*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: Tue, 24 Nov 2009 04:57:53 -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/24/t1259064129e5isj8s7anepl3u.htm/, Retrieved Tue, 24 Nov 2009 13:02:35 +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/24/t1259064129e5isj8s7anepl3u.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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97.4 116.7 97 109 105.4 119.5 102.7 115.1 98.1 107.1 104.5 109.7 87.4 110.4 89.9 105 109.8 115.8 111.7 116.4 98.6 111.1 96.9 119.5 95.1 110.9 97 115.1 112.7 125.2 102.9 116 97.4 112.9 111.4 121.7 87.4 123.2 96.8 116.6 114.1 136.2 110.3 120.9 103.9 119.6 101.6 125.9 94.6 116.1 95.9 107.5 104.7 116.7 102.8 112.5 98.1 113 113.9 126.4 80.9 114.1 95.7 112.5 113.2 112.4 105.9 113.1 108.8 116.3 102.3 111.7 99 118.8 100.7 116.5 115.5 125.1 100.7 113.1 109.9 119.6 114.6 114.4 85.4 114 100.5 117.8 114.8 117 116.5 120.9 112.9 115 102 117.3 106 119.4 105.3 114.9 118.8 125.8 106.1 117.6 109.3 117.6 117.2 114.9 92.5 121.9 104.2 117 112.5 106.4 122.4 110.5 113.3 113.6 100 114.2

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 6 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation ipchn[t] = + 46.4146793383104 + 0.746503234894817Tip[t] -0.892302272677017M1[t] -5.13511571343774M2[t] -4.30778629079102M3[t] -5.54756016461321M4[t] -5.90470959410443M5[t] -9.70605214891858M6[t] + 8.80895968214796M7[t] -2.01409591346731M8[t] -9.6705069071819M9[t] -11.1242994421722M10[t] -7.88526146792929M11[t] -0.104529017759257t + 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) 46.4146793383104 19.953483 2.3261 0.024472 0.012236 Tip 0.746503234894817 0.210242 3.5507 0.000899 0.00045 M1 -0.892302272677017 3.154317 -0.2829 0.778536 0.389268 M2 -5.13511571343774 3.15061 -1.6299 0.109957 0.054978 M3 -4.30778629079102 4.095137 -1.0519 0.298328 0.149164 M4 -5.54756016461321 3.24736 -1.7083 0.094316 0.047158 M5 -5.90470959410443 3.211719 -1.8385 0.072452 0.036226 M6 -9.70605214891858 4.136587 -2.3464 0.02332 0.01166 M7 8.80895968214796 4.149407 2.1229 0.039171 0.019586 M8 -2.01409591346731 3.171649 -0.635 0.528554 0.264277 M9 -9.6705069071819 4.134973 -2.3387 0.023751 0.011875 M10 -11.1242994421722 4.175721 -2.664 0.010609 0.005305 M11 -7.88526146792929 3.466862 -2.2745 0.027648 0.013824 t -0.104529017759257 0.053261 -1.9626 0.055761 0.02788 Multiple Linear Regression - Regression Statistics Multiple R 0.61415688381946 R-squared 0.377188677942829 Adjusted R-squared 0.201176782578846 F-TEST (value) 2.14297265058605 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 0.0291661287439557 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.94401772121584 Sum Squared Residuals 1124.39231647403 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 116.7 118.127263126630 -1.42726312662984 2 109 113.481319374152 -4.48131937415151 3 119.5 120.474746952155 -0.974746952155375 4 115.1 117.114885326358 -2.01488532635793 5 107.1 113.219291998591 -6.11929199859128 6 109.7 114.091041129345 -4.3910411293447 7 110.4 119.736318625951 -9.33631862595064 8 105 110.674992099813 -5.67499209981315 9 115.8 117.769466462746 -1.96946646274613 10 116.4 117.629501056297 -1.22950105629677 11 111.1 110.984817635658 0.115182364341702 12 119.5 117.496494586507 2.00350541349286 13 110.9 115.155957473260 -4.25595747326019 14 115.1 112.226971161040 2.87302883895962 15 125.2 124.669872353776 0.530127646223556 16 116 116.009837760226 -0.00983776022580646 17 112.9 111.442391521054 1.45760847894617 18 121.7 117.987565237008 