Seatbelt Law

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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: Thu, 27 Nov 2008 11:25:21 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/27/t1227810606ddinpdfvnaqhxcr.htm/, Retrieved Thu, 27 Nov 2008 18:30:15 +0000

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/2008/Nov/27/t1227810606ddinpdfvnaqhxcr.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

Feedback Forum:

2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc]  [reply]  test Post a new message

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

87,0 106,7 96,3 101,1 107,1 97,8 115,2 113,8 106,1 107,1 89,5 117,5 91,3 113,7 97,6 106,6 100,7 109,8 104,6 108,8 94,7 102,0 101,8 114,5 102,5 116,5 105,3 108,6 110,3 113,9 109,8 109,3 117,3 112,5 118,8 123,4 131,3 115,2 125,9 110,8 133,1 120,4 147,0 117,6 145,8 111,2 164,4 131,1 149,8 118,9 137,7 115,7 151,7 119,6 156,8 113,1 180,0 106,4 180,4 115,5 170,4 111,8 191,6 109,6 199,5 121,5 218,2 109,5 217,5 109,0 205,0 113,4 194,0 112,7 199,3 114,4 219,3 109,2 211,1 116,2 215,2 113,8 240,2 123,6 242,2 112,6 240,7 117,7 255,4 113,3 253,0 110,7 218,2 114,7 203,7 116,9 205,6 120,6 215,6 111,6 188,5 111,9 202,9 116,1 214,0 111,9 230,3 125,1 230,0 115,1 241,0 116,7 259,6 115,8 247,8 116,8 270,3 113,0 289,7 106,5

