Vertragingen

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R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Sat, 18 Dec 2010 11:45:57 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/18/t1292672774n0dv0aum3bglq3v.htm/, Retrieved Sat, 18 Dec 2010 12:46:25 +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/2010/Dec/18/t1292672774n0dv0aum3bglq3v.htm/}, year = {2010}, } @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 = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

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Dataseries X:

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104,7 116,7 107,5 116,1 102,8 112,5 116,7 107,5 98,1 113 112,5 116,7 113,9 126,4 113 112,5 80,9 114,1 126,4 113 95,7 112,5 114,1 126,4 113,2 112,4 112,5 114,1 105,9 113,1 112,4 112,5 108,8 116,3 113,1 112,4 102,3 111,7 116,3 113,1 99 118,8 111,7 116,3 100,7 116,5 118,8 111,7 115,5 125,1 116,5 118,8 100,7 113,1 125,1 116,5 109,9 119,6 113,1 125,1 114,6 114,4 119,6 113,1 85,4 114 114,4 119,6 100,5 117,8 114 114,4 114,8 117 117,8 114 116,5 120,9 117 117,8 112,9 115 120,9 117 102 117,3 115 120,9 106 119,4 117,3 115 105,3 114,9 119,4 117,3 118,8 125,8 114,9 119,4 106,1 117,6 125,8 114,9 109,3 117,6 117,6 125,8 117,2 114,9 117,6 117,6 92,5 121,9 114,9 117,6 104,2 117 121,9 114,9 112,5 106,4 117 121,9 122,4 110,5 106,4 117 113,3 113,6 110,5 106,4 100 114,2 113,6 110,5 110,7 125,4 114,2 113,6 112,8 124,6 125,4 114,2 109,8 120,2 124,6 125,4 117,3 120,8 120,2 124,6 109,1 111,4 120,8 120,2 115,9 124,1 111,4 120,8 96 120,2 124,1 111,4 99,8 125,5 120,2 124,1 116,8 116 125,5 120,2 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 7 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation I.P.C.N.[t] = + 17.888666290104 + 0.593242377727027T.I.P.[t] + 0.205154983132475`y(t-1)`[t] + 0.115152970700046`y(t-2)`[t] + 1.45879444891353M1[t] -2.14950402416358M2[t] -1.21608635241408M3[t] -1.28121836133136M4[t] + 10.7917317668094M5[t] + 4.87747224861314M6[t] -7.95768982198348M7[t] -4.4592279731663M8[t] -3.79312308338613M9[t] + 0.925313075396348M10[t] + 6.08788829036565M11[t] -0.0896622450989522t + 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) 17.888666290104 11.042792 1.6199 0.11273 0.056365 T.I.P. 0.593242377727027 0.109649 5.4104 3e-06 1e-06 `y(t-1)` 0.205154983132475 0.117405 1.7474 0.087875 0.043937 `y(t-2)` 0.115152970700046 0.116605 0.9875 0.329031 0.164515 M1 1.45879444891353 2.868214 0.5086 0.613689 0.306844 M2 -2.14950402416358 2.497623 -0.8606 0.394334 0.197167 M3 -1.21608635241408 2.806613 -0.4333 0.667019 0.333509 M4 -1.28121836133136 2.863701 -0.4474 0.656886 0.328443 M5 10.7917317668094 3.040126 3.5498 0.000966 0.000483 M6 4.87747224861314 2.721254 1.7924 0.08028 0.04014 M7 -7.95768982198348 2.744783 -2.8992 0.005926 0.002963 M8 -4.4592279731663 2.985327 -1.4937 0.142725 0.071363 M9 -3.79312308338613 2.56813 -1.477 0.147136 0.073568 M10 0.925313075396348 2.713631 0.341 0.734813 0.367407 M11 6.08788829036565 2.746191 2.2168 0.032102 0.016051 t -0.0896622450989522 0.033877 -2.6467 0.011394 0.005697 Multiple Linear Regression - Regression Statistics Multiple R 0.90677540764535 R-squared 0.82224163991039 Adjusted R-squared 0.758756511306957 F-TEST (value) 12.9517204737289 F-TEST (DF numerator) 15 F-TEST (DF denominator) 42 p-value 3.16493498075943e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.71652920335122 Sum Squared Residuals 580.128751413224 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 116.7 116.793696026955 -0.0936960269545418 2 112.5 112.865685087896 -0.365685087895517 3 113 111.118957740513 1.88104225948693 4 126.4 119.95632806921 6.4436719307901 5 114.1 115.169270746585 -1.06927074658506 6 112.5 116.964979688501 -4.46497968850098 