Mulitple Regression Model 4

*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: Thu, 19 Nov 2009 14:10:36 -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/19/t12586652399xm6sgj7fo04qyv.htm/, Retrieved Thu, 19 Nov 2009 22:14:10 +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/19/t12586652399xm6sgj7fo04qyv.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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.6 21.3 9.5 9.2 9.2 10 9.5 21.3 9.6 9.5 9.2 9.2 9.1 19.1 9.5 9.6 9.5 9.2 8.9 19.1 9.1 9.5 9.6 9.5 9 19.1 8.9 9.1 9.5 9.6 10.1 26.2 9 8.9 9.1 9.5 10.3 26.2 10.1 9 8.9 9.1 10.2 26.2 10.3 10.1 9 8.9 9.6 21.7 10.2 10.3 10.1 9 9.2 21.7 9.6 10.2 10.3 10.1 9.3 21.7 9.2 9.6 10.2 10.3 9.4 19.4 9.3 9.2 9.6 10.2 9.4 19.4 9.4 9.3 9.2 9.6 9.2 19.4 9.4 9.4 9.3 9.2 9 19.5 9.2 9.4 9.4 9.3 9 19.5 9 9.2 9.4 9.4 9 19.5 9 9 9.2 9.4 9.8 28.7 9 9 9 9.2 10 28.7 9.8 9 9 9 9.8 28.7 10 9.8 9 9 9.3 21.8 9.8 10 9.8 9 9 21.8 9.3 9.8 10 9.8 9 21.8 9 9.3 9.8 10 9.1 20 9 9 9.3 9.8 9.1 20 9.1 9 9 9.3 9.1 20 9.1 9.1 9 9 9.2 22.6 9.1 9.1 9.1 9 8.8 22.6 9.2 9.1 9.1 9.1 8.3 22.6 8.8 9.2 9.1 9.1 8.4 22.4 8.3 8.8 9.2 9.1 8.1 22.4 8.4 8.3 8.8 9.2 7.7 22.4 8.1 8.4 8.3 8.8 7.9 18.6 7.7 8.1 8.4 8.3 7.9 18.6 7.9 7.7 8.1 8.4 8 18.6 7.9 7.9 7.7 8.1 7.9 16.2 8 7.9 7.9 7.7 7.6 16.2 7.9 8 7.9 7.9 7.1 16.2 7.6 7.9 8 7.9 6.8 13.8 7.1 7.6 7.9 8 6.5 13.8 6.8 7.1 7.6 7.9 6.9 13.8 6.5 6.8 7.1 7.6 8.2 24.1 6.9 6.5 6.8 7.1 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = -3.40051685044881 -0.134543923383781X[t] + 2.11094925623521`Y(t-1)`[t] -0.9087922772981`Y(t-2)`[t] + 0.928796384659762`Y(t-3)`[t] -0.536884959196374`Y(t-4)`[t] -1.77521792588231M1[t] -0.303259869607554M2[t] -0.398487322461913M3[t] -0.233131366754861M4[t] + 0.279722394838491M5[t] + 1.73437634941900M6[t] + 0.305099087362743M7[t] + 0.182267571428939M8[t] -0.752535129732793M9[t] -0.324731479878309M10[t] + 0.384426209322359M11[t] + 0.0369476158030248t + 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) -3.40051685044881 5.922119 -0.5742 0.569212 0.284606 X -0.134543923383781 0.15339 -0.8771 0.385925 0.192963 `Y(t-1)` 2.11094925623521 1.279515 1.6498 0.107226 0.053613 `Y(t-2)` -0.9087922772981 1.814831 -0.5008 0.619429 0.309715 `Y(t-3)` 0.928796384659762 1.802582 0.5153 0.609357 0.304678 `Y(t-4)` -0.536884959196374 1.007742 -0.5328 0.597301 0.298651 M1 -1.77521792588231 0.933856 -1.901 0.064912 0.032456 M2 -0.303259869607554 0.981059 -0.3091 0.758923 0.379461 M3 -0.398487322461913 0.993127 -0.4012 0.690487 0.345244 M4 -0.233131366754861 0.974736 -0.2392 0.812256 0.406128 M5 0.279722394838491 1.009996 0.277 0.783317 0.391658 M6 1.73437634941900 1.506449 1.1513 0.256801 0.128401 M7 0.305099087362743 1.122502 0.2718 0.787245 0.393623 M8 0.182267571428939 1.436923 0.1268 0.899731 0.449866 M9 -0.752535129732793 1.304439 -0.5769 0.567407 0.283703 M10 -0.324731479878309 1.049079 -0.3095 0.758602 0.379301 M11 0.384426209322359 1.002269 0.3836 0.703445 0.351723 t 0.0369476158030248 0.033765 1.0943 0.280731 0.140366 Multiple Linear Regression - Regression Statistics Multiple R 0.6652577704075 R-squared 0.442567901087558 Adjusted R-squared 0.193190383153044 F-TEST (value) 1.77469045627351 F-TEST (DF numerator) 17 F-TEST (DF denominator) 38 p-value 0.0704654438906093 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.25163224664294 Sum Squared Residuals 59.5301646717848 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 0.6 6.86463340139552 -6.26463340139552 2 9.5 8.7415042832644 0.758495716735606 3 9.1 8.95588583970197 