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: Thu, 19 Nov 2009 11:56:53 -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/t12586573031zt37ddxh4z6eei.htm/, Retrieved Thu, 19 Nov 2009 20:01:55 +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/t12586573031zt37ddxh4z6eei.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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7.2 102.9 7.4 97.4 8.8 111.4 9.3 87.4 9.3 96.8 8.7 114.1 8.2 110.3 8.3 103.9 8.5 101.6 8.6 94.6 8.5 95.9 8.2 104.7 8.1 102.8 7.9 98.1 8.6 113.9 8.7 80.9 8.7 95.7 8.5 113.2 8.4 105.9 8.5 108.8 8.7 102.3 8.7 99 8.6 100.7 8.5 115.5 8.3 100.7 8 109.9 8.2 114.6 8.1 85.4 8.1 100.5 8 114.8 7.9 116.5 7.9 112.9 8 102 8 106 7.9 105.3 8 118.8 7.7 106.1 7.2 109.3 7.5 117.2 7.3 92.5 7 104.2 7 112.5 7 122.4 7.2 113.3 7.3 100 7.1 110.7 6.8 112.8 6.4 109.8 6.1 117.3 6.5 109.1 7.7 115.9 7.9 96 7.5 99.8 6.9 116.8 6.6 115.7 6.9 99.4 7.7 94.3 8 91 8 93.2 7.7 103.1 7.3 94.1 7.4 91.8 8.1 102.7 8.3 82.6 8.2 89.1

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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Werkl.graad[t] = + 12.3090819339331 -0.0412129184085256Industr.prod.[t] -0.57362530141987M1[t] -0.680636505218328M2[t] + 0.482179560840401M3[t] -0.43765867046735M4[t] -0.149933354060247M5[t] + 0.220730381793249M6[t] + 0.0157848315842262M7[t] -0.112099138071189M8[t] -0.146141576344155M9[t] -0.0970747342942795M10[t] -0.162673681995025M11[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) 12.3090819339331 1.629838 7.5523 0 0 Industr.prod. -0.0412129184085256 0.01452 -2.8384 0.006452 0.003226 M1 -0.57362530141987 0.411697 -1.3933 0.169451 0.084725 M2 -0.680636505218328 0.416688 -1.6334 0.108417 0.054208 M3 0.482179560840401 0.402396 1.1983 0.236245 0.118122 M4 -0.43765867046735 0.52111 -0.8399 0.404832 0.202416 M5 -0.149933354060247 0.441423 -0.3397 0.735481 0.367741 M6 0.220730381793249 0.422728 0.5222 0.603779 0.301889 M7 0.0157848315842262 0.422498 0.0374 0.97034 0.48517 M8 -0.112099138071189 0.420776 -0.2664 0.790977 0.395488 M9 -0.146141576344155 0.445009 -0.3284 0.743927 0.371963 M10 -0.0970747342942795 0.443941 -0.2187 0.827766 0.413883 M11 -0.162673681995025 0.437971 -0.3714 0.71183 0.355915 Multiple Linear Regression - Regression Statistics Multiple R 0.523233314270716 R-squared 0.273773101162718 Adjusted R-squared 0.106182278354114 F-TEST (value) 1.63358050622724 F-TEST (DF numerator) 12 F-TEST (DF denominator) 52 p-value 0.110962144497039 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.662367940128446 Sum Squared Residuals 22.81402698172 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 7.2 7.4946473282759 -0.294647328275905 2 7.4 7.61430717572433 -0.214307175724331 3 8.8 8.2001423840637 0.599857615936296 4 9.3 8.26941419456057 1.03058580543943 5 9.3 8.16973807792753 1.13026192207247 6 8.7 7.82741832531353 0.872581674686465 7 8.2 7.7790818650569 0.420918134943090 8 8.3 7.91496057321606 0.385039426783945 9 8.5 7.9757078472827 0.5242921527173 10 8.6 8.31326511819226 0.286734881807745 11 8.5 8.19408937656043 0.305910623439575 12 8.2 7.99408937656043 0.205910623439574 13 8.1 7.49876862011676 0.601231379883244 14 7.9 7.58545813283837 0.314541867161635 15 8.6 8.0971100880424 0.502889911957608 16 8.7 8.53729816421598 0.162701835784015 17 8.7 8.21507228817691 0.484927711823091 18 8.5 7.8645099518812 0.635490048118793 19 8.4 7.96041870605442 0.439581293945580 20 8.5 7.71301727301428 0.786982726985718 21 8.7 7.94685880439673 0.753141195603267 22 8.7 8.13192827719474 0.568071722805258 23 8.6 7.9962673681995 0.603732631800497 24 8.5 7.54898985774835 0.95101014225165 25 8.3 7.58531574877466 0.714684251225343 26 8 7.09914569561776 0.900854304382236 27 8.2 8.06826104515642 0.131738954843575 28 8.1 8.35184003137762 -0.251840031377620 29 8.1 8.01725027981599 