opl oef 2.1

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

Title produced by software: Multiple Regression

Date of computation: Thu, 08 May 2008 08:14:44 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/May/08/t1210256252qromv1259slrr77.htm/, Retrieved Thu, 08 May 2008 16:17:32 +0200

User-defined keywords:

Dataseries X:

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56421 53152 53536 52408 41454 38271 35306 26414 31917 38030 27534 18387 50556 43901 48572 43899 37532 40357 35489 29027 34485 42598 30306 26451 47460 50104 61465 53726 39477 43895 31481 29896 33842 39120 33702 25094 51442 45594 52518 48564 41745 49585 32747 33379 35645 37034 35681 20972 58552 54955 65540 51570 51145 46641 35704 33253 35193 41668 34865 21210 56126 49231 59723 48103 47472 50497 40059 34149 36860 46356 36577

Text written by user:

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 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation geg[t] = + 35088.3529411765 + 8651.86928104575Q1[t] + 9966.59150326797Q2[t] + 6623.03594771242Q3[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) 35088.3529411765 2394.221421 14.6554 0 0 Q1 8651.86928104575 3338.582263 2.5915 0.011719 0.005859 Q2 9966.59150326797 3338.582263 2.9853 0.003953 0.001976 Q3 6623.03594771242 3338.582263 1.9838 0.051379 0.02569 Multiple Linear Regression - Regression Statistics Multiple R 0.367185043913029 R-squared 0.134824856473413 Adjusted R-squared 0.0960856709423719 F-TEST (value) 3.48032243386686 F-TEST (DF numerator) 3 F-TEST (DF denominator) 67 p-value 0.0205858313344059 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 9871.62781130904 Sum Squared Residuals 6529085388.21568 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 56421 43740.2222222223 12680.7777777777 2 53152 45054.9444444444 8097.05555555556 3 53536 41711.3888888889 11824.6111111111 4 52408 35088.3529411765 17319.6470588235 5 41454 43740.2222222222 -2286.22222222222 6 38271 45054.9444444444 -6783.94444444444 7 35306 41711.3888888889 -6405.38888888889 8 26414 35088.3529411765 -8674.35294117647 9 31917 43740.2222222222 -11823.2222222222 10 38030 45054.9444444444 -7024.94444444444 11 27534 41711.3888888889 -14177.3888888889 12 18387 35088.3529411765 -16701.3529411765 13 50556 43740.2222222222 6815.77777777778 14 43901 45054.9444444444 -1153.94444444444 15 48572 41711.3888888889 6860.61111111111 16 43899 35088.3529411765 8810.64705882353 17 37532 43740.2222222222 -6208.22222222222 18 40357 45054.9444444444 -4697.94444444444 19 35489 41711.3888888889 -6222.38888888889 20 29027 35088.3529411765 -6061.35294117647 21 34485 43740.2222222222 -9255.22222222222 22 42598 45054.9444444444 -2456.94444444444 23 30306 41711.3888888889 -11405.3888888889 24 26451 35088.3529411765 -8637.35294117647 25 47460 43740.2222222222 3719.77777777778 26 50104 45054.9444444444 5049.05555555556 27 61465 41711.3888888889 19753.6111111111 28 53726 35088.3529411765 18637.6470588235 29 39477 43740.2222222222 -4263.22222222222 30 43895 45054.9444444444 -1159.94444444444 31 31481 41711.3888888889 -10230.3888888889 32 29896 35088.3529411765 -5192.35294117647 33 33842 43740.2222222222 -9898.22222222222 34 39120 45054.9444444444 -5934.94444444444 35 33702 41711.3888888889 -8009.38888888889 36 25094 35088.3529411765 -9994.35294117647 37 51442 43740.2222222222 7701.77777777778 38 45594 45054.9444444444 539.055555555556 39 52518 41711.3888888889 10806.6111111111 40 48564 35088.3529411765 13475.6470588235 41 41745 43740.2222222222 -1995.22222222222 42 49585 45054.9444444444 4530.05555555556 43 32747 41711.3888888889 -8964.38888888889 44 33379 35088.3529411765 -1709.35294117647 45 35645 43740.2222222222 -8095.22222222222 46 37034 45054.9444444444 -8020.94444444445 47 35681 41711.3888888889 -6030.38888888889 48 20972 35088.3529411765 -14116.3529411765 49 58552 43740.2222222222 14811.7777777778 50 54955 45054.9444444444 9900.05555555555 51 65540 41711.3888888889 23828.6111111111 52 51570 35088.3529411765 16481.6470588235 53 51145 43740.2222222222 7404.77777777778 54 46641 45054.9444444444 1586.05555555556 55 35704 41711.3888888889 -6007.38888888889 56 33253 35088.3529411765 -1835.35294117647 57 35193 43740.2222222222 -8547.22222222222 58 41668 45054.9444444444 -3386.94444444445 59 34865 41711.3888888889 -6846.38888888889 60 21210 35088.3529411765 -13878.3529411765 61 56126 43740.2222222222 12385.7777777778 62 49231 45054.9444444444 4176.05555555556 63 59723 41711.3888888889 18011.6111111111 64 48103 35088.3529411765 13014.6470588235 65 47472 43740.2222222222 3731.77777777778 66 50497 45054.9444444444 5442.05555555556 67 40059 41711.3888888889 -1652.38888888889 68 34149 35088.3529411765 -939.352941176472 69 36860 43740.2222222222 -6880.22222222222 70 46356 45054.9444444444 1301.05555555556 71 36577 41711.3888888889 -5134.38888888889 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 7 0.734571393492289 0.530857213015422 0.265428606507711 8 0.87527445861617 0.249451082767661 0.124725541383831 9 0.895696828122532 0.208606343754937 0.104303171877468 10 0.85173870721077 0.29652258557846 0.14826129278923 11 0.881044106117108 0.237911787765783 0.118955893882892 12 0.933708537614718 0.132582924770564 0.066291462385282 13 0.909034296687236 0.181931406625528 0.0909657033127639 14 0.863198670357769 0.273602659284463 0.136801329642231 15 0.838065142418071 0.323869715163858 0.161934857581929 16 0.825616608625261 0.348766782749478 0.174383391374739 17 0.787541010017599 0.424917979964803 0.212458989982401 18 0.72768229165722 0.544635416685559 0.272317708342779 19 0.674583102044063 0.650833795911874 0.325416897955937 20 0.620895349722991 0.758209300554018 0.379104650277009 21 0.597838194071662 0.804323611856676 0.402161805928338 22 0.520926489273866 0.958147021452268 0.479073510726134 23 0.519639621829706 0.960720756340588 0.480360378170294 24 0.487676638955248 0.975353277910496 0.512323361044752 25 0.425993850274537 0.851987700549074 0.574006149725463 26 0.379040660297099 0.758081320594197 0.620959339702901 27 0.606106179526114 0.787787640947772 0.393893820473886 28 0.759918336477087 0.480163327045827 0.240081663522913 29 0.709203477441756 0.581593045116488 0.290796522558244 30 0.644737111046604 0.710525777906792 0.355262888953396 31 0.642604494638033 0.714791010723934 0.357395505361967 32 0.591511451051056 0.816977097897887 0.408488548948944 33 0.586781960367944 0.826436079264113 0.413218039632057 34 0.540288448166202 0.919423103667596 0.459711551833798 35 0.513841074563858 0.972317850872285 0.486158925436143 36 0.51292632775651 0.97414734448698 0.48707367224349 37 0.483474706701814 0.966949413403628 0.516525293298186 38 0.414260271342383 0.828520542684766 0.585739728657617 39 0.42249656403158 0.84499312806316 0.57750343596842 40 0.474608166529712 0.949216333059424 0.525391833470288 41 0.408506926008104 0.817013852016208 0.591493073991896 42 0.351234834243325 0.70246966848665 0.648765165756675 43 0.341584162555833 0.683168325111666 0.658415837444167 44 0.277884296348614 0.555768592697229 0.722115703651386 45 0.26823012764633 0.53646025529266 0.73176987235367 46 0.255358151433054 0.510716302866108 0.744641848566946 47 0.228558654817348 0.457117309634696 0.771441345182652 48 0.295937834865047 0.591875669730094 0.704062165134953 49 0.349105375915003 0.698210751830007 0.650894624084997 50 0.328005836473075 0.65601167294615 0.671994163526925 51 0.648713070667359 0.702573858665281 0.351286929332641 52 0.764049951582143 0.471900096835715 0.235950048417857 53 0.7261393959218 0.547721208156401 0.273860604078200 54 0.646421749794507 0.707156500410985 0.353578250205493 55 0.592485646423006 0.815028707153989 0.407514353576994 56 0.499446862247955 0.99889372449591 0.500553137752045 57 0.490667349863933 0.981334699727867 0.509332650136067 58 0.420076364023132 0.840152728046263 0.579923635976868 59 0.390447798401224 0.780895596802447 0.609552201598776 60 0.554102463137741 0.891795073724518 0.445897536862259 61 0.59847958288545 0.8030408342291 0.40152041711455 62 0.466580579629551 0.933161159259102 0.533419420370449 63 0.808551129800409 0.382897740399182 0.191448870199591 64 0.880962945143881 0.238074109712238 0.119037054856119 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 Quarterly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Quarterly 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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