*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, 15 Dec 2009 11:47:48 -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/15/t1260903434e2a4421cjqd736i.htm/, Retrieved Tue, 15 Dec 2009 19:57:27 +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/15/t1260903434e2a4421cjqd736i.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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564 -0.9 581 -1 597 -0.7 587 -1.7 536 -1 524 -0.2 537 0.7 536 0.6 533 1.9 528 2.1 516 2.7 502 3.2 506 4.8 518 5.5 534 5.4 528 5.9 478 5.8 469 5.1 490 4.1 493 4.4 508 3.6 517 3.5 514 3.1 510 2.9 527 2.2 542 1.4 565 1.2 555 1.3 499 1.3 511 1.3 526 1.8 532 1.8 549 1.8 561 1.7 557 2.1 566 2 588 1.7 620 1.9 626 2.3 620 2.4 573 2.5 573 2.8 574 2.6 580 2.2 590 2.8 593 2.8 597 2.8 595 2.3 612 2.2 628 3 629 2.9 621 2.7 569 2.7 567 2.3 573 2.4 584 2.8 589 2.3 591 2 595 1.9 594 2.3

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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 574.162403631772 -8.1741746581782X[t] + 1.58594568458370M1[t] + 21.2938136298923M2[t] + 34.184264109383M3[t] + 25.3668466435652M4[t] -24.6887689042899M5[t] -26.8887689042899M6[t] -15.1983184247992M7[t] -9.87135143847206M8[t] -0.090450479490666M9[t] + 3.61909904101863M10[t] + 2.23651650683645M11[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) 574.162403631772 18.99184 30.2321 0 0 X -8.1741746581782 3.155104 -2.5908 0.012714 0.006357 M1 1.58594568458370 24.409742 0.065 0.948472 0.474236 M2 21.2938136298923 24.379708 0.8734 0.386873 0.193437 M3 34.184264109383 24.371132 1.4027 0.167291 0.083646 M4 25.3668466435652 24.386241 1.0402 0.303563 0.151782 M5 -24.6887689042899 24.36623 -1.0132 0.316135 0.158067 M6 -26.8887689042899 24.36623 -1.1035 0.275417 0.137708 M7 -15.1983184247992 24.360101 -0.6239 0.535708 0.267854 M8 -9.87135143847206 24.356832 -0.4053 0.68711 0.343555 M9 -0.090450479490666 24.350946 -0.0037 0.997052 0.498526 M10 3.61909904101863 24.353153 0.1486 0.882498 0.441249 M11 2.23651650683645 24.350292 0.0918 0.927209 0.463605 Multiple Linear Regression - Regression Statistics Multiple R 0.551464014387481 R-squared 0.304112559164356 Adjusted R-squared 0.126439170014830 F-TEST (value) 1.71163819534292 F-TEST (DF numerator) 12 F-TEST (DF denominator) 47 p-value 0.094537415037612 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 38.5010623246821 Sum Squared Residuals 69669.5946060655 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 564 583.105106508717 -19.1051065087171 2 581 603.630391919843 -22.6303919198431 3 597 614.06859000188 -17.0685900018803 4 587 613.425347194241 -26.4253471942407 5 536 557.647809385661 -21.6478093856610 6 524 548.908469659118 -24.9084696591184 7 537 553.242162946249 -16.2421629462487 8 536 559.386547398394 -23.3865473983936 9 533 558.541021301743 -25.5410213017433 10 528 560.615735890617 -32.615735890617 11 516 554.328648561528 -38.3286485615279 12 502 548.005044725602 -46.0050447256024 13 506 536.512310957101 -30.512310957101 14 518 550.498256641685 -32.4982566416848 15 534 564.206124586993 -30.2061245869933 16 528 551.301619792086 -23.3016197920864 17 478 502.063421710049 -24.0634217100492 18 469 505.585343970774 -36.5853439707739 19 490 525.449969108443 -35.4499691084428 20 493 528.324683697316 -35.3246836973165 21 508 544.64492438284 -36.6449243828404 22 517 549.171891369167 -32.1718913691675 23 514 551.058978698257 -37.0589786982567 24 510 550.457297123056 -40.4572971230559 25 527 557.765165068364 -30.7651650683643 26 542 584.012372740215 -42.0123727402154 27 565 598.537658151342 -33.5376581513417 28 555 588.902823219706 -33.9028232197061 29 499 538.847207671851 -39.847207671851 30 511 536.647207671851 -25.6472076718511 31 526 544.250570822253 -18.2505708222527 32 532 549.57753780858 -17.5775378085798 33 549 559.358438767561 -10.3584387675612 34 561 563.885405753888 -2.8854057538883 35 557 559.233153356435 -2.23315335643485 36 566 557.814054315416 8.18594568458379 37 588 561.852252397453 26.1477476025466 38 620 579.925285411126 40.0747145888737 39 626 589.546066027346 36.4539339726543 40 620 579.91123109571 40.0887689042899 41 573 529.038198082037 43.9618019179628 42 573 524.385945684584 48.6140543154162 43 574 537.71123109571 36.2887689042899 44 580 546.307867945309 33.6921320546915 45 590 551.184264109383 38.815735890617 46 593 554.893813629892 38.1061863701077 47 597 553.51123109571 43.4887689042899 48 595 555.361801917963 39.6381980820372 49 612 557.765165068364 54.2348349316357 50 628 570.93369328713 57.0663067128697 51 629 584.641561232439 44.3584387675612 52 621 577.458978698257 43.5410213017433 53 569 527.403363150402 41.5966368495984 54 567 528.473033013673 38.5269669863271 55 573 539.346066027346 33.6539339726543 56 584 541.403363150402 42.5966368495984 57 589 555.271351438472 33.7286485615279 58 591 561.433153356435 29.5668466435652 59 595 560.86798828807 34.1320117119295 60 594 555.361801917963 38.6381980820372 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.00415037466664197 0.00830074933328394 0.995849625333358 17 0.000583351216898594 0.00116670243379719 0.999416648783101 18 0.000108663195959247 0.000217326391918494 0.99989133680404 19 9.22595830294697e-05 0.000184519166058939 0.99990774041697 20 2.88810563720328e-05 5.77621127440656e-05 0.999971118943628 21 1.36370213994757e-05 2.72740427989514e-05 0.9999863629786 22 6.77336906762662e-06 1.35467381352532e-05 0.999993226630932 23 5.64301710395524e-06 1.12860342079105e-05 0.999994356982896 24 2.56100458012116e-05 5.12200916024231e-05 0.9999743899542 25 0.000240832257044868 0.000481664514089736 0.999759167742955 26 0.00159554431201641 0.00319108862403282 0.998404455687984 27 0.00147626325148597 0.00295252650297194 0.998523736748514 28 0.00134602097149987 0.00269204194299974 0.9986539790285 29 0.00492209373514541 0.00984418747029082 0.995077906264855 30 0.00342254380991250 0.00684508761982499 0.996577456190088 31 0.00455743000058861 0.00911486000117721 0.995442569999411 32 0.0150464810468403 0.0300929620936805 0.98495351895316 33 0.0629248818180869 0.125849763636174 0.937075118181913 34 0.228993733214701 0.457987466429402 0.771006266785299 35 0.894069550610718 0.211860898778565 0.105930449389282 36 0.999530752273662 0.000938495452675676 0.000469247726337838 37 0.999999991153538 1.76929241069276e-08 8.84646205346381e-09 38 0.999999995790936 8.41812861216765e-09 4.20906430608383e-09 39 0.999999981947267 3.61054652711620e-08 1.80527326355810e-08 40 0.999999892235788 2.15528424826655e-07 1.07764212413328e-07 41 0.999999885839264 2.28321472155226e-07 1.14160736077613e-07 42 0.999999942339378 1.15321244310672e-07 5.76606221553361e-08 43 0.999998290342012 3.41931597681473e-06 1.70965798840737e-06 44 0.999996678780829 6.64243834242217e-06 3.32121917121109e-06 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 25 0.862068965517241 NOK 5% type I error level 26 0.896551724137931 NOK 10% type I error level 26 0.896551724137931 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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