*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, 20 Dec 2009 09:56:31 -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/20/t1261328363wja4yvnz7fqcmc4.htm/, Retrieved Sun, 20 Dec 2009 17:59:35 +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/20/t1261328363wja4yvnz7fqcmc4.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:

» Textbox « » Textfile « » CSV «

5560 611 3922 594 3759 595 4138 591 4634 589 3996 584 4308 573 4143 567 4429 569 5219 621 4929 629 5755 628 5592 612 4163 595 4962 597 5208 593 4755 590 4491 580 5732 574 5731 573 5040 573 6102 620 4904 626 5369 620 5578 588 4619 566 4731 557 5011 561 5299 549 4146 532 4625 526 4736 511 4219 499 5116 555 4205 565 4121 542 5103 527 4300 510 4578 514 3809 517 5526 508 4247 493 3830 490 4394 469 4826 478 4409 528 4569 534 4106 518 4794 506 3914 502 3793 516 4405 528 4022 533 4100 536 4788 537 3163 524 3585 536

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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 1424.56447367454 + 5.91539952569404X[t] + 536.156276110696M1[t] -514.54657119362M2[t] -347.743530055286M3[t] -211.157409011813M4[t] + 146.687268996102M5[t] -452.457215177790M6[t] + 37.7197824506796M7[t] -119.227742861547M8[t] -145.841621818074M9[t] + 350.088401897224M10[t] -254.027094545481M11[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) 1424.56447367454 1124.391372 1.267 0.211833 0.105917 X 5.91539952569404 1.891514 3.1273 0.003124 0.001562 M1 536.156276110696 363.057194 1.4768 0.146856 0.073428 M2 -514.54657119362 365.462253 -1.4079 0.166177 0.083089 M3 -347.743530055286 364.93557 -0.9529 0.345851 0.172926 M4 -211.157409011813 364.50178 -0.5793 0.565338 0.282669 M5 146.687268996102 365.370608 0.4015 0.690014 0.345007 M6 -452.457215177790 367.741275 -1.2304 0.225097 0.112548 M7 37.7197824506796 369.415748 0.1021 0.919136 0.459568 M8 -119.227742861547 374.008152 -0.3188 0.751399 0.375699 M9 -145.841621818074 373.015589 -0.391 0.697699 0.348849 M10 350.088401897224 382.421341 0.9155 0.364944 0.182472 M11 -254.027094545481 382.964755 -0.6633 0.510588 0.255294 Multiple Linear Regression - Regression Statistics Multiple R 0.657806268854861 R-squared 0.432709087344753 Adjusted R-squared 0.277993383893322 F-TEST (value) 2.79680134396048 F-TEST (DF numerator) 12 F-TEST (DF denominator) 44 p-value 0.0063779180725756 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 540.71958819666 Sum Squared Residuals 12864617.6146209 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 5560 5575.02985998427 -15.0298599842679 2 3922 4423.76522074318 -501.765220743178 3 3759 4596.48366140721 -837.483661407206 4 4138 4709.4081843479 -571.408184347904 5 4634 5055.42206330443 -421.42206330443 6 3996 4426.70058150207 -430.700581502068 7 4308 4851.8081843479 -543.808184347903 8 4143 4659.36826188151 -516.368261881512 9 4429 4644.58518197637 -215.585181976373 10 5219 5448.11598102776 -229.115981027762 11 4929 4891.32368079061 37.6763192093915 12 5755 5139.43537581040 615.564624189605 13 5592 5580.94525950999 11.0547404900125 14 4163 4429.68062026887 -266.680620268872 15 4962 4608.31446045859 353.685539541405 16 5208 4721.23898339929 486.761016600709 17 4755 5061.33746283012 -306.337462830124 18 4491 4403.03898339929 87.9610166007085 19 5732 4857.7235838736 874.276416126403 20 5731 4694.86065903568 1036.13934096432 21 5040 4668.24678007915 371.753219920850 22 6102 5442.20058150207 659.799418497933 23 4904 4873.57748221353 30.4225177864735 24 5369 5092.11217960484 276.887820395157 25 5578 5438.97567089333 139.024329106669 26 4619 4258.13403402374 360.865965976255 27 4731 4371.69847943083 359.301520569167 28 5011 4531.94619857708 479.053801422918 29 5299 4818.80608227667 480.193917723331 30 4146 4119.09980616598 26.9001938340225 31 4625 4573.78440664028 51.2155933597165 32 4736 4328.10588844265 407.894111557354 33 4219 4230.50721517779 -11.5072151777908 34 5116 5057.69961233195 58.3003876680452 35 4205 4512.73811114619 -307.73811114619 36 4121 4630.71101660071 -509.711016600708 37 5103 5078.136299826 24.8637001740056 38 4300 3926.87166058488 373.128339415121 39 4578 4117.33629982599 460.663700174010 40 3809 4271.66861944654 -462.668619446545 41 5526 4576.27470172321 949.725298276787 42 4247 3888.39922466391 358.60077533609 43 3830 4360.8300237153 -530.830023715298 44 4394 4079.6591083635 314.340891636503 45 4826 4106.28382513822 719.716174861784 46 4409 4897.98382513822 -488.983825138216 47 4569 4329.36072584967 239.639274150325 48 4106 4488.74142798405 -382.741427984052 49 4794 4953.91290978642 -159.912909786420 50 3914 3879.54846437933 34.4515356206733 51 3793 4129.16709887738 -336.167098877378 52 4405 4336.73801422918 68.261985770821 53 4022 4724.15968986556 -702.159689865564 54 4100 4142.76140426875 -42.7614042687536 55 4788 4638.85380142292 149.146198577082 56 3163 4405.00608227667 -1242.00608227667 57 3585 4449.37699762847 -864.37699762847 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.0905251533777133 0.181050306755427 0.909474846622287 17 0.0565295913770162 0.113059182754032 0.943470408622984 18 0.464094009581645 0.928188019163291 0.535905990418355 19 0.643042599014843 0.713914801970315 0.356957400985157 20 0.609141615290843 0.781716769418314 0.390858384709157 21 0.501580586072251 0.996838827855498 0.498419413927749 22 0.586891743753183 0.826216512493634 0.413108256246817 23 0.507672294366112 0.984655411267775 0.492327705633888 24 0.519643508416608 0.960712983166785 0.480356491583392 25 0.61627924795043 0.76744150409914 0.38372075204957 26 0.600693183576881 0.798613632846237 0.399306816423119 27 0.532046342481981 0.935907315036038 0.467953657518019 28 0.534762357713258 0.930475284573484 0.465237642286742 29 0.490406116323515 0.98081223264703 0.509593883676485 30 0.411124190739981 0.822248381479962 0.588875809260019 31 0.363366163780696 0.726732327561393 0.636633836219304 32 0.41209663968194 0.82419327936388 0.58790336031806 33 0.33468948058876 0.66937896117752 0.66531051941124 34 0.343316095227004 0.686632190454008 0.656683904772996 35 0.266372937944738 0.532745875889476 0.733627062055262 36 0.247232338671353 0.494464677342706 0.752767661328647 37 0.185123906228969 0.370247812457938 0.814876093771031 38 0.138684304745095 0.277368609490190 0.861315695254905 39 0.115697545750973 0.231395091501947 0.884302454249027 40 0.09652638500818 0.19305277001636 0.90347361499182 41 0.162902287334478 0.325804574668957 0.837097712665521 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 = 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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Software written by Ed van Stee & Patrick Wessa

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