13	14	14	9	9
0	120	120	38	38	16	14	14	15	15
0	121	121	33	33	13	12	12	15	15
0	122	122	31	31	16	14	14	14	14
0	123	123	38	38	13	15	15	11	11
0	124	124	37	37	16	15	15	8	8
0	125	125	33	33	15	15	15	11	11
0	126	126	31	31	16	13	13	11	11
0	127	127	39	39	15	17	17	8	8
0	128	128	44	44	17	17	17	10	10
0	129	129	33	33	15	19	19	11	11
0	130	130	35	35	12	15	15	13	13
0	131	131	32	32	16	13	13	11	11
0	132	132	28	28	10	9	9	20	20
0	133	133	40	40	16	15	15	10	10
0	134	134	27	27	12	15	15	15	15
0	135	135	37	37	14	15	15	12	12
0	136	136	32	32	15	16	16	14	14
0	137	137	28	28	13	11	11	23	23
0	138	138	34	34	15	14	14	14	14
0	139	139	30	30	11	11	11	16	16
0	140	140	35	35	12	15	15	11	11
0	141	141	31	31	8	13	13	12	12
0	142	142	32	32	16	15	15	10	10
0	143	143	30	30	15	16	16	14	14
0	144	144	30	30	17	14	14	12	12
0	145	145	31	31	16	15	15	12	12
0	146	146	40	40	10	16	16	11	11
0	147	147	32	32	18	16	16	12	12
0	148	148	36	36	13	11	11	13	13
0	149	149	32	32	16	12	12	11	11
0	150	150	35	35	13	9	9	19	19
0	151	151	38	38	10	16	16	12	12
0	152	152	42	42	15	13	13	17	17
0	153	153	34	34	16	16	16	9	9
0	154	154	35	35	16	12	12	12	12
0	155	155	35	35	14	9	9	19	19
0	156	156	33	33	10	13	13	18	18
0	157	157	36	36	17	13	13	15	15
0	158	158	32	32	13	14	14	14	14
0	159	159	33	33	15	19	19	11	11
0	160	160	34	34	16	13	13	9	9
0	161	161	32	32	12	12	12	18	18
0	162	162	34	34	13	13	13	16	16

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Gwilym Jenkins' @ jenkins.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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157801&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157801&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157801&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	3 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

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Parameters (Session):

par1 = 6 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 6 ; 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