Home » date » 2007 » Nov » 18 » attachments

WS8 Q3 incl monthly dummy's en trend

R Software Module: rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Sun, 18 Nov 2007 09:42:23 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2007/Nov/18/t1195403747arphob345s0f2ho.htm/, Retrieved Sun, 18 Nov 2007 17:35:57 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

1178 0 2141 0 2238 0 2685 0 4341 0 5376 0 4478 0 6404 0 4617 0 3024 0 1897 0 2075 0 1351 0 2211 0 2453 0 3042 0 4765 0 4992 1 4601 1 6266 1 4812 1 3159 1 1916 1 2237 1 1595 1 2453 1 2226 1 3597 1 4706 1 4974 1 5756 1 5493 1 5004 1 3225 1 2006 1 2291 1 1588 1 2105 1 2191 1 3591 1 4668 1 4885 1 5822 1 5599 1 5340 1 3082 1 2010 1 2301 1 1514 1 1979 1 2480 1 3499 1 4676 1 5585 1 5610 1 5796 1 6199 1 3030 1 1930 1 2552 1

Text written by user:

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits!

Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	5 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation

Huwelijken[t] = + 2039.51506352087 -33.8675136116152Dummy[t] -767.591046581972M1[t] -42.7349062310934M2[t] + 89.3212341197802M3[t] + 1046.77737447066M4[t] + 2387.43351482154M5[t] + 2917.66315789474M6[t] + 3000.91929824562M7[t] + 3651.37543859649M8[t] + 2926.43157894737M9[t] + 828.287719298245M10[t] -331.656140350877M11[t] + 7.7438596491228t + e[t]

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.D.	T-STAT H0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	2039.51506352087	167.664007	12.1643	0	0
Dummy	-33.8675136116152	148.875468	-0.2275	0.821052	0.410526
M1	-767.591046581972	203.545075	-3.7711	0.000463	0.000231
M2	-42.7349062310934	203.215872	-0.2103	0.834368	0.417184
M3	89.3212341197802	202.959456	0.4401	0.66193	0.330965
M4	1046.77737447066	202.776103	5.1622	5e-06	3e-06
M5	2387.43351482154	202.666012	11.7801	0	0
M6	2917.66315789474	203.084546	14.3667	0	0
M7	3000.91929824562	202.6812	14.8061	0	0
M8	3651.37543859649	202.350592	18.0448	0	0
M9	2926.43157894737	202.093078	14.4806	0	0
M10	828.287719298245	201.908939	4.1023	0.000165	8.3e-05
M11	-331.656140350877	201.798374	-1.6435	0.107098	0.053549
t	7.7438596491228	3.857272	2.0076	0.050581	0.02529

Multiple Linear Regression - Regression Statistics
Multiple R	0.983319506786941
R-squared	0.966917252427713
Adjusted R-squared	0.957567780287719
F-TEST (value)	103.419448493946
F-TEST (DF numerator)	13
F-TEST (DF denominator)	46
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	319.012951593109
Sum Squared Residuals	4681386.11107077

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	1178	1279.66787658802	-101.667876588022
2	2141	2012.26787658802	128.732123411979
3	2238	2152.06787658802	85.93212341198
4	2685	3117.26787658802	-432.267876588023
5	4341	4465.66787658802	-124.667876588015
6	5376	5003.64137931035	372.358620689652
7	4478	5094.64137931034	-616.64137931034
8	6404	5752.84137931035	651.158620689654
9	4617	5035.64137931035	-418.641379310348
10	3024	2945.24137931035	78.7586206896523
11	1897	1793.04137931035	103.958620689654
12	2075	2132.44137931034	-57.4413793103445
13	1351	1372.59419237750	-21.5941923774956
14	2211	2105.19419237750	105.805807622505
15	2453	2244.99419237750	208.005807622504
16	3042	3210.19419237749	-168.194192377495
17	4765	4558.5941923775	206.405807622503
18	4992	5062.7001814882	-70.7001814882028
19	4601	5153.7001814882	-552.700181488204
20	6266	5811.9001814882	454.099818511798
21	4812	5094.7001814882	-282.700181488202
22	3159	3004.30018148820	154.699818511797
23	1916	1852.10018148820	63.8998185117969
24	2237	2191.50018148820	45.499818511797
25	1595	1431.65299455535	163.347005444646
26	2453	2164.25299455535	288.747005444646
27	2226	2304.05299455535	-78.0529945553543
28	3597	3269.25299455535	327.747005444646
29	4706	4617.65299455536	88.3470054446444
30	4974	5155.62649727768	-181.626497277676
31	5756	5246.62649727768	509.373502722322
32	5493	5904.82649727768	-411.826497277677
33	5004	5187.62649727768	-183.626497277676
34	3225	3097.22649727768	127.773502722324
35	2006	1945.02649727768	60.9735027223232
36	2291	2284.42649727768	6.57350272232332
37	1588	1524.57931034483	63.4206896551723
38	2105	2257.17931034483	-152.179310344828
39	2191	2396.97931034483	-205.979310344828
40	3591	3362.17931034483	228.820689655173
41	4668	4710.57931034483	-42.5793103448292
42	4885	5248.55281306715	-363.55281306715
43	5822	5339.55281306715	482.447186932848
44	5599	5997.75281306715	-398.75281306715
45	5340	5280.55281306715	59.4471869328502
46	3082	3190.15281306715	-108.15281306715
47	2010	2037.95281306715	-27.9528130671504
48	2301	2377.35281306715	-76.3528130671503
49	1514	1617.5056261343	-103.505626134301
50	1979	2350.1056261343	-371.105626134301
51	2480	2489.9056261343	-9.90562613430169
52	3499	3455.1056261343	43.8943738656991
53	4676	4803.5056261343	-127.505626134303
54	5585	5341.47912885662	243.520871143376
55	5610	5432.47912885663	177.520871143374
56	5796	6090.67912885662	-294.679128856624
57	6199	5373.47912885662	825.520871143377
58	3030	3283.07912885662	-253.079128856624
59	1930	2130.87912885662	-200.879128856624
60	2552	2470.27912885662	81.720871143376

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Parameters:

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

R code (references can be found in the software module):

library(lattice)

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))

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')

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()

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('http://www.xycoon.com/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<br />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<br />Forecast', 1, TRUE)

a<-table.element(a, 'Residuals<br />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')

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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