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Workshop 2 vraag 3

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

Title produced by software: Multiple Regression

Date of computation: Thu, 22 Nov 2007 02:35:12 -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/22/t1195723973h0919f2ths9ynnh.htm/, Retrieved Thu, 22 Nov 2007 10:32:53 +0100

User-defined keywords:

nog antwoorden op de vraag en verklaringen geven aan de grafieken

Dataseries X:

» Textbox « » Textfile « » CSV «

168.836 102.161 66.674 150.581 90.488 60.093 149.514 113.022 36.492 148.281 98.250 50.031 125.968 111.717 14.250 96.566 3.027 93.538 84.416 32.943 51.473 84.222 15.236 68.986 82.354 8.606 73.747 75.213 67.359 7.854 71.639 66.225 5.414 70.339 18.636 51.703 68.503 39.376 29.127 68.183 39.383 28.800 66.893 40.266 26.627 61.926 11.407 50.520 61.630 47.735 13.895 53.911 53.284 627 53.077 8.769 44.309 51.337 982 50.355 51.314 117 51.197 50.978 25.464 25.513 48.921 6.915 42.007 48.809 32.405 16.404 47.727 25.255 22.472 47.216 47.121 95 45.698 8.350 37.348 45.568 4.521 41.047 44.102 10.756 33.346 42.489 32.693 9.796 42.102 17.061 25.041 38.251 242 38.009 37.657 12.185 25.472 36.817 12.165 24.652 35.818 13.060 22.758 35.685 2.644 33.041 35.516 12.853 22.663 35.101 370 34.732 34.173 9.495 24.678 33.234 26.133 7.101 29.635 917 28.718 27.750 12.118 15.632 27.086 25.649 1.437 26.385 20.752 5.633 25.009 14.616 10.393 24.076 2.994 21.082 23.779 4.790 18.989 23.296 16.362 6.934 23.010 19.962 3.048 22.971 22.753 218 22.723 5.096 17.627 21.938 9.411 12.527 21.446 703 20.743 21.402 4.333 17.069 21.200 9.835 11.365 20.890 15.452 5.438 20.850 1.814 19.037 19.730 216 19.514 19.661 2.580 17.082 19.264 11.426 7.838 18.980 3.335 15.644 18.836 113 18.723 17.203 4.191 13.013 17.060 7.932 9.128 16.828 544 16.283 16.574 943 15.631 16.218 5.593 10.625 16.055 1.745 14.310 15.471 2.550 12.921 15.237 1.803 13.434 15.105 395 14.710 14.560 100 14.460 14.290 11.176 3.115 14.148 1.478 12.669 14.105 2.787 11.318 13.995 12.425 1.570 13.961 4.227 9.734 13.916 13.387 528 12.982 4.956 8.026 12.671 1.119 11.553 11.415 1.036 10.380 11.393 2.308 9.085 11.363 3.620 7.743 11.152 9.734 1.418 10.730 425 10.305 10.402 7.383 3.018 10.004 2.975 7.028 9.902 2.818 7.084 9.857 7.029 2.829 9.738 554 9.184 9.625 7.197 2.428 9.228 5.354 3.873 9.145 6.297 2.849 8.846 4.816 4.030 8.749 0 8.749 8.718 4.577 4.142 8.569 3.656 4.913 8.473 280 8.193 8.309 321 7.988 8.103 1.315 6.788

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	6 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Multiple Linear Regression - Estimated Regression Equation

Totaal[t] = + 80.6199751233202 -0.00283909874382477Vrouwen[t] -0.00159293366137467Mannen[t] + 10.4049928272578M1[t] + 9.26659394050718M2[t] + 9.2121611220132M3[t] + 9.1050997513571M4[t] + 5.5323317390141M5[t] + 1.32699196787480M6[t] -0.438357788220186M7[t] -0.0177278005565451M8[t] -0.186935229537426M9[t] -0.554201233792353M10[t] -0.447555437283408M11[t] -0.95454723952818t + 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)	80.6199751233202	7.989903	10.0902	0	0
Vrouwen	-0.00283909874382477	0.011099	-0.2558	0.798728	0.399364
Mannen	-0.00159293366137467	0.028008	-0.0569	0.954778	0.477389
M1	10.4049928272578	9.602324	1.0836	0.28161	0.140805
M2	9.26659394050718	9.690956	0.9562	0.341678	0.170839
M3	9.2121611220132	9.590675	0.9605	0.339511	0.169756
M4	9.1050997513571	9.582632	0.9502	0.344721	0.172361
M5	5.5323317390141	10.313817	0.5364	0.593083	0.296542
M6	1.32699196787480	10.946942	0.1212	0.903803	0.451901
M7	-0.438357788220186	9.865543	-0.0444	0.964663	0.482332
M8	-0.0177278005565451	9.983864	-0.0018	0.998587	0.499294
M9	-0.186935229537426	9.86326	-0.019	0.984923	0.492462
M10	-0.554201233792353	9.861989	-0.0562	0.955318	0.477659
M11	-0.447555437283408	9.86793	-0.0454	0.963931	0.481966
t	-0.95454723952818	0.069849	-13.6658	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.838575876760288
R-squared	0.703209501084286
Adjusted R-squared	0.654326360086404
F-TEST (value)	14.3855220169823
F-TEST (DF numerator)	14
F-TEST (DF denominator)	85
p-value	1.11022302462516e-16
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	19.7181113195452
Sum Squared Residuals	33048.3326908480

