*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: Fri, 27 Nov 2009 06:17:40 -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/Nov/27/t1259327983ugoos18jptl6195.htm/, Retrieved Fri, 27 Nov 2009 14:19:56 +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/Nov/27/t1259327983ugoos18jptl6195.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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543 0 594 0 611 0 613 0 611 0 594 0 595 0 591 0 589 0 584 0 573 0 567 0 569 0 621 0 629 0 628 0 612 0 595 0 597 0 593 0 590 0 580 0 574 0 573 0 573 0 620 0 626 0 620 0 588 0 566 0 557 0 561 0 549 0 532 0 526 0 511 0 499 0 555 0 565 0 542 0 527 0 510 0 514 0 517 0 508 0 493 0 490 0 469 1 478 1 528 1 534 1 518 1 506 1 502 1 516 1 528 1 533 1 536 1 537 1 524 1 536 1

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 Yt[t] = + 548.326582278481 -48.8164556962025X[t] + 0.945569620252883M1[t] + 45.0367088607595M2[t] + 54.4367088607595M3[t] + 45.6367088607595M4[t] + 30.2367088607595M5[t] + 14.8367088607595M6[t] + 17.2367088607595M7[t] + 19.4367088607595M8[t] + 15.2367088607595M9[t] + 6.43670886075953M10[t] + 1.43670886075952M11[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) 548.326582278481 16.168896 33.9124 0 0 X -48.8164556962025 10.739561 -4.5455 3.7e-05 1.9e-05 M1 0.945569620252883 21.118103 0.0448 0.964472 0.482236 M2 45.0367088607595 22.148853 2.0334 0.047565 0.023782 M3 54.4367088607595 22.148853 2.4578 0.017642 0.008821 M4 45.6367088607595 22.148853 2.0605 0.044797 0.022399 M5 30.2367088607595 22.148853 1.3652 0.178568 0.089284 M6 14.8367088607595 22.148853 0.6699 0.506155 0.253077 M7 17.2367088607595 22.148853 0.7782 0.440258 0.220129 M8 19.4367088607595 22.148853 0.8775 0.38456 0.19228 M9 15.2367088607595 22.148853 0.6879 0.494812 0.247406 M10 6.43670886075953 22.148853 0.2906 0.772601 0.3863 M11 1.43670886075952 22.148853 0.0649 0.94855 0.474275 Multiple Linear Regression - Regression Statistics Multiple R 0.676505460555468 R-squared 0.457659638161366 Adjusted R-squared 0.322074547701707 F-TEST (value) 3.37544221573194 F-TEST (DF numerator) 12 F-TEST (DF denominator) 48 p-value 0.00128608346648806 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 34.8553494462629 Sum Squared Residuals 58314.9784810127 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 543 549.272151898736 -6.27215189873589 2 594 593.36329113924 0.6367088607595 3 611 602.76329113924 8.23670886075943 4 613 593.96329113924 19.0367088607595 5 611 578.56329113924 32.4367088607595 6 594 563.16329113924 30.8367088607595 7 595 565.56329113924 29.4367088607595 8 591 567.76329113924 23.2367088607595 9 589 563.56329113924 25.4367088607595 10 584 554.76329113924 29.2367088607595 11 573 549.76329113924 23.2367088607595 12 567 548.326582278481 18.6734177215190 13 569 549.272151898734 19.7278481012662 14 621 593.36329113924 27.6367088607595 15 629 602.76329113924 26.2367088607595 16 628 593.96329113924 34.0367088607595 17 612 578.56329113924 33.4367088607595 18 595 563.16329113924 31.8367088607595 19 597 565.56329113924 31.4367088607595 20 593 567.76329113924 25.2367088607595 21 590 563.56329113924 26.4367088607595 22 580 554.76329113924 25.2367088607595 23 574 549.76329113924 24.2367088607595 24 573 548.326582278481 24.6734177215190 25 573 549.272151898734 23.7278481012662 26 620 593.36329113924 26.6367088607595 27 626 602.76329113924 23.2367088607595 28 620 593.96329113924 26.0367088607595 29 588 578.56329113924 9.4367088607595 30 566 563.16329113924 2.83670886075950 31 557 565.56329113924 -8.5632911392405 32 561 567.76329113924 -6.76329113924049 33 549 563.56329113924 -14.5632911392405 34 532 554.76329113924 -22.7632911392405 35 526 549.76329113924 -23.7632911392405 36 511 548.326582278481 -37.326582278481 37 499 549.272151898734 -50.2721518987338 38 555 593.36329113924 -38.3632911392405 39 565 602.76329113924 -37.7632911392405 40 542 593.96329113924 -51.9632911392405 41 527 578.56329113924 -51.5632911392405 42 510 563.16329113924 -53.1632911392405 43 514 565.56329113924 -51.5632911392405 44 517 567.76329113924 -50.7632911392405 45 508 563.56329113924 -55.5632911392405 46 493 554.76329113924 -61.7632911392405 47 490 549.76329113924 -59.7632911392405 48 469 499.510126582279 -30.5101265822785 49 478 500.455696202531 -22.4556962025313 50 528 544.546835443038 -16.546835443038 51 534 553.946835443038 -19.9468354430380 52 518 545.146835443038 -27.1468354430380 53 506 529.746835443038 -23.7468354430380 54 502 514.346835443038 -12.3468354430380 55 516 516.746835443038 -0.746835443038022 56 528 518.946835443038 9.05316455696198 57 533 514.746835443038 18.253164556962 58 536 505.946835443038 30.0531645569620 59 537 500.946835443038 36.053164556962 60 524 499.510126582279 24.4898734177215 61 536 500.455696202531 35.5443037974686 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.127033487868323 0.254066975736646 0.872966512131677 17 0.0528231358280137 0.105646271656027 0.947176864171986 18 0.0208432336224651 0.0416864672449301 0.979156766377535 19 0.00801138951655168 0.0160227790331034 0.991988610483448 20 0.00284610917457617 0.00569221834915233 0.997153890825424 21 0.00100205409339170 0.00200410818678339 0.998997945906608 22 0.000361248924233579 0.000722497848467159 0.999638751075766 23 0.000123048130542147 0.000246096261084294 0.999876951869458 24 5.06523531574319e-05 0.000101304706314864 0.999949347646843 25 5.08076254960606e-05 0.000101615250992121 0.999949192374504 26 4.67070319199194e-05 9.34140638398389e-05 0.99995329296808 27 3.61050458323834e-05 7.22100916647668e-05 0.999963894954168 28 5.84154312178197e-05 0.000116830862435639 0.999941584568782 29 0.000360551838054588 0.000721103676109175 0.999639448161945 30 0.00241005650294787 0.00482011300589573 0.997589943497052 31 0.0155049911583652 0.0310099823167304 0.984495008841635 32 0.0332522575750782 0.0665045151501565 0.966747742424922 33 0.0743933208812975 0.148786641762595 0.925606679118703 34 0.148640787577965 0.297281575155930 0.851359212422035 35 0.199692056753496 0.399384113506992 0.800307943246504 36 0.294507973213609 0.589015946427219 0.70549202678639 37 0.380404540619725 0.760809081239449 0.619595459380275 38 0.449016042030111 0.898032084060222 0.550983957969889 39 0.52751909574456 0.94496180851088 0.47248090425544 40 0.639834197231778 0.720331605536445 0.360165802768222 41 0.711540803480342 0.576918393039315 0.288459196519658 42 0.722075239789891 0.555849520420219 0.277924760210109 43 0.687038100694656 0.625923798610687 0.312961899305344 44 0.613824950317476 0.772350099365049 0.386175049682524 45 0.493151073666961 0.986302147333923 0.506848926333039 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 11 0.366666666666667 NOK 5% type I error level 14 0.466666666666667 NOK 10% type I error level 15 0.5 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259327983ugoos18jptl6195/10qdou1259327855.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259327983ugoos18jptl6195/10qdou1259327855.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259327983ugoos18jptl6195/19a361259327855.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259327983ugoos18jptl6195/19a361259327855.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259327983ugoos18jptl6195/2j5qr1259327855.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259327983ugoos18jptl6195/2j5qr1259327855.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259327983ugoos18jptl6195/399va1259327855.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259327983ugoos18jptl6195/399va1259327855.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259327983ugoos18jptl6195/436w91259327855.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259327983ugoos18jptl6195/436w91259327855.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259327983ugoos18jptl6195/5ie201259327855.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259327983ugoos18jptl6195/5ie201259327855.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259327983ugoos18jptl6195/6vq3o1259327855.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259327983ugoos18jptl6195/6vq3o1259327855.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259327983ugoos18jptl6195/7f7vk1259327855.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259327983ugoos18jptl6195/7f7vk1259327855.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259327983ugoos18jptl6195/8qk0u1259327855.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259327983ugoos18jptl6195/8qk0u1259327855.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259327983ugoos18jptl6195/9ud9g1259327855.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259327983ugoos18jptl6195/9ud9g1259327855.ps (open in new window)

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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