paper

*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: Tue, 28 Dec 2010 18:22:03 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/28/t1293560820cdsv2tawsjj10dl.htm/, Retrieved Tue, 28 Dec 2010 19:27:11 +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/2010/Dec/28/t1293560820cdsv2tawsjj10dl.htm/}, year = {2010}, } @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 = {2010}, 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:

multiple regression met dummy

Dataseries X:

» Textbox « » Textfile « » CSV «

0 1 0 18919 921365 0 48873 0 137852 0 0 2 0 19147 987921 0 52118 0 145224 0 0 3 0 21518 1132614 0 60530 0 163575 0 0 4 0 20941 1332224 0 55644 0 190761 0 0 5 0 22401 1418133 0 57121 0 196562 0 0 6 0 22181 1411549 0 55697 0 204493 0 0 7 0 22494 1695920 0 56483 0 259479 0 0 8 0 21479 1636173 0 51541 0 259479 0 0 9 0 22322 1539653 0 56328 0 223164 0 0 10 0 21829 1395314 0 54349 0 194886 0 0 11 0 20370 1127575 0 59885 0 160407 0 0 12 0 18467 1036076 0 55806 0 151747 0 0 13 0 18780 989236 0 54559 0 152448 0 0 14 0 18815 1008380 0 55590 0 148388 0 0 15 0 20881 1207763 0 63442 0 168510 0 0 16 0 21443 1368839 0 61258 0 188041 0 0 17 0 22333 1469798 0 55829 0 192020 0 0 18 0 22944 1498721 0 58023 0 205250 0 0 19 0 22536 1761769 0 58887 0 261642 0 0 20 0 21658 1653214 0 51510 0 251614 0 0 21 0 23035 1599104 0 60006 0 222726 0 0 22 0 21969 1421179 0 60831 0 179039 0 0 23 0 20297 1163995 0 61559 0 151462 0 0 24 0 18564 1037735 0 61325 0 143653 0 0 25 0 18844 1015407 0 55222 0 143762 0 0 26 0 18 etc...