0.144114160298025 4 8.9 8.33650308715484 0.563496912845157 5 9 8.6810633898378 0.318936610162192 6 10.1 9.29242642733536 0.807573572664635 7 10.3 10.1602564419576 0.139743558042351 8 10.2 9.69714751835125 0.502852481648744 9 9.6 9.97987423434252 -0.37987423434252 10 9.2 8.86412099580466 0.335879004195342 11 9.3 9.11086533438787 0.189134665612129 12 9.4 9.14386026631778 0.256139733682221 13 9.4 7.47641807578612 1.92358192421388 14 9.2 9.20207814227862 -0.00207814227862302 15 9 8.7473452041882 0.252654795811797 16 9 8.65552888399122 0.344471116008777 17 9 9.20132943991526 -0.201329439915265 18 9.8 9.37674463007534 0.423255369924664 19 10 9.78055138064955 0.219448619350453 20 9.8 9.38982350992733 0.410176490072674 21 9.3 9.55941029693786 -0.25941029693786 22 9 8.90669669951224 0.0933033004877626 23 9 9.18077709752319 -0.180777097523188 24 9.1 8.99109404879349 0.108905951206515 25 9.1 7.45372222853798 1.64627777146202 26 9.1 9.03281416064486 0.0671858393551382 27 9.2 8.71759976126167 0.482400238738328 28 8.8 9.07730976247563 -0.277309762475630 29 8.3 8.69185220964812 -0.391852209648117 30 8.4 9.61128448597602 -1.21128448597602 31 8.1 8.45923885421182 -0.359238854211815 32 7.7 7.39954674082933 0.300453259170672 33 7.9 6.8025386630885 1.0974613369115 34 7.9 7.72066927959473 0.179330720405275 35 8 8.0745630630338 -0.0745630630338049 36 7.9 8.66159807186957 -0.76159807186957 37 7.6 6.51397661659768 1.08602338340232 38 7.1 7.57335637800068 -0.473356378000682 39 6.8 6.90857687775663 -0.108576877756635 40 6.5 6.7070413915669 -0.207041391566907 41 6.9 6.59286297071118 0.307137029288818 42 8.2 7.80548308012554 0.394516919874456 43 8.7 8.67629712841982 0.0237028715801756 44 8.3 8.99704193754194 -0.697041937541937 45 7.9 8.35817680563112 -0.458176805631121 46 7.5 8.10851302508838 -0.60851302508838 47 7.8 7.73379450505514 0.0662054949448635 48 8.3 7.90344761301917 0.396552386980827 49 8.4 6.79124967768271 1.60875032231729 50 8.2 8.55024703581144 -0.35024703581144 51 7.7 8.47059231709152 -0.770592317091515 52 7.2 7.6236168748114 -0.423616874811398 53 7.3 7.33289198988763 -0.0328919898876289 54 8.1 8.51406137648774 -0.414061376487735 55 8.5 8.52365619476116 -0.0236561947611641 56 8.4 8.91644029335015 -0.516440293350152 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.999999999422232 1.15553604809741e-09 5.77768024048704e-10 22 0.999999999981861 3.62780054313983e-11 1.81390027156991e-11 23 0.9999999998869 2.26200309557485e-10 1.13100154778743e-10 24 0.99999999955124 8.97521821857054e-10 4.48760910928527e-10 25 0.999999997287287 5.42542516826538e-09 2.71271258413269e-09 26 0.999999996777257 6.44548500741335e-09 3.22274250370667e-09 27 0.999999999123011 1.75397767101586e-09 8.76988835507932e-10 28 0.99999999772735 4.54530199453031e-09 2.27265099726515e-09 29 0.99999997801668 4.39666388834681e-08 2.19833194417340e-08 30 0.999999994602313 1.07953731860369e-08 5.39768659301845e-09 31 0.999999937790685 1.24418630365924e-07 6.22093151829618e-08 32 0.999999004610797 1.99077840599051e-06 9.95389202995255e-07 33 0.99999299955111 1.40008977822431e-05 7.00044889112154e-06 34 0.999990351226243 1.92975475137934e-05 9.6487737568967e-06 35 0.999845458551998 0.000309082896003076 0.000154541448001538 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 15 1 NOK 5% type I error level 15 1 NOK 10% type I error level 15 1 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = 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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