*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: Mon, 23 Nov 2009 06:04:23 -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/23/t12589815208awthdwz2lxtj3i.htm/, Retrieved Mon, 23 Nov 2009 14:05:33 +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/23/t12589815208awthdwz2lxtj3i.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?

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User-defined keywords:

Dataseries X:

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5560 543 3922 594 3759 611 4138 613 4634 611 3996 594 4308 595 4143 591 4429 589 5219 584 4929 573 5755 567 5592 569 4163 621 4962 629 5208 628 4755 612 4491 595 5732 597 5731 593 5040 590 6102 580 4904 574 5369 573 5578 573 4619 620 4731 626 5011 620 5299 588 4146 566 4625 557 4736 561 4219 549 5116 532 4205 526 4121 511 5103 499 4300 555 4578 565 3809 542 5526 527 4247 510 3830 514 4394 517 4826 508 4409 493 4569 490 4106 469 4794 478 3914 528 3793 534 4405 518 4022 506 4100 502 4788 516 3163 528 3585 533 3903 536 4178 537 3863 524 4187 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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 687.377724284438 + 7.4799967392503X[t] + 461.450680361815M1[t] -869.103821310916M2[t] -758.415790659869M3[t] -542.991819354467M4[t] -94.7998695700121M5[t] -630.807919785557M6[t] -188.159911959758M7[t] -427.815904786109M8[t] -409.999918481258M9[t] + 185.824052824145M10[t] -169.575963479603M11[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) 687.377724284438 1033.968889 0.6648 0.509363 0.254681 X 7.4799967392503 1.899469 3.9379 0.000265 0.000133 M1 461.450680361815 332.291292 1.3887 0.171337 0.085668 M2 -869.103821310916 362.244322 -2.3992 0.020361 0.010181 M3 -758.415790659869 367.77281 -2.0622 0.044625 0.022313 M4 -542.991819354467 362.573452 -1.4976 0.140784 0.070392 M5 -94.7998695700121 355.188404 -0.2669 0.790689 0.395345 M6 -630.807919785557 350.099179 -1.8018 0.077859 0.03893 M7 -188.159911959758 350.736721 -0.5365 0.594111 0.297056 M8 -427.815904786109 351.37208 -1.2176 0.229344 0.114672 M9 -409.999918481258 350.201395 -1.1708 0.247477 0.123738 M10 185.824052824145 348.328733 0.5335 0.596168 0.298084 M11 -169.575963479603 347.618487 -0.4878 0.627897 0.313948 Multiple Linear Regression - Regression Statistics Multiple R 0.632309405720561 R-squared 0.399815184562689 Adjusted R-squared 0.249768980703362 F-TEST (value) 2.66461379414521 F-TEST (DF numerator) 12 F-TEST (DF denominator) 48 p-value 0.00800634103013076 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 548.602832503709 Sum Squared Residuals 14446323.2558924 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 5560 5210.46663405917 349.53336594083 2 3922 4261.3919660882 -339.391966088203 3 3759 4499.23994130650 -740.239941306505 4 4138 4729.62390609041 -591.62390609041 5 4634 5162.85586239636 -528.855862396363 6 3996 4499.68786761356 -503.687867613562 7 4308 4949.81587217861 -641.815872178612 8 4143 4680.23989239526 -537.23989239526 9 4429 4683.09588522161 -254.095885221611 10 5219 5241.51987283076 -22.5198728307618 11 4929 4803.83989239526 125.160107604740 12 5755 4928.53587543936 826.464124560638 13 5592 5404.94654927968 187.053450720323 14 4163 4463.35187804796 -300.351878047962 15 4962 4633.87988261301 328.120117386989 16 5208 4841.82385717916 366.176142820837 17 4755 5170.33585913561 -415.335859135613 18 4491 4507.16786435281 -16.1678643528127 19 5732 4964.77586565711 767.224134342887 20 5731 4695.19988587376 1035.80011412624 21 5040 4690.57588196086 349.424118039139 22 6102 5211.59988587376 890.40011412624 23 4904 4811.31988913451 