paper: Multiple Regression (t-24)

*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: Sun, 19 Dec 2010 10:14:36 +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/19/t129275362136m7llb7omex99n.htm/, Retrieved Sun, 19 Dec 2010 11:13:41 +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/19/t129275362136m7llb7omex99n.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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591 0 595 594 611 613 562 519 589 0 591 595 594 611 561 517 584 0 589 591 595 594 555 510 573 0 584 589 591 595 544 509 567 0 573 584 589 591 537 501 569 0 567 573 584 589 543 507 621 0 569 567 573 584 594 569 629 0 621 569 567 573 611 580 628 0 629 621 569 567 613 578 612 0 628 629 621 569 611 565 595 0 612 628 629 621 594 547 597 0 595 612 628 629 595 555 593 0 597 595 612 628 591 562 590 0 593 597 595 612 589 561 580 0 590 593 597 595 584 555 574 0 580 590 593 597 573 544 573 0 574 580 590 593 567 537 573 0 573 574 580 590 569 543 620 0 573 573 574 580 621 594 626 0 620 573 573 574 629 611 620 0 626 620 573 573 628 613 588 0 620 626 620 573 612 611 566 0 588 620 626 620 595 594 557 0 566 588 620 626 597 595 561 0 557 566 588 620 593 591 549 0 561 557 566 588 590 589 532 0 549 561 557 566 580 584 526 0 532 549 561 557 574 573 511 0 526 532 549 561 573 567 499 0 511 526 532 549 573 569 555 1 499 511 526 532 620 621 565 1 555 499 511 526 626 629 542 1 565 555 499 511 620 628 5 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 5 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 R Framework error message The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'. Multiple Linear Regression - Estimated Regression Equation Totaal[t] = + 121.350385460641 + 15.4495309520155crisis[t] + 1.07950932409880`t-1`[t] -0.50927530639777`t-2`[t] + 0.0759563844468494`t-3`[t] + 0.0672167107393819`t-4`[t] + 0.440072107331956`t-12`[t] -0.382095098205888`t-24 `[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) 121.350385460641 87.277162 1.3904 0.170329 0.085165 crisis 15.4495309520155 8.971025 1.7222 0.090985 0.045492 `t-1` 1.07950932409880 0.142087 7.5975 0 0 `t-2` -0.50927530639777 0.20721 -2.4578 0.01735 0.008675 `t-3` 0.0759563844468494 0.205224 0.3701 0.7128 0.3564 `t-4` 0.0672167107393819 0.14843 0.4529 0.652539 0.326269 `t-12` 0.440072107331956 0.15909 2.7662 0.007834 0.003917 `t-24 ` -0.382095098205888 0.152642 -2.5032 0.015486 0.007743 Multiple Linear Regression - Regression Statistics Multiple R 0.92733413415113 R-squared 0.859948596361827 Adjusted R-squared 0.84109552279515 F-TEST (value) 45.6131777834778 F-TEST (DF numerator) 7 F-TEST (DF denominator) 52 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 16.2044643843294 Sum Squared Residuals 13654.402631116 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 591 597.775264231122 -6.7752642311221 2 589 591.846377760334 -2.84637776033359 3 584 590.691965683054 -6.69196568305394 4 573 581.617662765862 -8.6176627658618 5 567 571.844913155236 -4.84491315523601 6 569 570.803532292062 -1.80353229206206 7 621 573.600380381199 47.3996196188013 8 629 630.799372241105 -1.79937224110505 9 628 614.346077816744 13.6539221832555 10 612 617.363623516191 -5.36362351619113 11 595 604.100155614093 -9.10015561409346 12 597 591.741990629931 5.25800937006879 13 593 596.841216508233 -3.84121650823289 14 590 588.639853575158 1.36014642484243 15 580 586.539865567352 -6.539865567352 16 574 576.465459028862 -2.46545902886191 17 573 574.618653195398 -1.61865319539820 18 573 574.221155358428 -1.22115535842797 19 620 576.999424823512 43.0005751764878 20 626 624.282066596428 1.71793340357167 21 620 605.551704125843 14.4482958741572 22 588 593.311982890966 -5.31198289096582 23 566 564.45265091448 1.54734908552033 24 557 557.445866663248 -0.445866663247895 25 561 555.86852688387 5.13147311613013 26 549 560.39204061077 -11.39204061077 27 532 540.748206817415 -8.74820681741515 28 526 529.769340561915 -3.76934056191475 29 511 533.159853537583 -22.1598535375827 30 499 517.160816253607 -18.1608162536066 31 555 526.511386461048 28.4886135389518 32 565 591.11623811456 -26.1162381145599 33 542 569.213849377034 -27.2138493770340 34 527 534.770552995607 -7.7705529956065 35 510 531.628975135344 -21.6289751353441 36 514 515.116777324348 -1.11677732434796 37 517 528.695833537948 -11.6958335379481 38 508 523.4631710946 -15.4631710946005 39 493 507.720627871151 -14.7206278711515 40 490 496.260339708791 -6.26033970879102 41 469 493.959997492884 -24.9599974928842 42 478 465.792966154662 12.2070338453380 43 528 491.652780086386 36.3472199136141 44 534 541.356184812228 -7.35618481222837 45 518 513.812444092028 4.18755590797234 46 506 503.513374219666 2.48662578033381 47 502 503.449107412381 -1.44910741238136 48 516 509.629516219227 6.37048378077309 49 528 524.584639926181 3.41536007381878 50 533 529.922963671621 3.07703632837886 51 536 529.898264214161 6.10173578583897 52 537 533.415280485422 3.58471951457841 53 524 530.643258560551 -6.64325856055116 54 536 525.210104892365 10.7898951076353 55 587 545.668682148454 41.3313178515456 56 597 592.511619375583 4.4883806244168 57 581 579.118364905459 1.88163509454067 58 564 561.884399976668 2.11560002333245 59 558 560.604090701701 -2.60409070170147 60 575 566.874209031939 8.1257909680612 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 11 0.110948631231029 0.221897262462059 0.88905136876897 12 0.0482329476659703 0.0964658953319405 0.95176705233403 13 0.0195503049620977 0.0391006099241954 0.980449695037902 14 0.0127386497038309 0.0254772994076618 0.98726135029617 15 0.0157369617954466 0.0314739235908933 0.984263038204553 16 0.0116793007389843 0.0233586014779686 0.988320699261016 17 0.00813113124147431 0.0162622624829486 0.991868868758526 18 0.00603013024879473 0.0120602604975895 0.993969869751205 19 0.00940571175264478 0.0188114235052896 0.990594288247355 20 0.00439325279037848 0.00878650558075696 0.995606747209622 21 0.00433311760453439 0.00866623520906877 0.995666882395466 22 0.00484923706649171 0.00969847413298342 0.995150762933508 23 0.00241477010448375 0.0048295402089675 0.997585229895516 24 0.00207581136788206 0.00415162273576413 0.997924188632118 25 0.00260678792008841 0.00521357584017682 0.997393212079912 26 0.0162500038945677 0.0325000077891355 0.983749996105432 27 0.0340006347137202 0.0680012694274404 0.96599936528628 28 0.0372938171773005 0.074587634354601 0.9627061828227 29 0.088727377920656 0.177454755841312 0.911272622079344 30 0.110324888236256 0.220649776472511 0.889675111763744 31 0.175724342942134 0.351448685884267 0.824275657057866 32 0.252778693323834 0.505557386647669 0.747221306676166 33 0.255466219370446 0.510932438740893 0.744533780629554 34 0.266284582270009 0.532569164540019 0.73371541772999 35 0.278588352213623 0.557176704427245 0.721411647786377 36 0.302086138167179 0.604172276334357 0.697913861832821 37 0.295089748133549 0.590179496267099 0.70491025186645 38 0.320700926601763 0.641401853203526 0.679299073398237 39 0.407317993872806 0.814635987745613 0.592682006127194 40 0.497682566369999 0.995365132739997 0.502317433630001 41 0.69374149948125 0.6125170010375 0.30625850051875 42 0.747616617571168 0.504766764857664 0.252383382428832 43 0.87073909149684 0.258521817006321 0.129260908503161 44 0.937082320687497 0.125835358625006 0.0629176793125032 45 0.93038397448665 0.139232051026699 0.0696160255133496 46 0.900177813034472 0.199644373931057 0.0998221869655284 47 0.824322291370719 0.351355417258562 0.175677708629281 48 0.715682492581568 0.568635014836864 0.284317507418432 49 0.624371888259115 0.751256223481769 0.375628111740885 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 6 0.153846153846154 NOK 5% type I error level 14 0.358974358974359 NOK 10% type I error level 17 0.435897435897436 NOK

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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