Multiple regression (with seiz, with linear)

*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, 16 Dec 2010 12:40:22 +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/16/t12925032019r9221r1wbkftog.htm/, Retrieved Thu, 16 Dec 2010 13:40:01 +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/16/t12925032019r9221r1wbkftog.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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300 2.26 302 2.57 400 3.07 392 2.76 373 2.51 379 2.87 303 3.14 324 3.11 353 3.16 392 2.47 327 2.57 376 2.89 329 2.63 359 2.38 413 1.69 338 1.96 422 2.19 390 1.87 370 1.60 367 1.63 406 1.22 418 1.21 346 1.49 350 1.64 330 1.66 318 1.77 382 1.82 337 1.78 372 1.28 422 1.29 428 1.37 426 1.12 396 1.51 458 2.24 315 2.94 337 3.09 386 3.46 352 3.64 383 4.39 439 4.15 397 5.21 453 5.80 363 5.91 365 5.39 474 5.46 373 4.72 403 3.14 384 2.63 364 2.32 361 1.93 419 0.62 352 0.60 363 -0.37 410 -1.10 361 -1.68 383 -0.78 342 -1.19 369 -0.79 361 -0.12 317 0.26 386 0.62 318 0.70 407 1.66 393 1.80 404 2.27 498 2.46 438 2.57