92.6801108654894 24 5369 4973.41585587486 395.584144125136 25 5578 5434.86653623668 143.133463763321 26 4619 4455.87188130871 163.128118691289 27 4731 4611.43989239526 119.56010760474 28 5011 4781.98388326516 229.016116734839 29 5299 4990.81593739361 308.184062606394 30 4146 4290.24795891455 -144.247958914554 31 4625 4665.5759960871 -40.5759960871004 32 4736 4455.83999021775 280.160009782249 33 4219 4383.8960156516 -164.896015651599 34 5116 4852.56004238975 263.439957610254 35 4205 4452.2800456505 -247.280045650496 36 4121 4509.65605804134 -388.656058041345 37 5103 4881.34677753216 221.653222467844 38 4300 3969.67209325744 330.327906742558 39 4578 4155.16009130099 422.839908699009 40 3809 4198.54413760364 -389.544137603637 41 5526 4534.53613629934 991.463863700663 42 4247 3871.36814151654 375.631858483463 43 3830 4343.93613629934 -513.936136299337 44 4394 4126.72013369074 267.279866309263 45 4826 4077.21614934234 748.783850657664 46 4409 4560.84016955898 -151.840169558984 47 4569 4183.00016303748 385.999836962515 48 4106 4195.49619499283 -89.4961949928316 49 4794 4724.2668460079 69.7331539921005 50 3914 3767.71218129768 146.287818702317 51 3793 3923.28019238423 -130.280192384232 52 4405 4019.02421586163 385.975784138370 53 4022 4377.45620477508 -355.456204775081 54 4100 3811.52816760253 288.471832397466 55 4788 4358.89612977784 429.103870222162 56 3163 4209.00009782249 -1046.00009782249 57 3585 4264.21606782359 -679.216067823593 58 3903 4882.48002934675 -979.480029346747 59 4178 4534.56000978225 -356.560009782249 60 3863 4606.8960156516 -743.896015651598 61 4187 5158.10665688442 -971.106656884417 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.528428582412661 0.943142835174678 0.471571417587339 17 0.380855012366666 0.761710024733331 0.619144987633334 18 0.295946717027065 0.59189343405413 0.704053282972935 19 0.557706686346595 0.88458662730681 0.442293313653405 20 0.794356925565582 0.411286148868836 0.205643074434418 21 0.739896622474288 0.520206755051424 0.260103377525712 22 0.809856900660788 0.380286198678424 0.190143099339212 23 0.7307241254523 0.5385517490954 0.2692758745477 24 0.725288163725319 0.549423672549363 0.274711836274681 25 0.674188334061156 0.651623331877687 0.325811665938844 26 0.593831693484564 0.812336613030871 0.406168306515436 27 0.506889783932027 0.986220432135946 0.493110216067973 28 0.462278489014712 0.924556978029424 0.537721510985288 29 0.504891306103726 0.990217387792547 0.495108693896274 30 0.412687222136259 0.825374444272519 0.58731277786374 31 0.330020280246427 0.660040560492854 0.669979719753573 32 0.345861407882483 0.691722815764966 0.654138592117517 33 0.263256853618508 0.526513707237017 0.736743146381492 34 0.292478304937289 0.584956609874578 0.707521695062711 35 0.21739370103753 0.43478740207506 0.78260629896247 36 0.187372560286397 0.374745120572794 0.812627439713603 37 0.159066916446900 0.318133832893799 0.8409330835531 38 0.149509946332259 0.299019892664517 0.850490053667741 39 0.182940502277945 0.36588100455589 0.817059497722055 40 0.130769049289888 0.261538098579775 0.869230950710112 41 0.503007261498255 0.99398547700349 0.496992738501745 42 0.403327254055699 0.806654508111398 0.596672745944301 43 0.493703400325226 0.987406800650451 0.506296599674774 44 0.703451929387459 0.593096141225082 0.296548070612541 45 0.982639195414118 0.0347216091717641 0.0173608045858820 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 1 0.0333333333333333 OK 10% type I error level 1 0.0333333333333333 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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