*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: Sat, 11 Dec 2010 18:46:03 +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/11/t1292093077d2yw4vs6ykov6py.htm/, Retrieved Sat, 11 Dec 2010 19:44:47 +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/11/t1292093077d2yw4vs6ykov6py.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:

Dataseries X:

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356 182 89 386 213 97 444 227 154 387 209 81 327 219 110 448 221 116 225 114 73 182 97 73 460 205 174 411 215 103 342 224 130 361 189 91 377 182 136 331 201 106 428 198 136 340 173 122 352 238 131 461 258 135 221 122 75 198 101 68 422 259 143 329 243 115 320 188 93 375 173 128 364 224 152 351 215 125 380 196 107 319 159 116 322 187 220 386 208 137 221 131 34 187 93 51 344 210 153 342 228 145 365 176 116 313 195 145 356 188 98 337 188 118 389 190 139 326 188 140 343 176 113 357 225 149 220 93 79 218 79 47 391 235 166 425 247 180 332 195 122 298 197 134 360 211 114 336 156 125 325 209 181 393 180 142 301 185 143 426 303 187 265 129 137 210 85 62 429 249 239 440 231 157 357 212 139 431 240 187 442 234 99 442 217 146 544 287 175 420 221 148 396 208 130 482 241 183 261 156 115 211 96 80 448 320 223 468 242 131 464 227 201 425 200 157

