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dummy3

*The author of this computation has been verified*

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

Title produced by software: Multiple Regression

Date of computation: Thu, 11 Dec 2008 07:24:38 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/11/t1229005540sqkdwled31z4gc3.htm/, Retrieved Thu, 11 Dec 2008 14:25:41 +0000

BibTeX entries for LaTeX users:

@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2008/Dec/11/t1229005540sqkdwled31z4gc3.htm/},
    year = {2008},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2008},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}

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

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

3030,29 0 2803,47 0 2767,63 0 2882,6 0 2863,36 0 2897,06 0 3012,61 0 3142,95 0 3032,93 0 3045,78 0 3110,52 0 3013,24 0 2987,1 0 2995,55 0 2833,18 0 2848,96 0 2794,83 0 2845,26 0 2915,02 0 2892,63 0 2604,42 0 2641,65 0 2659,81 0 2638,53 0 2720,25 0 2745,88 0 2735,7 0 2811,7 0 2799,43 0 2555,28 0 2304,98 0 2214,95 0 2065,81 0 1940,49 0 2042 0 1995,37 0 1946,81 0 1765,9 0 1635,25 0 1833,42 0 1910,43 0 1959,67 0 1969,6 0 2061,41 0 2093,48 0 2120,88 0 2174,56 0 2196,72 0 2350,44 0 2440,25 0 2408,64 0 2472,81 0 2407,6 0 2454,62 0 2448,05 0 2497,84 0 2645,64 0 2756,76 0 2849,27 0 2921,44 0 2981,85 0 3080,58 0 3106,22 0 3119,31 0 3061,26 0 3097,31 0 3161,69 0 3257,16 0 3277,01 0 3295,32 0 3363,99 0 3494,17 0 3667,03 0 3813,06 0 3917,96 0 3895,51 0 3801,06 0 3570,12 0 3701,61 0 3862,27 0 3970,1 0 4138,52 0 4199,75 0 4290,89 0 4443,91 0 4502,64 0 4356,98 0 4591,27 0 4696,96 0 4621,4 0 4562,84 0 4202,52 0 4296,49 0 4435,23 0 4105,18 0 4116,68 0 3844,49 1 3720,98 1 3674,4 1 3857,62 1 3801,06 1 3504,37 1 3032,6 1 3047,03 1 2962,34 1 2197,82 1 2014,45 1

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 computational 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

BEL-20[t] = + 2091.23875 -772.189431818182`Wel(1)_geen(0)_financiële_crisis`[t] + 202.302645202020M1[t] + 172.389659090909M2[t] + 105.977784090909M3[t] + 185.075909090909M4[t] + 147.012922979798M5[t] + 58.5399368686865M6[t] -3.84304924242442M7[t] -14.4649242424245M8[t] -58.4534659090913M9[t] -118.578674242424M10[t] -142.831660353536M11[t] + 18.3729861111111t + 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)	2091.23875	255.317836	8.1907	0	0
`Wel(1)_geen(0)_financiële_crisis`	-772.189431818182	237.103251	-3.2568	0.001573	0.000787
M1	202.302645202020	307.142885	0.6587	0.511742	0.255871
M2	172.389659090909	306.956936	0.5616	0.575734	0.287867
M3	105.977784090909	306.788598	0.3454	0.730542	0.365271
M4	185.075909090909	306.637902	0.6036	0.547602	0.273801
M5	147.012922979798	306.504873	0.4796	0.632607	0.316304
M6	58.5399368686865	306.389535	0.1911	0.848892	0.424446
M7	-3.84304924242442	306.291907	-0.0125	0.990016	0.495008
M8	-14.4649242424245	306.212007	-0.0472	0.962425	0.481212
M9	-58.4534659090913	306.149848	-0.1909	0.848996	0.424498
M10	-118.578674242424	306.105441	-0.3874	0.699361	0.349681
M11	-142.831660353536	306.078793	-0.4666	0.641842	0.320921
t	18.3729861111111	2.331889	7.879	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.639511886232537
R-squared	0.408975452632698
Adjusted R-squared	0.326359118054473
F-TEST (value)	4.95029771921751
F-TEST (DF numerator)	13
F-TEST (DF denominator)	93
p-value	1.55710322635727e-06
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	628.209214384781
Sum Squared Residuals	36702153.9845288

