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: Sun, 22 Nov 2009 06:44:03 -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/22/t1258897570sgcuatnb1bvx2wx.htm/, Retrieved Sun, 22 Nov 2009 14:46:22 +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/22/t1258897570sgcuatnb1bvx2wx.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 6,5 8 17,4 7,4 6,6 8,5 17 8,8 7,6 10,4 18 9,3 8 11,1 23,8 9,3 8,1 10,9 25,6 8,7 7,7 10 23,7 8,2 7,5 9,2 22 8,3 7,6 9,2 21,3 8,5 7,8 9,5 20,7 8,6 7,8 9,6 20,4 8,5 7,8 9,5 20,3 8,2 7,5 9,1 20,4 8,1 7,5 8,9 19,8 7,9 7,1 9 19,5 8,6 7,5 10,1 23,1 8,7 7,5 10,3 23,5 8,7 7,6 10,2 23,5 8,5 7,7 9,6 22,9 8,4 7,7 9,2 21,9 8,5 7,9 9,3 21,5 8,7 8,1 9,4 20,5 8,7 8,2 9,4 20,2 8,6 8,2 9,2 19,4 8,5 8,2 9 19,2 8,3 7,9 9 18,8 8 7,3 9 18,8 8,2 6,9 9,8 22,6 8,1 6,6 10 23,3 8,1 6,7 9,8 23 8 6,9 9,3 21,4 7,9 7 9 19,9 7,9 7,1 9 18,8 8 7,2 9,1 18,6 8 7,1 9,1 18,4 7,9 6,9 9,1 18,6 8 7 9,2 19,9 7,7 6,8 8,8 19,2 7,2 6,4 8,3 18,4 7,5 6,7 8,4 21,1 7,3 6,6 8,1 20,5 7 6,4 7,7 19,1 7 6,3 7,9 18,1 7 6,2 7,9 17 7,2 6,5 8 17,1 7,3 6,8 7,9 17,4 7,1 6,8 7,6 16,8 6,8 6,4 7,1 15,3 6,4 6,1 6,8 14,3 6,1 5,8 6,5 13,4 6,5 6,1 6,9 15,3 7,7 7,2 8,2 22,1 7,9 7,3 8,7 23,7 7,5 6,9 8,3 22,2 6,9 6,1 7,9 19,5 6,6 5,8 7,5 16,6 6,9 6,2 7,8 17,3 7,7 7,1 8,3 19,8 8 7,7 8,4 21,2 8 7,9 8,2 21,5 7,7 7,7 7, 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 TW[t] = + 0.211999605127861 + 0.527374917646042WM[t] + 0.424575943486697WV[t] + 0.00763345863895995WJ[t] -0.0107192009268042M1[t] -0.0253430461300658M2[t] + 0.0173207640937708M3[t] -0.0147025622825291M4[t] -0.0111383824972702M5[t] -0.0127332059870329M6[t] + 0.0137345467647528M7[t] -0.0027356307527948M8[t] + 0.0198790659864952M9[t] + 0.00495812503304638M10[t] + 0.0148365517192163M11[t] + 0.000127469705657836t + 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) 0.211999605127861 0.08483 2.4991 0.015851 0.007925 WM 0.527374917646042 0.011295 46.6927 0 0 WV 0.424575943486697 0.010829 39.209 0 0 WJ 0.00763345863895995 0.00403 1.894 0.064136 0.032068 M1 -0.0107192009268042 0.02007 -0.5341 0.595695 0.297847 M2 -0.0253430461300658 0.020091 -1.2614 0.213138 0.106569 M3 0.0173207640937708 0.022227 0.7793 0.439563 0.219781 M4 -0.0147025622825291 0.024848 -0.5917 0.556773 0.278387 M5 -0.0111383824972702 0.024261 -0.4591 0.648191 0.324096 M6 -0.0127332059870329 0.023597 -0.5396 0.591904 0.295952 M7 0.0137345467647528 0.021752 0.6314 0.530701 0.265351 M8 -0.0027356307527948 0.020922 -0.1308 0.896507 0.448253 M9 0.0198790659864952 0.020771 0.9571 0.34323 0.171615 M10 0.00495812503304638 0.020789 0.2385 0.812486 0.406243 M11 0.0148365517192163 0.02064 0.7188 0.475655 0.237827 t 0.000127469705657836 0.000426 0.2993 0.76599 0.382995 Multiple Linear Regression - Regression Statistics Multiple R 0.999180255803478 R-squared 0.998361183587504 Adjusted R-squared 0.997859505093883 F-TEST (value) 1990.04182216648 F-TEST (DF numerator) 15 F-TEST (DF denominator) 49 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.0324139473504168 Sum Squared Residuals 0.0514825351589441 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 7.2 7.15877456681749 0.0412254331825123 2 7.4 7.40625027137223 -0.00625027137223209 3 8.8 8.79074422021145 0.00925577978854648 4 9.3 9.31127555114588 -0.0112755511458815 5 9.3 9.2965297292542 0.00347027074580880 6 8.7 8.68749048785962 0.0125095121403803 7 8.2 8.25597309231226 -0.055973092312265 8 8.3 8.2870244552177 0.0129755447822942 9 8.5 8.5380343130545 -0.0380343130544964 10 8.6 8.56340839856369 0.0365916014363128 11 8.5 8.53019335474295 -0.0301933547429491 12 8.2 8.1882047659048 0.0117952340952040 13 8.1 8.08811777080293 0.0118822291970658 14 7.9 7.9028389850039 -0.00283898500389447 15 8.6 8.65109422092743 -0.051094220927429 16 8.7 8.70716693640971 -0.00716693640971106 17 8.7 8.72113848331656 -0.0211384833165615 18 8.5 8.51308298002167 -0.0130829800216662 19 8.4 8.36221436644547 0.0377856335545296 20 8.5 8.49075085305588 0.0092491469441242 21 8.7 8.65379213873974 0.046207861260258 22 8.7 8.68944612166487 0.0105538783351330 23 8.6 8.60843006244819 -0.00843006244818653 24 8.5 8.5072791000095 -0.00727910000949656 25 8.3 8.33542151003895 -0.0354215100389536 26 8 8.00450018395373 -0.00450018395372530 27 8.2 8.2050093944422 -0.00500939444220988 28 8.1 8.10515967222237 -0.00515967222236557 29 8.1 8.07438358718886 0.0256164128111402 30 8 7.95388971136828 0.0461102886317216 31 7.9 7.89439945458588 0.00560054541412379 32 7.9 7.92239743403573 -0.0223974340357345 33 8 8.03880799486616 -0.0388079948661648 34 8 7.96975034012598 0.0302496598740227 35 7.9 7.8758079447164 0.0241920552836112 36 8 7.96621744504675 0.033782554953248 37 7.7 7.67497693185445 0.0250230681455531 38 7.2 7.23113585064391 -0.0311358506439103 39 7.5 7.49520753854108 0.00479246145892127 40 7.3 7.27862133187645 0.0213786681235531 41 7 6.99632077834893 0.00367922165106692 42 7 7.0193976628586 -0.0193976628586033 43 7 6.98485858904859 0.0151414109514131 44 7.2 7.16994929674308 0.030050703256925 45 7.3 7.31073638172485 -0.0107363817248539 46 7.1 7.16399005224768 -0.0639900522476777 47 6.8 6.7393078218793 0.0606921781206996 48 6.4 6.43138002288696 -0.0313800228869595 49 6.1 6.12833292055093 -0.0283329205509286 50 6.5 6.45638296915584 0.0436170308441603 51 7.7 7.68314290377361 0.0168570962263866 52 7.9 7.92848604443326 -0.0284860444332596 53 7.5 7.53994716151264 -0.0399471615126423 54 6.9 6.92613915789183 -0.0261391578918324 55 6.6 6.6025544976078 -0.00255449760780150 56 6.9 6.92987796094761 -0.0298779609476088 57 7.7 7.65862917161474 0.0413708283852571 58 8 8.0134050873978 -0.0134050873977908 59 8 8.04626081621318 -0.0462608162131751 60 7.7 7.706918666152 -0.00691866615199587 61 7.3 7.31437629993525 -0.0143762999352490 62 7.4 7.3988917398704 0.00110826012960181 63 8.1 8.07480172210422 0.0251982778957845 64 8.3 8.26929046391234 0.0307095360876646 65 8.2 8.17168026037881 0.0283197396211879 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 19 0.788536238017317 0.422927523965366 0.211463761982683 20 0.657884034790941 0.684231930418118 0.342115965209059 21 0.731877116478965 0.536245767042069 0.268122883521034 22 0.715834236381099 0.568331527237803 0.284165763618901 23 0.607085298161478 0.785829403677044 0.392914701838522 24 0.525523396694702 0.948953206610595 0.474476603305298 25 0.646387585020649 0.707224829958703 0.353612414979351 26 0.561972531240254 0.876054937519493 0.438027468759746 27 0.49078300875173 0.98156601750346 0.50921699124827 28 0.411955331367317 0.823910662734634 0.588044668632683 29 0.325076217395206 0.650152434790412 0.674923782604794 30 0.31961182494046 0.63922364988092 0.68038817505954 31 0.244089627255098 0.488179254510196 0.755910372744902 32 0.271358446271108 0.542716892542217 0.728641553728892 33 0.465949928113051 0.931899856226102 0.534050071886949 34 0.382361250707983 0.764722501415966 0.617638749292017 35 0.338422818489542 0.676845636979084 0.661577181510458 36 0.282465873613098 0.564931747226195 0.717534126386902 37 0.301135535947727 0.602271071895455 0.698864464052273 38 0.249268221981106 0.498536443962212 0.750731778018894 39 0.182683509643585 0.365367019287170 0.817316490356415 40 0.146455238902516 0.292910477805032 0.853544761097484 41 0.125889067468071 0.251778134936142 0.87411093253193 42 0.105615902276104 0.211231804552207 0.894384097723896 43 0.060842997946705 0.121685995893410 0.939157002053295 44 0.105973546658404 0.211947093316807 0.894026453341596 45 0.056001108392844 0.112002216785688 0.943998891607156 46 0.223734712428962 0.447469424857925 0.776265287571038 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 = 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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