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 X[t] = + 193.401871931899 -0.97702580141358Y[t] -11.8816409113039M1[t] -16.6592006863323M2[t] -15.0716314542927M3[t] -11.2934443019842M4[t] -10.3640869229770M5[t] + 2.24271270787681M6[t] -6.87649260274204M7[t] -5.07216465296427M8[t] + 5.87085952827723M9[t] + 3.78297381111479M10[t] -6.82283178094506M11[t] + 3.14783592824319t + 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) 193.401871931899 65.449545 2.955 0.004917 0.002458 Y -0.97702580141358 0.573204 -1.7045 0.095034 0.047517 M1 -11.8816409113039 12.516825 -0.9493 0.347452 0.173726 M2 -16.6592006863323 12.843418 -1.2971 0.201065 0.100532 M3 -15.0716314542927 12.814242 -1.1762 0.245581 0.122791 M4 -11.2934443019842 12.515301 -0.9024 0.371561 0.18578 M5 -10.3640869229770 12.83301 -0.8076 0.423471 0.211735 M6 2.24271270787681 12.786771 0.1754 0.86154 0.43077 M7 -6.87649260274204 12.498931 -0.5502 0.584867 0.292433 M8 -5.07216465296427 12.61036 -0.4022 0.689384 0.344692 M9 5.87085952827723 12.415853 0.4729 0.638555 0.319277 M10 3.78297381111479 12.581127 0.3007 0.765009 0.382504 M11 -6.82283178094506 12.939065 -0.5273 0.600516 0.300258 t 3.14783592824319 0.160552 19.6064 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.953457037397714 R-squared 0.909080322163226 Adjusted R-squared 0.88338563060066 F-TEST (value) 35.3800830786242 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 19.6184169034144 Sum Squared Residuals 17704.5849626241 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 87 80.4194139380092 6.58058606199082 2 96.3 84.26103457914 12.03896542086 3 107.1 92.2206248840875 14.8793751159124 4 115.2 83.514235142022 31.6857648579781 5 106.1 94.1375013187433 11.9624986812566 6 89.5 99.7310685431392 -10.2310685431392 7 91.3 97.472397206135 -6.17239720613504 8 97.6 109.361444274192 -11.7614442741925 9 100.7 120.325821819154 -19.6258218191537 10 104.6 122.362797831648 -17.762797831648 11 94.7 121.548603617444 -26.8486036174437 12 101.8 119.306448808962 -17.5064488089623 13 102.5 108.618592223074 -6.11859222307438 14 105.3 114.707372207457 -9.40737220745651 15 110.3 114.264540620247 -3.96454062024723 16 109.8 125.684882387301 -15.8848823873014 17 117.3 126.635593130028 -9.33559313002834 18 118.8 131.740647453717 -12.9406474537173 19 131.3 133.780889642933 -2.48088964293304 20 125.9 143.031967047174 -17.1319670471738 21 133.1 147.743379463088 -14.6433794630881 22 147 151.539001918127 -4.53900191812688 23 145.8 150.333997383357 -4.5339973833571 24 164.4 140.861851644415 23.5381483555849 25 149.8 144.0477614386 5.75223856139991 26 137.7 145.544520156338 -7.84452015633842 27 151.7 146.469524691108 5.23047530889184 28 156.8 159.746215480848 -2.94621548084815 29 180 170.369481657569 9.6305183424305 30 180.4 177.233182423803 3.16681757619706 31 170.4 174.876808506658 -4.47680850665752 32 191.6 181.978429147788 9.6215708522116 33 199.5 184.442682220451 15.0573177795485 34 218.2 197.226942048495 20.9730579515048 35 217.5 190.257485285385 27.2425147146147 36 205 195.929239468354 9.07076053164617 37 194 187.879352546283 6.12064745371737 38 199.3 184.588684837094 14.7113151629056 39 219.3 194.404624164728 24.8953758352723 40 211.1 194.491466635384 16.6085333646156 41 215.2 200.913521866027 14.2864781339726 42 240.2 207.093304571271 33.1066954287287 43 242.2 211.869219004445 30.330780995555 44 240.7 211.838551295257 28.8614487047433 45 255.4 230.228324930961 25.1716750690388 46 253 233.828542225717 19.1714577742828 47 218.2 222.462469356246 -4.26246935624625 48 203.7 230.283680302325 -26.5836803023247 49 205.6 217.934879854034 -12.3348798540337 50 215.6 225.098388219971 -9.49838821997076 51 188.5 229.540685639829 -41.0406856398294 52 202.9 232.363200354444 -29.4632003544441 53 214 240.543902027631 -26.5439020276315 54 230.3 243.401797008069 -13.1017970080692 55 230 247.200685639829 -17.2006856398294 56 241 250.589608235589 -9.58960823558864 57 259.6 265.559791566346 -5.95979156634553 58 247.8 265.642715976013 -17.8427159760127 59 270.3 261.897444357568 8.40255564243237 60 289.7 278.218779775944 11.4812202240558 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.0266225184259325 0.053245036851865 0.973377481574067 18 0.0566272929976776 0.113254585995355 0.943372707002322 19 0.108373762534011 0.216747525068023 0.891626237465989 20 0.0819995386883988 0.163999077376798 0.918000461311601 21 0.0733690825159418 0.146738165031884 0.926630917484058 22 0.0838861091031605 0.167772218206321 0.91611389089684 23 0.136912367648152 0.273824735296304 0.863087632351848 24 0.166665020260335 0.333330040520669 0.833334979739665 25 0.141449045072920 0.282898090145841 0.85855095492708 26 0.105963052165075 0.211926104330150 0.894036947834925 27 0.064800896090277 0.129601792180554 0.935199103909723 28 0.0462164449602396 0.0924328899204792 0.95378355503976 29 0.0635837196586472 0.127167439317294 0.936416280341353 30 0.111446186690276 0.222892373380551 0.888553813309724 31 0.125283310698505 0.250566621397009 0.874716689301495 32 0.285696642536907 0.571393285073813 0.714303357463093 33 0.297485955808065 0.594971911616129 0.702514044191936 34 0.357783588993897 0.715567177987794 0.642216411006103 35 0.482537668867475 0.96507533773495 0.517462331132525 36 0.416814991254459 0.833629982508917 0.583185008745541 37 0.6248881595009 0.750223680998199 0.375111840499099 38 0.526795317219468 0.946409365561064 0.473204682780532 39 0.51101357498682 0.977972850026359 0.488986425013179 40 0.468975083588131 0.937950167176261 0.531024916411869 41 0.518501697493204 0.962996605013592 0.481498302506796 42 0.507372603341517 0.985254793316966 0.492627396658483 43 0.454873655064561 0.909747310129122 0.545126344935439 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 2 0.0740740740740741 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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