Model 2

*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: Wed, 18 Nov 2009 13:35:45 -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/18/t1258576615ja8a51n2yie2rfi.htm/, Retrieved Wed, 18 Nov 2009 21:37:07 +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/18/t1258576615ja8a51n2yie2rfi.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 «

115.6 0 111.3 0 114.6 0 137.5 0 83.7 0 106.0 0 123.4 0 126.5 0 120.0 0 141.6 0 90.5 0 96.5 0 113.5 0 120.1 0 123.9 0 144.4 0 90.8 0 114.2 0 138.1 0 135.0 0 131.3 0 144.6 0 101.7 0 108.7 0 135.3 0 124.3 0 138.3 0 158.2 0 93.5 0 124.8 0 154.4 0 152.8 0 148.9 0 170.3 0 124.8 0 134.4 0 154.0 0 147.9 0 168.1 0 175.7 0 116.7 0 140.8 0 164.2 0 173.8 0 167.8 0 166.6 0 135.1 1 158.1 1 151.8 1 166.7 1 165.3 1 187.0 1 125.2 1 144.4 1 181.7 1 175.9 1 166.3 1 181.5 1 121.8 1 134.8 1 162.9 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 Y[t] = + 114.77 + 29.325X[t] + 14.305M1[t] + 13.425M2[t] + 21.4050000000000M3[t] + 39.925M4[t] -18.655M5[t] + 5.40499999999998M6[t] + 31.7250000000000M7[t] + 32.165M8[t] + 26.225M9[t] + 40.285M10[t] -11.72M11[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) 114.77 7.303854 15.7136 0 0 X 29.325 4.767892 6.1505 0 0 M1 14.305 9.551663 1.4976 0.140773 0.070387 M2 13.425 10.016356 1.3403 0.186455 0.093228 M3 21.4050000000000 10.016356 2.137 0.037721 0.018861 M4 39.925 10.016356 3.986 0.000228 0.000114 M5 -18.655 10.016356 -1.8625 0.068666 0.034333 M6 5.40499999999998 10.016356 0.5396 0.591956 0.295978 M7 31.7250000000000 10.016356 3.1673 0.002675 0.001337 M8 32.165 10.016356 3.2112 0.00236 0.00118 M9 26.225 10.016356 2.6182 0.011791 0.005895 M10 40.285 10.016356 4.0219 0.000203 0.000102 M11 -11.72 9.970862 -1.1754 0.245622 0.122811 Multiple Linear Regression - Regression Statistics Multiple R 0.836555444451901 R-squared 0.699825011642118 Adjusted R-squared 0.624781264552648 F-TEST (value) 9.32556060677188 F-TEST (DF numerator) 12 F-TEST (DF denominator) 48 p-value 6.2330476335859e-09 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 15.7653162961187 Sum Squared Residuals 11930.1695 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 115.6 129.075 -13.4750000000000 2 111.3 128.195 -16.8950000000000 3 114.6 136.175 -21.575 4 137.5 154.695 -17.1950000000000 5 83.7 96.115 -12.415 6 106 120.175 -14.1750000000000 7 123.4 146.495 -23.0950000000000 8 126.5 146.935 -20.435 9 120 140.995 -20.995 10 141.6 155.055 -13.455 11 90.5 103.05 -12.5500000000000 12 96.5 114.77 -18.27 13 113.5 129.075 -15.575 14 120.1 128.195 -8.095 15 123.9 136.175 -12.275 16 144.4 154.695 -10.2950000000000 17 90.8 96.115 -5.31500000000001 18 114.2 120.175 -5.97499999999999 19 138.1 146.495 -8.39499999999999 20 135 146.935 -11.935 21 131.3 140.995 -9.695 22 144.6 155.055 -10.455 23 101.7 103.05 -1.35000000000000 24 108.7 114.77 -6.07000000000002 25 135.3 129.075 6.225 26 124.3 128.195 -3.89500000000000 27 138.3 136.175 2.12500000000001 28 158.2 154.695 3.50500000000001 29 93.5 96.115 -2.61500000000001 30 124.8 120.175 4.625 31 154.4 146.495 7.90500000000002 32 152.8 146.935 5.86500000000001 33 148.9 140.995 7.90499999999999 34 170.3 155.055 15.2450000000000 35 124.8 103.05 21.75 36 134.4 114.77 19.6300000000000 37 154 129.075 24.925 38 147.9 128.195 19.705 39 168.1 136.175 31.925 40 175.7 154.695 21.005 41 116.7 96.115 20.585 42 140.8 120.175 20.625 43 164.2 146.495 17.705 44 173.8 146.935 26.865 45 167.8 140.995 26.805 46 166.6 155.055 11.545 47 135.1 132.375 2.72499999999999 48 158.1 144.095 14.0050000000000 49 151.8 158.4 -6.6 50 166.7 157.52 9.18 51 165.3 165.5 -0.199999999999981 52 187 184.02 2.98000000000004 53 125.2 125.44 -0.240000000000006 54 144.4 149.5 -5.09999999999999 55 181.7 175.82 5.88 56 175.9 176.26 -0.359999999999999 57 166.3 170.32 -4.02 58 181.5 184.38 -2.88000000000001 59 121.8 132.375 -10.575 60 134.8 144.095 -9.29500000000001 61 162.9 158.4 4.49999999999999 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.116270447909649 0.232540895819299 0.88372955209035 17 0.06378978860129 0.127579577202580 0.93621021139871 18 0.0407775014441242 0.0815550028882484 0.959222498555876 19 0.0628288273794114 0.125657654758823 0.937171172620589 20 0.0545588901994837 0.109117780398967 0.945441109800516 21 0.0608360055708416 0.121672011141683 0.939163994429158 22 0.0450406048285889 0.0900812096571778 0.954959395171411 23 0.0450104967037246 0.0900209934074492 0.954989503296275 24 0.065829284769356 0.131658569538712 0.934170715230644 25 0.171916277490966 0.343832554981932 0.828083722509034 26 0.230389604487920 0.460779208975840 0.76961039551208 27 0.428370461368324 0.856740922736649 0.571629538631676 28 0.556776499752148 0.886447000495703 0.443223500247852 29 0.65325694027305 0.693486119453899 0.346743059726949 30 0.706351625305958 0.587296749388084 0.293648374694042 31 0.839495632635343 0.321008734729314 0.160504367364657 32 0.933420022997966 0.133159954004068 0.0665799770020338 33 0.969046730444477 0.0619065391110455 0.0309532695555228 34 0.973363968001073 0.0532720639978533 0.0266360319989267 35 0.976548444591755 0.0469031108164903 0.0234515554082452 36 0.979004543549607 0.0419909129007866 0.0209954564503933 37 0.979989330060362 0.0400213398792759 0.0200106699396380 38 0.981723878539904 0.036552242920193 0.0182761214600965 39 0.986176932757818 0.0276461344843630 0.0138230672421815 40 0.977225825206447 0.0455483495871058 0.0227741747935529 41 0.959313201129706 0.0813735977405889 0.0406867988702944 42 0.928512030923478 0.142975938153045 0.0714879690765224 43 0.895221205862077 0.209557588275845 0.104778794137923 44 0.826417333956136 0.347165332087727 0.173582666043864 45 0.74925148873775 0.501497022524501 0.250748511262251 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 6 0.2 NOK 10% type I error level 12 0.4 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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Software written by Ed van Stee & Patrick Wessa

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We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

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