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	Interpolation Forecast	Residuals Prediction Error
1	3030.29	2311.91438131313	718.375618686866
2	2803.47	2300.37438131313	503.095618686868
3	2767.63	2252.33549242424	515.294507575758
4	2882.6	2349.80660353535	532.793396464646
5	2863.36	2330.11660353535	533.243396464647
6	2897.06	2260.01660353535	637.043396464647
7	3012.61	2216.00660353535	796.603396464647
8	3142.95	2223.75771464646	919.192285353535
9	3032.93	2198.14215909091	834.787840909091
10	3045.78	2156.38993686869	889.390063131313
11	3110.52	2150.50993686869	960.010063131314
12	3013.24	2311.71458333333	701.525416666666
13	2987.1	2532.39021464646	454.709785353536
14	2995.55	2520.85021464646	474.699785353536
15	2833.18	2472.81132575758	360.368674242424
16	2848.96	2570.28243686869	278.677563131313
17	2794.83	2550.59243686869	244.237563131313
18	2845.26	2480.49243686869	364.767563131313
19	2915.02	2436.48243686869	478.537563131313
20	2892.63	2444.2335479798	448.396452020202
21	2604.42	2418.61799242424	185.802007575758
22	2641.65	2376.86577020202	264.784229797980
23	2659.81	2370.98577020202	288.824229797980
24	2638.53	2532.19041666667	106.339583333333
25	2720.25	2752.8660479798	-32.6160479797978
26	2745.88	2741.3260479798	4.55395202020212
27	2735.7	2693.28715909091	42.4128409090909
28	2811.7	2790.75827020202	20.9417297979795
29	2799.43	2771.06827020202	28.3617297979798
30	2555.28	2700.96827020202	-145.68827020202
31	2304.98	2656.95827020202	-351.97827020202
32	2214.95	2664.70938131313	-449.759381313131
33	2065.81	2639.09382575758	-573.283825757575
34	1940.49	2597.34160353535	-656.851603535353
35	2042	2591.46160353535	-549.461603535353
36	1995.37	2752.66625	-757.29625
37	1946.81	2973.34188131313	-1026.53188131313
38	1765.9	2961.80188131313	-1195.90188131313
39	1635.25	2913.76299242424	-1278.51299242424
40	1833.42	3011.23410353535	-1177.81410353535
41	1910.43	2991.54410353535	-1081.11410353535
42	1959.67	2921.44410353535	-961.774103535353
43	1969.6	2877.43410353535	-907.834103535353
44	2061.41	2885.18521464646	-823.775214646465
45	2093.48	2859.56965909091	-766.089659090909
46	2120.88	2817.81743686869	-696.937436868687
47	2174.56	2811.93743686869	-637.377436868687
48	2196.72	2973.14208333333	-776.422083333333
49	2350.44	3193.81771464646	-843.377714646464
50	2440.25	3182.27771464646	-742.027714646465
51	2408.64	3134.23882575758	-725.598825757576
52	2472.81	3231.70993686869	-758.899936868687
53	2407.6	3212.01993686869	-804.419936868687
54	2454.62	3141.91993686869	-687.299936868687
55	2448.05	3097.90993686869	-649.859936868687
56	2497.84	3105.6610479798	-607.821047979798
57	2645.64	3080.04549242424	-434.405492424243
58	2756.76	3038.29327020202	-281.53327020202
59	2849.27	3032.41327020202	-183.143270202020
60	2921.44	3193.61791666667	-272.177916666667
61	2981.85	3414.2935479798	-432.443547979798
62	3080.58	3402.7535479798	-322.173547979798
63	3106.22	3354.71465909091	-248.494659090910
64	3119.31	3452.18577020202	-332.875770202020
65	3061.26	3432.49577020202	-371.23577020202
66	3097.31	3362.39577020202	-265.08577020202
67	3161.69	3318.38577020202	-156.695770202020
68	3257.16	3326.13688131313	-68.9768813131319
69	3277.01	3300.52132575758	-23.5113257575756
70	3295.32	3258.76910353535	36.5508964646464
71	3363.99	3252.88910353535	111.100896464646
72	3494.17	3414.09375	80.0762499999997
73	3667.03	3634.76938131313	32.2606186868692
74	3813.06	3623.22938131313	189.830618686869
75	3917.96	3575.19049242424	342.769507575758
76	3895.51	3672.66160353535	222.848396464646
77	3801.06	3652.97160353535	148.088396464646
78	3570.12	3582.87160353535	-12.7516035353539
79	3701.61	3538.86160353535	162.748396464646
80	3862.27	3546.61271464646	315.657285353535
81	3970.1	3520.99715909091	449.102840909091
82	4138.52	3479.24493686869	659.275063131313
83	4199.75	3473.36493686869	726.385063131313
84	4290.89	3634.56958333333	656.320416666667
85	4443.91	3855.24521464646	588.664785353536
86	4502.64	3843.70521464646	658.934785353536
87	4356.98	3795.66632575758	561.313674242424
88	4591.27	3893.13743686869	698.132563131314
89	4696.96	3873.44743686869	823.512563131313
90	4621.4	3803.34743686869	818.052563131313
91	4562.84	3759.33743686869	803.502563131313
92	4202.52	3767.0885479798	435.431452020202
93	4296.49	3741.47299242424	555.017007575757
94	4435.23	3699.72077020202	735.509229797979
95	4105.18	3693.84077020202	411.33922979798
96	4116.68	3855.04541666667	261.634583333333
97	3844.49	3303.53161616162	540.958383838384
98	3720.98	3291.99161616162	428.988383838384
99	3674.4	3243.95272727273	430.447272727273
100	3857.62	3341.42383838384	516.196161616161
101	3801.06	3321.73383838384	479.326161616162
102	3504.37	3251.63383838384	252.736161616161
103	3032.6	3207.62383838384	-175.023838383839
104	3047.03	3215.37494949495	-168.344949494949
105	2962.34	3189.75939393939	-227.419393939394
106	2197.82	3148.00717171717	-950.187171717171
107	2014.45	3142.12717171717	-1127.67717171717