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 7 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation bewegingen[t] = + 11104.6440399319 + 4225.56576238093Jaar[t] -37.3481020578114t -49.6789568610272jaar_t[t] + 0.0109958091107766passagiers[t] + 0.00336145250419538passagiers_t[t] + 0.0515622341305363cargo[t] -0.0196435832213318cargo_t[t] -0.0374540787285641auto[t] -0.0295962326254998auto_t[t] + 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) 11104.6440399319 1244.838992 8.9205 0 0 Jaar 4225.56576238093 4831.015093 0.8747 0.385127 0.192563 t -37.3481020578114 9.532235 -3.9181 0.000225 0.000113 jaar_t -49.6789568610272 49.364245 -1.0064 0.318147 0.159073 passagiers 0.0109958091107766 0.001325 8.3011 0 0 passagiers_t 0.00336145250419538 0.003192 1.0532 0.29632 0.14816 cargo 0.0515622341305363 0.01946 2.6497 0.010209 0.005104 cargo_t -0.0196435832213318 0.044203 -0.4444 0.658301 0.329151 auto -0.0374540787285641 0.008846 -4.2338 7.7e-05 3.9e-05 auto_t -0.0295962326254998 0.024193 -1.2233 0.225838 0.112919 Multiple Linear Regression - Regression Statistics Multiple R 0.94165624630337 R-squared 0.886716486202154 Adjusted R-squared 0.870272105166983 F-TEST (value) 53.9221564074471 F-TEST (DF numerator) 9 F-TEST (DF denominator) 62 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 670.047183907392 Sum Squared Residuals 27835720.1770580 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 18919 18555.3310069964 363.668993003559 2 19147 19141.0279574821 5.97204251794675 3 21518 20441.1181778480 1076.88182215197 4 20941 21328.4838721158 -387.483872115797 5 22401 22094.6610440621 306.338955937896 6 22181 21614.4436150208 566.556384979197 7 22494 22685.0626886614 -191.062688661422 8 21479 21735.9274185889 -256.927418588930 9 22322 22244.2371049696 77.7628950303554 10 21829 21576.8496886135 252.150311386548 11 20370 20172.3223596742 197.677640325765 12 18467 19242.8986885604 -775.898688560384 13 18780 18599.9534726043 180.046527395706 14 18815 18978.3333631897 -163.333363189744 15 20881 20784.5783592827 96.4216407172934 16 21443 21674.2636745637 -231.263674563671 17 22333 22318.0803161651 14.9196838348845 18 22944 22216.3740811218 727.625918878211 19 22536 23003.8909366631 -467.890936663138 20 21658 21768.1076768940 -110.107676894047 21 23035 22655.8225113359 379.17748866409 22 21969 22340.8402538156 -371.840253815644 23 20297 20545.9544169565 -248.954416956506 24 18564 19400.6887945769 -836.688794576853 25 18844 18799.0594572135 44.940542786454 26 18762 19426.5413950871 -664.54139508708 27 21757 21145.7198600340 611.28013996602 28 20501 22575.1302040895 -2074.13020408946 29 23181 22978.8480551971 202.151944802869 30 23015 22527.5310330018 487.468966998222 31 22828 23120.4399779674 -292.439977967374 32 21597 21839.0495621093 -242.049562109254 33 23005 22710.9112370132 294.088762986786 34 22243 22498.4625016093 -255.462501609251 35 20729 20638.76199431 90.2380056899998 36 18310 19301.6764464270 -991.67644642702 37 19427 18554.9702375451 872.02976245489 38 18849 19031.4925545623 -182.492554562350 39 21817 21418.1363676459 398.863632354125 40 21101 22034.4683189930 -933.468318992965 41 23546 22593.1026146929 952.897385307086 42 23456 22743.6563797771 712.343620222933 43 23649 23720.9936457563 -71.993645756309 44 22432 22816.4368286502 -384.436828650181 45 23745 23807.3008014867 -62.3008014867034 46 23874 23485.8935887218 388.106411278185 47 22327 21780.7633530731 546.236646926939 48 20143 20703.3782942684 -560.378294268416 49 21252 20085.9515321389 1166.04846786112 50 21094 20973.507225444 120.492774556011 51 21800 22615.1019826587 -815.10198265867 52 22480 22485.8420505919 -5.84205059186684 53 23055 23228.6283092016 -173.628309201624 54 23352 22732.9927109704 619.007289029602 55 23171 22774.1358939866 396.864106013363 56 20691 22333.769207359 -1642.76920735899 57 23183 22793.1973953809 389.802604619092 58 22412 21865.2876420195 546.712357980542 59 18958 19167.6627331343 -209.662733134293 60 17347 17947.5296721796 -600.529672179646 61 17353 16940.4520812548 412.547918745207 62 17153 17141.9139150346 11.0860849654209 63 20141 18961.2224691768 1179.77753082321 64 19699 20823.6810222511 -1124.68102225113 65 20780 20676.1556892508 103.844310749235 66 21101 19541.7670218074 1559.23297819263 67 20871 20881.1668916059 -10.1668916059027 68 19574 19869.8784740707 -295.878474070695 69 21002 20605.9506013822 396.049398617784 70 20105 20114.3302055639 -9.33020556393274 71 17772 18090.3079986607 -318.307998660669 72 16117 16901.5910858812 -784.591085881226 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 13 0.664892290671711 0.670215418656578 0.335107709328289 14 0.500076251048607 0.999847497902786 0.499923748951393 15 0.353576271939736 0.707152543879473 0.646423728060264 16 0.23718085217888 0.47436170435776 0.76281914782112 17 0.164223931891956 0.328447863783912 0.835776068108044 18 0.226367272739826 0.452734545479652 0.773632727260174 19 0.154305599889973 0.308611199779946 0.845694400110027 20 0.114916036936252 0.229832073872505 0.885083963063748 21 0.0892707625731197 0.178541525146239 0.91072923742688 22 0.0749417367223979 0.149883473444796 0.925058263277602 23 0.046993522358498 0.093987044716996 0.953006477641502 24 0.0403560789136637 0.0807121578273274 0.959643921086336 25 0.0322788589739702 0.0645577179479405 0.96772114102603 26 0.0229429801567477 0.0458859603134953 0.977057019843252 27 0.0313025383084250 0.0626050766168501 0.968697461691575 28 0.290049815414872 0.580099630829743 0.709950184585128 29 0.295694845314811 0.591389690629622 0.704305154685189 30 0.317585261941436 0.635170523882873 0.682414738058564 31 0.251159938373824 0.502319876747648 0.748840061626176 32 0.196925422066634 0.393850844133268 0.803074577933366 33 0.170780861280610 0.341561722561220 0.82921913871939 34 0.125645705810713 0.251291411621426 0.874354294189287 35 0.0929610907930724 0.185922181586145 0.907038909206928 36 0.113176568559355 0.226353137118710 0.886823431440645 37 0.165016897773254 0.330033795546508 0.834983102226746 38 0.135671465587804 0.271342931175607 0.864328534412196 39 0.109086572151602 0.218173144303203 0.890913427848398 40 0.219881470930314 0.439762941860628 0.780118529069686 41 0.259032679546161 0.518065359092321 0.74096732045384 42 0.229833677381987 0.459667354763974 0.770166322618013 43 0.176468102352210 0.352936204704420 0.82353189764779 44 0.135750805963982 0.271501611927963 0.864249194036018 45 0.101863558339443 0.203727116678885 0.898136441660557 46 0.0734145081955161 0.146829016391032 0.926585491804484 47 0.0919322638189173 0.183864527637835 0.908067736181083 48 0.0749377859106163 0.149875571821233 0.925062214089384 49 0.0776472433813037 0.155294486762607 0.922352756618696 50 0.0500792527508653 0.100158505501731 0.949920747249135 51 0.0394231541892622 0.0788463083785244 0.960576845810738 52 0.0234062021188885 0.0468124042377769 0.976593797881112 53 0.0129796821069569 0.0259593642139138 0.987020317893043 54 0.00799966175331742 0.0159993235066348 0.992000338246683 55 0.0045954533838444 0.0091909067676888 0.995404546616156 56 0.0256011667163313 0.0512023334326626 0.974398833283669 57 0.0126732776909126 0.0253465553818252 0.987326722309087 58 0.00559535925205232 0.0111907185041046 0.994404640747948 59 0.0031549396642941 0.0063098793285882 0.996845060335706 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 2 0.0425531914893617 NOK 5% type I error level 8 0.170212765957447 NOK 10% type I error level 14 0.297872340425532 NOK

Charts produced by software:

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Parameters (Session):

par1 = 4 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 4 ; 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$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='') } } myeq <- paste(myeq, ' + e[t]') a<-table.row.start(a) a<-table.element(a, myeq) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Variable',header=TRUE) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'S.D.',header=TRUE) a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE) a<-table.element(a,'2-tail p-value',header=TRUE) a<-table.element(a,'1-tail p-value',header=TRUE) a<-table.row.end(a) for (i in 1:k){ a<-table.row.start(a) a<-table.element(a,rownames(mysum$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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