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 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Vlaanderen[t] = + 86.9586400040947 + 1.23220559598646`Wallonië`[t] + 0.215180265869656Brussel[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) 86.9586400040947 20.028099 4.3418 4.7e-05 2.4e-05 `Wallonië` 1.23220559598646 0.142653 8.6378 0 0 Brussel 0.215180265869656 0.174624 1.2322 0.22204 0.11102 Multiple Linear Regression - Regression Statistics Multiple R 0.857834973293507 R-squared 0.735880841405472 Adjusted R-squared 0.728225213620123 F-TEST (value) 96.1228604679297 F-TEST (DF numerator) 2 F-TEST (DF denominator) 69 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 41.4333614395668 Sum Squared Residuals 118453.917372543 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 356 330.371102136030 25.6288978639695 2 386 370.290917738568 15.7090822614322 3 444 399.807071236949 44.1929287630512 4 387 361.919211100708 25.0807888992925 5 327 380.481494770792 -53.4814947707922 6 448 384.236987557983 63.763012442017 7 225 243.138237355036 -18.1382373550363 8 182 222.190742223266 -40.1907422232665 9 460 377.00215344264 82.9978465573603 10 411 374.046410525759 36.9535894742413 11 342 390.946128068118 -48.9461280681176 12 361 339.426901839675 21.5730981603252 13 377 340.484574631904 36.5154253680959 14 331 357.441072979557 -26.4410729795572 15 428 360.199864167688 67.8001358323124 16 340 326.382200545851 13.6177994541492 17 352 408.412186677798 -56.4121866777978 18 461 433.917019661006 27.0829803389943 19 221 253.426242654667 -32.4262426546673 20 198 226.043663277864 -28.0436632778640 21 422 436.870667383949 -14.8706673839494 22 329 411.130330403816 -82.1303304038156 23 320 338.625056775428 -18.6250567754277 24 375 327.673282141069 47.3267178589313 25 364 395.68009391725 -31.6800939172501 26 351 378.780376374891 -27.7803763748912 27 380 351.495225265495 28.5047747345054 28 319 307.840240606822 11.1597593931776 29 322 364.720744944888 -42.7207449448876 30 386 372.737100393422 13.2628996065782 31 221 255.693702117890 -34.6937021178896 32 187 212.527953990188 -25.5279539901882 33 344 378.644395839309 -34.6443958393092 34 342 399.102654440108 -57.1026544401083 35 365 328.787735738592 36.2122642614078 36 313 358.439869772555 -45.4398697725551 37 356 339.700958104776 16.2990418952240 38 337 344.004563422169 -7.0045634221691 39 389 350.987760197405 38.0122398025952 40 326 348.738529271302 -22.7385292713015 41 343 328.142194940983 14.8578050590167 42 357 396.266758715628 -39.2667587156276 43 220 218.553001434539 1.44699856546146 44 218 194.416354582899 23.5836454171009 45 391 412.246879195276 -21.2468791952763 46 425 430.045870069289 -5.04587006928909 47 332 353.490723657553 -21.4907236575530 48 298 358.537298039962 -60.5372980399618 49 360 371.484571066379 -11.4845710663791 50 336 306.08024621169 29.9197537883101 51 325 383.437237687673 -58.4372376876732 52 393 339.311245035149 53.6887549648508 53 301 345.687453280951 -44.6874532809511 54 426 500.555645305619 -74.5556453056186 55 265 275.392858310491 -10.3928583104913 56 210 205.037292146863 4.9627078531373 57 429 445.205916947572 -16.2059169475718 58 440 405.381434418504 34.6185655814964 59 357 378.096283309107 -21.096283309107 60 431 422.926692758471 8.07330724152855 61 442 396.597595786023 45.4024042139771 62 442 385.763573150127 56.2364268498731 63 544 478.258192579399 65.7418074206007 64 420 391.122756065812 28.8772439341879 65 396 371.230838532334 24.7691614676658 66 482 423.298177290979 58.7018227090207 67 261 303.928443552993 -42.9284435529933 68 211 222.464798488368 -11.4647984883676 69 448 529.249630008696 -81.249630008696 70 468 413.341009061744 54.6589909382564 71 464 409.920543732823 54.0794562671774 72 425 367.183060942923 57.8169390570768 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 6 0.759060281570113 0.481879436859774 0.240939718429887 7 0.652132384360399 0.695735231279202 0.347867615639601 8 0.538894987922612 0.922210024154776 0.461105012077388 9 0.509162729141888 0.981674541716223 0.490837270858112 10 0.416684413400884 0.833368826801768 0.583315586599116 11 0.708643441167009 0.582713117665981 0.291356558832991 12 0.633563315445071 0.732873369109857 0.366436684554929 13 0.552048851384107 0.895902297231786 0.447951148615893 14 0.530283227601438 0.939433544797124 0.469716772398562 15 0.548371502213831 0.903256995572338 0.451628497786169 16 0.462858923523821 0.925717847047641 0.53714107647618 17 0.67061216580384 0.65877566839232 0.32938783419616 18 0.603270242871023 0.793459514257954 0.396729757128977 19 0.548808301269428 0.902383397461143 0.451191698730571 20 0.481448699329475 0.96289739865895 0.518551300670525 21 0.464814192194541 0.929628384389082 0.535185807805459 22 0.685614864921974 0.628770270156051 0.314385135078026 23 0.623627574782897 0.752744850434206 0.376372425217103 24 0.601687219976111 0.796625560047777 0.398312780023889 25 0.64156999092858 0.716860018142841 0.358430009071420 26 0.614178411160342 0.771643177679316 0.385821588839658 27 0.577699041582131 0.844601916835738 0.422300958417869 28 0.507741260590869 0.984517478818262 0.492258739409131 29 0.628493283497198 0.743013433005605 0.371506716502802 30 0.563860450705576 0.872279098588849 0.436139549294424 31 0.535412931808378 0.929174136383244 0.464587068191622 32 0.491102781552647 0.982205563105293 0.508897218447353 33 0.47856147060984 0.95712294121968 0.52143852939016 34 0.552479146382333 0.895041707235334 0.447520853617667 35 0.530051598414301 0.939896803171397 0.469948401585699 36 0.545322812574414 0.909354374851173 0.454677187425586 37 0.484159615175062 0.968319230350123 0.515840384824938 38 0.419067175750518 0.838134351501036 0.580932824249482 39 0.401598248661878 0.803196497323756 0.598401751338122 40 0.35610822848396 0.71221645696792 0.64389177151604 41 0.298360913826166 0.596721827652332 0.701639086173834 42 0.297078100205677 0.594156200411353 0.702921899794323 43 0.240331580212594 0.480663160425189 0.759668419787406 44 0.199648153908241 0.399296307816483 0.800351846091759 45 0.164915392352372 0.329830784704745 0.835084607647627 46 0.124405827621739 0.248811655243477 0.875594172378261 47 0.102791336872274 0.205582673744547 0.897208663127726 48 0.152114254476135 0.304228508952271 0.847885745523865 49 0.125688902147935 0.25137780429587 0.874311097852065 50 0.102145487401737 0.204290974803473 0.897854512598263 51 0.129701589099069 0.259403178198139 0.87029841090093 52 0.142380003678013 0.284760007356025 0.857619996321987 53 0.157335742917031 0.314671485834062 0.842664257082969 54 0.369896590311134 0.739793180622269 0.630103409688866 55 0.296750290119870 0.593500580239741 0.70324970988013 56 0.229576486812867 0.459152973625735 0.770423513187133 57 0.176002239481633 0.352004478963266 0.823997760518367 58 0.138726496171919 0.277452992343838 0.861273503828081 59 0.130231418143649 0.260462836287298 0.86976858185635 60 0.0894649236640546 0.178929847328109 0.910535076335945 61 0.0645683172658091 0.129136634531618 0.93543168273419 62 0.0567473456820624 0.113494691364125 0.943252654317938 63 0.0626085847420472 0.125217169484094 0.937391415257953 64 0.0372512596963209 0.0745025193926418 0.96274874030368 65 0.0196199202201570 0.0392398404403139 0.980380079779843 66 0.0179278055452604 0.0358556110905208 0.98207219445474 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 2 0.0327868852459016 OK 10% type I error level 3 0.0491803278688525 OK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; 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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