0.0827497201840136 30 8 7.79856928242757 0.201430717572433 31 7.9 7.52356177092405 0.37643822907595 32 7.9 7.54404430753933 0.355955692460674 33 8 7.95922267991929 0.0407773200807104 34 8 7.84343784833506 0.156562151664937 35 7.9 7.80668794352029 0.0933120564797152 36 8 7.41298722700022 0.587012772999785 37 7.7 7.36276598936862 0.337234010631379 38 7.2 7.12387344666288 0.0761265533371212 39 7.5 7.96110745729426 -0.461107457294257 40 7.3 8.05922831067709 -0.759228310677088 41 7 7.86476248170444 -0.864762481704441 42 7 7.89335899476718 -0.893358994767176 43 7 7.28040555231375 -0.280405552313749 44 7.2 7.52755914017592 -0.327559140175916 45 7.3 8.04164851673634 -0.74164851673634 46 7.1 7.64973713181499 -0.549737131814993 47 6.8 7.49759105545634 -0.697591055456344 48 6.4 7.78390349267695 -1.38390349267695 49 6.1 6.90118130319313 -0.801181303193134 50 6.5 7.13211603034458 -0.632116030344584 51 7.7 8.01468425122534 -0.31468425122534 52 7.9 7.91498309624725 -0.0149830962472480 53 7.5 8.04609932270195 -0.546099322701954 54 6.9 7.71614344561052 -0.816143445610515 55 6.6 7.55653210565087 -0.95653210565087 56 6.9 8.10041870605442 -1.20041870605442 57 7.7 8.27656215166494 -0.576562151664936 58 8 8.46163162446295 -0.461631624462946 59 8 8.30536425626345 -0.305364256263444 60 7.7 8.06003004601407 -0.360030046014067 61 7.3 7.85732101027093 -0.557321010270928 62 7.4 7.84509951881208 -0.445099518812076 63 8.1 8.55869477421788 -0.458694774217878 64 8.3 8.4672362029215 -0.167236202921491 65 8.2 8.48707754967318 -0.287077549673179 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.273608852358782 0.547217704717565 0.726391147641218 17 0.198048990927429 0.396097981854857 0.801951009072571 18 0.116128621706424 0.232257243412847 0.883871378293576 19 0.0877497695548899 0.175499539109780 0.91225023044511 20 0.0526537971323267 0.105307594264653 0.947346202867673 21 0.0329256555674415 0.0658513111348829 0.967074344432559 22 0.0185928771522766 0.0371857543045532 0.981407122847723 23 0.0107661958478210 0.0215323916956419 0.989233804152179 24 0.00793860304211726 0.0158772060842345 0.992061396957883 25 0.0221131775020419 0.0442263550040839 0.977886822497958 26 0.0190512012470193 0.0381024024940386 0.98094879875298 27 0.0216693772318784 0.0433387544637569 0.978330622768122 28 0.0502634717546868 0.100526943509374 0.949736528245313 29 0.100998324082061 0.201996648164121 0.89900167591794 30 0.135147206211383 0.270294412422767 0.864852793788617 31 0.1572941665597 0.3145883331194 0.8427058334403 32 0.202203795499257 0.404407590998514 0.797796204500743 33 0.219613434971257 0.439226869942514 0.780386565028743 34 0.224359635881482 0.448719271762963 0.775640364118518 35 0.220676367026307 0.441352734052615 0.779323632973693 36 0.464846086020128 0.929692172040255 0.535153913979872 37 0.619873702655717 0.760252594688566 0.380126297344283 38 0.669866208821693 0.660267582356614 0.330133791178307 39 0.688386837599442 0.623226324801116 0.311613162400558 40 0.821965167816934 0.356069664366133 0.178034832183066 41 0.887724500367428 0.224550999265145 0.112275499632572 42 0.905211842218246 0.189576315563509 0.0947881577817543 43 0.917057611264425 0.165884777471151 0.0829423887355754 44 0.977403855330987 0.0451922893380268 0.0225961446690134 45 0.965398860516612 0.0692022789667759 0.0346011394833880 46 0.934068182389303 0.131863635221394 0.0659318176106972 47 0.87990637575126 0.240187248497480 0.120093624248740 48 0.995047230730819 0.00990553853836234 0.00495276926918117 49 0.980895493751507 0.0382090124969857 0.0191045062484929 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 1 0.0294117647058824 NOK 5% type I error level 9 0.264705882352941 NOK 10% type I error level 11 0.323529411764706 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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