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 5 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Aantal_vergunningen[t] = + 314.705816342766 + 5.96101603224808Inflatie[t] -0.418563909059995M1[t] -15.3350853480929M2[t] + 49.3631559583583M3[t] + 23.3517418272819M4[t] + 35.9352203882489M5[t] + 71.9590887888935M6[t] + 23.3604882049137M7[t] + 23.0881467901967M8[t] + 43.9476151187114M9[t] + 51.4070834472261M10[t] -1.10570576335502M11[t] + 0.71011466548467t + 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) 314.705816342766 18.309283 17.1883 0 0 Inflatie 5.96101603224808 2.61961 2.2755 0.026943 0.013472 M1 -0.418563909059995 20.151655 -0.0208 0.983507 0.491753 M2 -15.3350853480929 20.141369 -0.7614 0.449809 0.224905 M3 49.3631559583583 20.133852 2.4517 0.017545 0.008773 M4 23.3517418272819 20.128185 1.1602 0.251187 0.125593 M5 35.9352203882489 20.125294 1.7856 0.07989 0.039945 M6 71.9590887888935 20.125194 3.5756 0.000756 0.000378 M7 23.3604882049137 20.12558 1.1607 0.250951 0.125475 M8 23.0881467901967 21.036781 1.0975 0.277378 0.138689 M9 43.9476151187114 21.030892 2.0897 0.041463 0.020731 M10 51.4070834472261 21.027652 2.4447 0.017854 0.008927 M11 -1.10570576335502 21.021815 -0.0526 0.95825 0.479125 t 0.71011466548467 0.218233 3.2539 0.001984 0.000992 Multiple Linear Regression - Regression Statistics Multiple R 0.707630098284765 R-squared 0.500740355998506 Adjusted R-squared 0.378280443318894 F-TEST (value) 4.08901447862843 F-TEST (DF numerator) 13 F-TEST (DF denominator) 53 p-value 0.000122121050988078 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 33.2330516823352 Sum Squared Residuals 58535.0933784005 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 300 328.469263332072 -28.469263332072 2 302 316.110771528520 -14.1107715285204 3 400 384.49963551658 15.5003644834197 4 392 357.350421080992 34.6495789190083 5 373 369.153760299381 3.84623970061865 6 379 408.03370913712 -29.0337091371199 7 303 361.754697547332 -58.7546975473317 8 324 362.013640317132 -38.013640317132 9 353 383.881274112744 -30.8812741127438 10 392 387.937756044492 4.06224395550801 11 327 336.73118310262 -9.73118310262034 12 376 340.454528661779 35.5454713382206 13 329 339.196215249820 -10.1962152498196 14 359 323.499554468209 35.5004455317907 15 413 384.794809377894 28.205190622106 16 338 361.102984241009 -23.1029842410093 17 422 375.767611154878 46.232388845122 18 390 410.594069090688 -20.5940690906878 19 370 361.096108843486 8.90389115651424 20 367 361.712712575221 5.28728742477916 21 406 380.838278995999 25.1617210040015 22 418 388.948251829675 29.0517481703246 23 346 338.814661773608 7.18533822639155 24 350 341.524634607285 8.47536539271465 25 330 341.935405684355 -11.9354056843550 26 318 328.384710674354 -10.384710674354 27 382 394.091117447902 -12.0911174479023 28 337 368.551377341021 -31.5513773410207 29 372 378.864462551348 -6.86446255134831 30 422 415.6580557778 6.34194422220001 31 428 368.246451141885 59.7535488581153 32 426 367.193970384590 58.8060296154096 33 396 391.088349631166 4.91165036883351 34 458 403.609474328707 54.390525671293 35 315 355.979511006184 -40.9795110061842 36 337 358.689483839861 -21.6894838398611 37 386 361.186610528218 24.8133894717825 38 352 348.053186640474 3.94681335952606 39 383 417.932304636596 -34.9323046365959 40 439 391.200361323265 47.7996386767354 41 397 410.812631543899 -13.8126315438993 42 453 451.063614069055 1.93638593094517 43 363 403.830839914107 -40.830839914107 44 365 401.168884828106 -36.1688848281057 45 474 423.155738944362 50.8442610556375 46 373 426.914170074498 -53.9141700744983 47 403 365.69309019845 37.3069098015502 48 384 364.468792450843 19.5312075491570 49 364 362.912428237271 1.08757176272920 50 361 346.381225211146 14.6187747888542 51 419 403.980650180837 15.0193498191633 52 352 378.5601303946 -26.5601303946 53 363 386.071538069771 -23.0715380697711 54 410 418.453979432359 -8.45397943235916 55 361 367.10810421516 -6.10810421516018 56 383 372.910791894951 10.0892081050489 57 342 392.036358315729 -50.0363583157288 58 369 402.590347722627 -33.5903477226274 59 361 354.781553919137 6.21844608086284 60 317 358.862560440231 -41.8625604402311 61 386 361.300076968265 24.6999230317349 62 318 347.570551477297 -29.5705514772967 63 407 418.701482840191 -11.7014828401907 64 393 394.234725619114 -1.23472561911373 65 404 410.329996380722 -6.32999638072201 66 498 448.196572492978 49.8034275070217 67 438 400.963798338031 37.0362016619695 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.56929676168561 0.86140647662878 0.43070323831439 18 0.412020123100505 0.82404024620101 0.587979876899495 19 0.495305231772272 0.990610463544545 0.504694768227728 20 0.379622251585633 0.759244503171266 0.620377748414367 21 0.286928909849975 0.57385781969995 0.713071090150025 22 0.201884306963993 0.403768613927985 0.798115693036007 23 0.131074321712162 0.262148643424324 0.868925678287838 24 0.154362486295327 0.308724972590653 0.845637513704673 25 0.112083688248553 0.224167376497106 0.887916311751447 26 0.101953413088870 0.203906826177739 0.89804658691113 27 0.092824449851827 0.185648899703654 0.907175550148173 28 0.0913115243018165 0.182623048603633 0.908688475698184 29 0.077530165239682 0.155060330479364 0.922469834760318 30 0.0608778468304469 0.121755693660894 0.939122153169553 31 0.155700237881196 0.311400475762393 0.844299762118804 32 0.236651328810402 0.473302657620804 0.763348671189598 33 0.172272672724867 0.344545345449734 0.827727327275133 34 0.387980557080144 0.775961114160288 0.612019442919856 35 0.400086245549978 0.800172491099956 0.599913754450022 36 0.327502699552067 0.655005399104134 0.672497300447933 37 0.362831993782429 0.725663987564858 0.637168006217571 38 0.288705708744559 0.577411417489119 0.71129429125544 39 0.257202611071301 0.514405222142602 0.742797388928699 40 0.420696477742933 0.841392955485866 0.579303522257067 41 0.330176995728719 0.660353991457438 0.669823004271281 42 0.280370060392104 0.560740120784207 0.719629939607896 43 0.393558662343992 0.787117324687985 0.606441337656008 44 0.647274916354759 0.705450167290481 0.352725083645241 45 0.731228591265982 0.537542817468035 0.268771408734018 46 0.909532476873222 0.180935046253557 0.0904675231267783 47 0.863329880373375 0.273340239253251 0.136670119626625 48 0.818920469175205 0.362159061649591 0.181079530824795 49 0.939200088793316 0.121599822413368 0.060799911206684 50 0.848659292452518 0.302681415094963 0.151340707547482 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 0 0 OK 10% type I error level 0 0 OK

Charts produced by software:

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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) 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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