mutiple regression

*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: Mon, 14 Dec 2009 12:31:04 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/14/t1260819123nahf0mr00er817u.htm/, Retrieved Mon, 14 Dec 2009 20:32:15 +0100

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/2009/Dec/14/t1260819123nahf0mr00er817u.htm/}, year = {2009}, } @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 = {2009}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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2058,00 0 2160,00 0 2260,00 0 2498,00 0 2695,00 0 2799,00 0 2947,00 0 2930,00 0 2318,00 0 2540,00 0 2570,00 0 2669,00 0 2450,00 0 2842,00 0 3440,00 0 2678,00 0 2981,00 0 2260,00 0 2844,00 0 2546,00 0 2456,00 0 2295,00 0 2379,00 0 2479,00 0 2057,00 0 2280,00 0 2351,00 0 2276,00 0 2548,00 0 2311,00 0 2201,00 0 2725,00 0 2408,00 0 2139,00 0 1898,00 0 2537,00 0 2069,00 0 2063,00 0 2526,00 0 2440,00 0 2191,00 0 2797,00 0 2074,00 0 2628,00 0 2287,00 0 2146,00 0 2430,00 1 2141,00 1 1827,00 1 2082,00 1 1788,00 1 1743,00 1 2245,00 1 1963,00 1 1828,00 1 2527,00 1 2114,00 1 2424,00 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Bouwvergunningen[t] = + 2746.77616279070 -111.695736434109dummy_1[t] -413.610158268736M1[t] -211.665083979328M2[t] -15.3200096899224M3[t] -152.574935400517M4[t] + 61.1701388888889M5[t] -36.0847868217053M6[t] -74.5397125322998M7[t] + 226.605361757106M8[t] -119.249563953488M9[t] -118.304489664083M10[t] -145.995074289406M11[t] -8.74507428940567t + 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) 2746.77616279070 156.950099 17.501 0 0 dummy_1 -111.695736434109 127.570665 -0.8756 0.386024 0.193012 M1 -413.610158268736 185.732139 -2.2269 0.031118 0.015559 M2 -211.665083979328 185.571927 -1.1406 0.260203 0.130102 M3 -15.3200096899224 185.464211 -0.0826 0.934541 0.467271 M4 -152.574935400517 185.409083 -0.8229 0.414997 0.207499 M5 61.1701388888889 185.40659 0.3299 0.743023 0.371511 M6 -36.0847868217053 185.456733 -0.1946 0.846623 0.423312 M7 -74.5397125322998 185.55947 -0.4017 0.689847 0.344924 M8 226.605361757106 185.714714 1.2202 0.228896 0.114448 M9 -119.249563953488 185.922333 -0.6414 0.524594 0.262297 M10 -118.304489664083 186.182152 -0.6354 0.528443 0.264222 M11 -145.995074289406 195.39788 -0.7472 0.458936 0.229468 t -8.74507428940567 3.124173 -2.7992 0.007579 0.003789 Multiple Linear Regression - Regression Statistics Multiple R 0.687985427411683 R-squared 0.473323948330836 Adjusted R-squared 0.317715114883128 F-TEST (value) 3.04175500737172 F-TEST (DF numerator) 13 F-TEST (DF denominator) 44 p-value 0.00288549698944451 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 276.299008771407 Sum Squared Residuals 3359010.25891473 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 2058 2324.42093023257 -266.420930232565 2 2160 2517.62093023256 -357.620930232557 3 2260 2705.22093023256 -445.220930232558 4 2498 2559.22093023256 -61.2209302325575 5 2695 2764.22093023256 -69.2209302325579 6 2799 2658.22093023256 140.779069767443 7 2947 2611.02093023256 335.979069767442 8 2930 2903.42093023256 26.5790697674421 9 2318 2548.82093023256 -230.820930232558 10 2540 2541.02093023256 -1.02093023255754 11 2570 2504.58527131783 65.4147286821708 12 2669 2641.83527131783 27.1647286821708 13 2450 2219.48003875969 230.519961240312 14 2842 2412.68003875969 429.319961240311 15 3440 2600.28003875969 839.71996124031 16 2678 2454.28003875969 223.71996124031 17 2981 2659.28003875969 321.71996124031 18 2260 2553.28003875969 -293.28003875969 19 2844 2506.08003875969 337.91996124031 20 2546 2798.48003875969 -252.480038759690 21 2456 2443.88003875969 12.1199612403102 22 2295 2436.08003875969 -141.080038759690 23 2379 2399.64437984496 -20.6443798449612 24 2479 2536.89437984496 -57.8943798449613 25 2057 2114.53914728682 -57.53914728682 26 2280 2307.73914728682 -27.7391472868218 27 2351 2495.33914728682 -144.339147286822 28 2276 2349.33914728682 -73.339147286822 29 2548 2554.33914728682 -6.33914728682182 30 2311 2448.33914728682 -137.339147286822 31 2201 2401.13914728682 -200.139147286822 32 2725 2693.53914728682 31.4608527131782 33 2408 2338.93914728682 69.0608527131781 34 2139 2331.13914728682 -192.139147286822 35 1898 2294.70348837209 -396.703488372093 36 2537 2431.95348837209 105.046511627907 37 2069 2009.59825581395 59.4017441860479 38 2063 2202.79825581395 -139.798255813954 39 2526 2390.39825581395 135.601744186046 40 2440 2244.39825581395 195.601744186046 41 2191 2449.39825581395 -258.398255813954 42 2797 2343.39825581395 453.601744186046 43 2074 2296.19825581395 -222.198255813954 44 2628 2588.59825581395 39.4017441860462 45 2287 2233.99825581395 53.0017441860461 46 2146 2226.19825581395 -80.198255813954 47 2430 2078.06686046512 351.933139534884 48 2141 2215.31686046512 -74.3168604651164 49 1827 1792.96162790698 34.0383720930248 50 2082 1986.16162790698 95.838372093023 51 1788 2173.76162790698 -385.761627906977 52 1743 2027.76162790698 -284.761627906977 53 2245 2232.76162790698 12.2383720930231 54 1963 2126.76162790698 -163.761627906977 55 1828 2079.56162790698 -251.561627906977 56 2527 2371.96162790698 155.038372093023 57 2114 2017.36162790698 96.638372093023 58 2424 2009.56162790698 414.438372093023 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.8564945622655 0.287010875469001 0.143505437734500 18 0.983725741204659 0.0325485175906820 0.0162742587953410 19 0.992765632237776 0.0144687355244478 0.00723436776222388 20 0.994632287554137 0.0107354248917264 0.00536771244586318 21 0.988199760823237 0.0236004783535265 0.0118002391767632 22 0.98337956905313 0.0332408618937412 0.0166204309468706 23 0.973799763271394 0.0524004734572127 0.0262002367286064 24 0.958420849528695 0.0831583009426097 0.0415791504713049 25 0.9399365641622 0.120126871675599 0.0600634358377994 26 0.91307557884393 0.173848842312142 0.086924421156071 27 0.903283754387741 0.193432491224518 0.0967162456122591 28 0.861633502025694 0.276732995948613 0.138366497974306 29 0.820227464719159 0.359545070561682 0.179772535280841 30 0.75544502032361 0.48910995935278 0.24455497967639 31 0.74834567178344 0.50330865643312 0.25165432821656 32 0.663610039904022 0.672779920191956 0.336389960095978 33 0.596273084881621 0.807453830236758 0.403726915118379 34 0.489713027527454 0.979426055054909 0.510286972472546 35 0.677314043885993 0.645371912228014 0.322685956114007 36 0.574246446629395 0.85150710674121 0.425753553370605 37 0.452827977182901 0.905655954365802 0.547172022817099 38 0.378852466165731 0.757704932331462 0.621147533834269 39 0.364076310861939 0.728152621723877 0.635923689138061 40 0.378163982225932 0.756327964451863 0.621836017774068 41 0.282762420412543 0.565524840825085 0.717237579587457 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 5 0.2 NOK 10% type I error level 7 0.28 NOK

Charts produced by software:

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Parameters (Session):

par1 = Industriële omzetcijfers volgens BTW ; par2 = ADSEI ; par3 = maandelijkse industriële omzet volgens BTW in België ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = 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$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='') } } myeq <- paste(myeq, ' + e[t]') a<-table.row.start(a) a<-table.element(a, myeq) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Variable',header=TRUE) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'S.D.',header=TRUE) a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE) a<-table.element(a,'2-tail p-value',header=TRUE) a<-table.element(a,'1-tail p-value',header=TRUE) a<-table.row.end(a) for (i in 1:k){ a<-table.row.start(a) a<-table.element(a,rownames(mysum$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') 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') }

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