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/11/t1229005540sqkdwled31z4gc3/1pusy1229005467.png (open in new window)

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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/11/t1229005540sqkdwled31z4gc3/2zo8g1229005467.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/11/t1229005540sqkdwled31z4gc3/31wrc1229005467.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/11/t1229005540sqkdwled31z4gc3/31wrc1229005467.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/11/t1229005540sqkdwled31z4gc3/4sbf31229005467.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/11/t1229005540sqkdwled31z4gc3/4sbf31229005467.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/11/t1229005540sqkdwled31z4gc3/57d6i1229005467.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/11/t1229005540sqkdwled31z4gc3/57d6i1229005467.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/11/t1229005540sqkdwled31z4gc3/6wqu21229005467.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/11/t1229005540sqkdwled31z4gc3/6wqu21229005467.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/11/t1229005540sqkdwled31z4gc3/7maxi1229005467.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/11/t1229005540sqkdwled31z4gc3/7maxi1229005467.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/11/t1229005540sqkdwled31z4gc3/83e0j1229005467.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/11/t1229005540sqkdwled31z4gc3/83e0j1229005467.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/11/t1229005540sqkdwled31z4gc3/9oe5s1229005467.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/11/t1229005540sqkdwled31z4gc3/9oe5s1229005467.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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')

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Software written by Ed van Stee & Patrick Wessa

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Error 001_3: History of computation (impact.txt) is not saved due to a technical problem. We are sorry for this inconveniance and will correct it A.S.A.P.