7 112.4 112.677267470406 -0.277267470405828 8 113.1 111.550637465283 1.54936253471653 9 116.3 113.979576196496 2.32042380350424 10 111.7 115.489377680468 -3.78937768046757 11 118.8 118.029367387670 0.770632612330493 12 116.5 113.787225609361 2.71277439063879 13 125.1 124.282074634301 0.817925365698576 14 113.1 113.303607748095 -0.203607748094541 15 119.6 118.133648800264 1.46635119973557 16 114.4 120.718765463526 -6.31876546352575 17 114 115.061064314200 -1.06106431419986 18 117.8 117.334245013689 0.465754986310517 19 117 113.626314447114 3.37368555288624 20 120.9 118.317083395122 2.58291660487787 21 115 117.465835537643 -2.46583553764268 22 117.3 114.866949719350 2.43305028064981 23 119.4 122.105286134203 -2.70528613420306 24 114.9 116.208143231518 -1.30814323151784 25 125.8 124.904671349021 0.895328650978752 26 117.6 115.390533381706 2.20946661829429 27 117.6 117.705560936027 -0.105560936026953 28 114.9 121.293127106314 -6.39312710631384 29 121.9 118.069409805040 3.83059019495955 30 117 120.131595722189 -3.13159572218863 31 106.4 111.931494519179 -5.53149451917855 32 110.5 118.47450128476 -7.9745012847599 33 113.6 113.272952233548 0.327047766452163 34 114.2 111.119710151043 3.08028984895724 35 125.4 123.020383761642 2.37961623835808 36 124.6 120.455469812908 4.14453018709217 37 120.2 121.170464168876 -0.970464168875852 38 120.8 120.927016981310 -0.127016981309563 39 111.4 116.522604829398 -5.12260482939777 40 124.1 118.5424936849 5.5575063150999 41 120.2 120.243288612376 -0.0432886123761048 42 125.5 117.156026178118 8.3439738218825 43 116 114.954547108653 1.04545289134670 44 117 116.372118501824 0.627881498176462 45 105.7 106.389912151036 -0.689912151036261 46 102 105.790051599615 -3.79005159961503 47 106.4 106.844962716486 -0.444962716485515 48 96.9 102.449161346213 -5.5491613462131 49 107.6 108.249093820847 -0.649093820846937 50 98.8 100.313156800995 -1.51315680099467 51 101.1 99.2192276937978 1.88077230620222 52 105.7 104.989285676050 0.710714323949584 53 104.6 106.256966521799 -1.65696652179852 54 103.2 104.413153397503 -1.21315339750342 55 101.6 100.210376454649 1.38962354535145 56 106.7 103.485659353011 3.21434064698903 57 99.5 98.9917238812775 0.508276118722535 58 101 98.9339108495244 2.06608915047556 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 19 0.805132733379345 0.38973453324131 0.194867266620655 20 0.705033605057932 0.589932789884136 0.294966394942068 21 0.587103703547356 0.825792592905288 0.412896296452644 22 0.618023772919378 0.763952454161244 0.381976227080622 23 0.514044815618347 0.971910368763307 0.485955184381653 24 0.426210961569951 0.852421923139902 0.573789038430049 25 0.324705111367582 0.649410222735164 0.675294888632418 26 0.292710787574653 0.585421575149307 0.707289212425346 27 0.216816586543329 0.433633173086658 0.783183413456671 28 0.274251341845868 0.548502683691736 0.725748658154132 29 0.336332320304827 0.672664640609654 0.663667679695173 30 0.276751170445045 0.553502340890089 0.723248829554955 31 0.224220336901904 0.448440673803808 0.775779663098096 32 0.549431459998418 0.901137080003163 0.450568540001582 33 0.455382583853671 0.910765167707343 0.544617416146329 34 0.402350090750459 0.804700181500918 0.597649909249541 35 0.305533197228286 0.611066394456572 0.694466802771714 36 0.451352713699889 0.902705427399778 0.548647286300111 37 0.344178946023515 0.688357892047031 0.655821053976485 38 0.229864827054047 0.459729654108094 0.770135172945953 39 0.309920199360235 0.61984039872047 0.690079800639765 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 = 2 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 2 ; 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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