3.71243476299214 19 123.2 118.481970412840 4.71802958716045 20 116.6 114.571516207476 2.02848379252370 21 136.2 119.725082159683 16.4749178403172 22 120.9 115.330048314333 5.56995168566706 23 119.6 113.686936567490 5.91306343251025 24 125.9 119.750711577402 6.14928842259831 25 116.1 113.528357642702 2.57164235729829 26 107.5 110.151469389545 -2.65146938954499 27 116.7 117.443498261507 -0.743498261506833 28 112.5 114.680839223625 -2.18083922362524 29 113 110.710595572369 2.28940442763088 30 126.4 118.599475111134 7.80052488886619 31 114.1 112.375351172912 1.72464882708782 32 112.5 112.496014435981 0.00398556401908479 33 112.4 117.798881035166 -5.39888103516634 34 113.1 110.791085867685 2.30891413231532 35 116.3 116.090454205363 0.209545794636744 36 111.7 119.018915628717 -7.31891562871698 37 118.8 115.558623663128 3.24137633687218 38 116.5 112.480336703929 4.01966329607097 39 125.1 124.251384985260 0.848615014740228 40 113.1 111.858834217235 1.24116578276495 41 119.6 118.264985531017 1.33501446898312 42 114.4 117.867679162449 -3.46767916244909 43 114 114.480267516828 -0.480267516827762 44 117.8 114.824881750365 2.97511824963505 45 117 117.738937997887 -0.738937997886962 46 120.9 117.449671944459 3.45032805554136 47 115 117.896769255321 -2.89676925532093 48 117.3 117.540616445137 -0.24061644513746 49 119.4 119.529798094280 -0.129798094280441 50 114.9 114.659903371334 0.240096628665911 51 125.8 125.460497447302 0.339502552698423 52 117.6 114.635603472556 2.96439652744403 53 117.6 116.562735376969 1.03726462303110 54 114.9 118.554239360065 -3.65423936006454 55 121.9 118.52609227147 3.37390772853014 56 117 116.332595506365 0.66740449363531 57 106.4 114.767632344518 -8.3676323445178 58 110.5 120.599692817227 -10.0996928172270 59 113.6 116.941022336168 -3.34102233616777 60 114.2 114.793261762237 -0.59326176223674 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.389795845757798 0.779591691515597 0.610204154242202 18 0.284967720196960 0.569935440393921 0.71503227980304 19 0.463585088333979 0.927170176667957 0.536414911666021 20 0.345186358345715 0.69037271669143 0.654813641654285 21 0.781373830157016 0.437252339685968 0.218626169842984 22 0.704886627253679 0.590226745492642 0.295113372746321 23 0.649876198640993 0.700247602718013 0.350123801359007 24 0.652358730631309 0.695282538737383 0.347641269368691 25 0.56962651514332 0.86074696971336 0.43037348485668 26 0.705078012925797 0.589843974148406 0.294921987074203 27 0.668281441578158 0.663437116843685 0.331718558421842 28 0.696391261764448 0.607217476471104 0.303608738235552 29 0.612418219039953 0.775163561920095 0.387581780960047 30 0.756392854043642 0.487214291912717 0.243607145956358 31 0.704575685542324 0.590848628915351 0.295424314457676 32 0.694255067648684 0.611489864702633 0.305744932351316 33 0.897561076075207 0.204877847849586 0.102438923924793 34 0.840486365284154 0.319027269431692 0.159513634715846 35 0.824233129634122 0.351533740731755 0.175766870365878 36 0.942451523328138 0.115096953343723 0.0575484766718617 37 0.900720116254906 0.198559767490188 0.0992798837450942 38 0.84164291648119 0.316714167037621 0.158357083518810 39 0.760610798707863 0.478778402584273 0.239389201292137 40 0.682366302026535 0.63526739594693 0.317633697973465 41 0.564571212117743 0.870857575764514 0.435428787882257 42 0.473624382985058 0.947248765970117 0.526375617014942 43 0.614279227124504 0.771441545750993 0.385720772875496 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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