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	168.836	89.6741682853434	79.1618317146566
2	150.581	87.6248460551269	62.9561539448731
3	149.514	86.5894845733534	62.9245154266466
4	148.281	85.5482484009716	62.7327515990284
5	125.968	81.039695765655	44.928304234345
6	96.566	76.0620898733107	20.5039101266893
7	84.416	73.324265154133	11.0917348458670
8	84.222	72.8127227765137	11.4092772234863
9	82.354	71.7002073755144	10.6537926244856
10	75.213	70.3165517409843	4.89644825901565
11	71.639	69.4757565940744	2.16324340592564
12	70.339	69.0301393556981	1.30886064430191
13	68.503	78.45766410582	-9.95466410582
14	68.183	76.3652189951572	-8.18221899515724
15	66.893	75.3571934577904	-8.46419345779045
16	61.926	74.339458434283	-12.413458434283
17	61.63	69.767345598594	-8.137345598594
18	53.911	63.6150688365399	-9.70406883653993
19	53.077	61.9497424295782	-8.87274242957818
20	51.337	58.6430953912457	-7.30609539124566
21	51.314	59.9738198860021	-8.65981988600213
22	50.978	58.9527992929925	-7.97479929299251
23	48.921	58.1312864447618	-9.21028644476177
24	48.809	57.5927098960691	-8.78370989606908
25	47.727	67.0537891183598	-19.3267891183598
26	47.216	64.7832309663564	-17.5672309663564
27	45.698	63.9761614171766	-18.2781614171766
28	45.568	62.919531454469	-17.3515314544690
29	44.102	58.3867816040563	-14.2847816040563
30	42.489	53.2021268719709	-10.7131268719709
31	42.102	50.5023263942436	-8.40032639424359
32	38.251	49.3091279463212	-11.0581279463212
33	37.657	48.8578113649368	-11.2008113649368
34	36.817	47.5373611087309	-10.7203611087309
35	35.818	46.6899356886906	-10.8719356886906
36	35.685	46.1961358021216	-10.5111358021216
37	35.516	55.6341284963133	-20.1181284963133
38	35.101	52.5079816546146	-17.4069816546146
39	34.173	52.5385262442664	-18.3655262442664
40	33.234	51.4576797041484	-18.2236797041484
41	29.635	44.3666706247043	-14.7316706247043
42	27.75	41.7966780934392	-14.0466780934392
43	27.086	39.0609769460366	-11.9749769460366
44	26.385	38.5342788110774	-12.1492788110774
45	25.009	37.4203624882323	-12.4113624882323
46	24.076	36.1145183821435	-12.0385183821435
47	23.779	35.2648519279336	-11.4858519279336
48	23.296	34.7442088903132	-11.4482088903132
49	23.01	44.1906238627731	-21.1806238627731
50	22.971	41.7473495355205	-18.7763495355205
51	22.723	41.1076803405487	-18.3846803405487
52	21.938	40.0419449809578	-18.1039449809578
53	21.446	33.5323745274941	-12.0863745274941
54	21.402	30.3619245571503	-8.95992455715032
55	21.2	27.6354929338431	-6.43549293384313
56	20.89	27.0950697821455	-6.20506978214547
57	20.85	25.9883724374437	-5.13837243744369
58	19.73	24.0577041607592	-4.32770416075922
59	19.661	23.8195971863115	-4.15859718631155
60	19.264	23.3022157953447	-4.03821579534465
61	18.98	32.7631980908499	-13.7831980908499
62	18.836	30.3539975580862	-11.5179975580862
63	17.203	29.6630326464873	-12.4600326464873
64	17.06	28.5969915151768	-11.5369915151768
65	16.828	22.5363288375538	-5.70832883755381
66	16.574	16.2446800208474	0.329319979152554
67	16.218	16.1941482872857	0.0238517127143203
68	16.055	15.6652859268452	0.389714073154772
69	15.471	14.5414583687030	0.929541631296982
70	15.237	13.2209487567133	2.01605124328673
71	15.105	11.2546896215665	3.85031037843353
72	14.56	11.5856301821653	2.97436981783465
73	14.29	21.3063277091048	-7.01632770910477
74	14.148	19.2256962742428	-5.07769627424279
75	14.105	18.2151518893415	-4.11015188934148
76	13.995	17.1417079627953	-3.14670796279532
77	13.961	12.6246629320145	1.33633706798546
78	13.916	6.6132064199076	7.3027935800924
79	12.982	4.74552995343328	8.23647004656672
80	12.671	4.21688804642512	8.45411195357488
81	11.415	3.0952375342966	8.3197624657034
82	11.393	1.77187580600281	9.62112419399719
83	11.363	0.922387182405236	10.4406128175948
84	11.152	0.408112435848917	10.7438875641511
85	10.73	8.6654204431768	2.06457955682320
86	10.402	7.76973792458827	2.63226207541173
87	10.004	6.7668849498468	3.2371150501532
88	9.902	5.70563287388027	4.19636712611973
89	9.857	1.17314010992798	8.68385989007202
90	9.738	-5.54977467316614	15.2877746731661
91	9.625	-6.70648209855343	16.3314820985534
92	9.228	-7.23746868057377	16.4654686805738
93	9.145	-8.36226945512902	17.507269455129
94	8.846	-9.68175924832662	18.5277592483266
95	8.749	-10.5235046457436	19.2725046457436
96	8.718	-11.0361523575609	19.7541523575609
97	8.569	-1.58432011174113	10.1533201117411
98	8.473	-4.46705896369276	12.9400589636928
99	8.309	-5.59211551881115	13.9011155188111
100	8.103	-5.74419532668216	13.8471953266822

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/22/t1195723973h0919f2ths9ynnh/122we1195724100.png (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/22/t1195723973h0919f2ths9ynnh/5jcnj1195724100.png (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/22/t1195723973h0919f2ths9ynnh/7uasg1195724101.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/22/t1195723973h0919f2ths9ynnh/88duf1195724101.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/22/t1195723973h0919f2ths9ynnh/88duf1195724101.ps (open in new window)

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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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