regressiemodel

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

Title produced by software: Multiple Regression

Date of computation: Fri, 02 May 2008 03:40:49 -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/02/t12097213441jm7fheabcav16d.htm/, Retrieved Fri, 02 May 2008 11:42:36 +0200

User-defined keywords:

eerste

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 149.0 101.6 59.5 165.5 103.8 61.3

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 8 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Number[t] = + 18397.5984126984 + 27135.1216175359M1[t] + 30853.500377929M2[t] + 38248.8836734693M3[t] + 31060.7669690099M4[t] + 24479.1502645502M5[t] + 26208.5335600907M6[t] + 16457.7501889645M7[t] + 12338.9668178382M8[t] + 15968.8501133787M9[t] + 22105.4000755858M10[t] + 14407.7833711262M11[t] + 7.4500377928953t + 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) 18397.5984126984 3761.563336 4.8909 8e-06 4e-06 M1 27135.1216175359 4445.016056 6.1046 0 0 M2 30853.500377929 4628.668011 6.6657 0 0 M3 38248.8836734693 4624.55046 8.2708 0 0 M4 31060.7669690099 4620.863225 6.7219 0 0 M5 24479.1502645502 4617.607338 5.3013 2e-06 1e-06 M6 26208.5335600907 4614.783711 5.6793 0 0 M7 16457.7501889645 4612.393138 3.5682 0.000714 0.000357 M8 12338.9668178382 4610.436292 2.6763 0.009583 0.004792 M9 15968.8501133787 4608.913727 3.4648 0.000986 0.000493 M10 22105.4000755858 4607.825872 4.7974 1.1e-05 6e-06 M11 14407.7833711262 4607.173036 3.1273 0.002721 0.001361 t 7.4500377928953 44.780516 0.1664 0.868427 0.434213 Multiple Linear Regression - Regression Statistics Multiple R 0.805412272978757 R-squared 0.648688929464808 Adjusted R-squared 0.578426715357769 F-TEST (value) 9.2324009100622 F-TEST (DF numerator) 12 F-TEST (DF denominator) 60 p-value 9.5757557438958e-10 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 7979.48082730627 Sum Squared Residuals 3820326856.40091 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 56421 45540.1700680273 10880.8299319727 2 53152 49265.9988662132 3886.00113378684 3 53536 56668.8321995466 -3132.83219954656 4 52408 49488.1655328797 2919.83446712025 5 41454 42913.9988662133 -1459.99886621327 6 38271 44650.8321995465 -6379.83219954645 7 35306 34907.4988662132 398.501133786832 8 26414 30796.1655328798 -4382.16553287981 9 31917 34433.4988662131 -2516.49886621314 10 38030 40577.4988662132 -2547.49886621317 11 27534 32887.3321995465 -5353.3321995465 12 18387 18486.9988662131 -99.998866213141 13 50556 45629.5705215419 4926.42947845806 14 43901 49355.3993197279 -5454.39931972788 15 48572 56758.2326530612 -8186.2326530612 16 43899 49577.5659863946 -5678.56598639456 17 37532 43003.3993197279 -5471.39931972786 18 40357 44740.2326530612 -4383.23265306122 19 35489 34996.8993197279 492.100680272119 20 29027 30885.5659863946 -1858.56598639455 21 34485 34522.8993197279 -37.8993197278869 22 42598 40666.8993197279 1931.10068027212 23 30306 32976.7326530612 -2670.73265306121 24 26451 18576.3993197279 7874.60068027211 25 47460 45718.9709750567 1741.02902494333 26 50104 49444.7997732426 659.200226757375 27 61465 56847.6331065759 4617.36689342406 28 53726 49666.9664399093 4059.03356009069 29 39477 43092.7997732426 -3615.79977324260 30 43895 44829.633106576 -934.633106575965 31 31481 35086.2997732426 -3605.29977324262 32 29896 30974.9664399093 -1078.96643990930 33 33842 34612.2997732426 -770.29977324263 34 39120 40756.2997732426 -1636.29977324262 35 33702 33066.1331065760 635.866893424043 36 25094 18665.7997732426 6428.20022675737 37 51442 45808.3714285714 5633.62857142858 38 45594 49534.2002267574 -3940.20022675737 39 52518 56937.0335600907 -4419.03356009069 40 48564 49756.3668934240 -1192.36689342405 41 41745 43182.2002267573 -1437.20022675735 42 49585 44919.0335600907 4665.96643990929 43 32747 35175.7002267574 -2428.70022675737 44 33379 31064.3668934240 2314.63310657596 45 35645 34701.7002267574 943.299773242627 46 37034 40845.7002267574 -3811.70022675736 47 35681 33155.5335600907 2525.4664399093 48 20972 18755.2002267574 2216.79977324262 49 58552 45897.7718820862 12654.2281179138 50 54955 49623.6006802721 5331.39931972789 51 65540 57026.4340136054 8513.56598639457 52 51570 49845.7673469388 1724.23265306121 53 51145 43271.6006802721 7873.3993197279 54 46641 45008.4340136055 1632.56598639455 55 35704 35265.1006802721 438.899319727889 56 33253 31153.7673469388 2099.23265306122 57 35193 34791.1006802721 401.899319727883 58 41668 40935.1006802721 732.899319727893 59 34865 33244.9340136054 1620.06598639456 60 21210 18844.6006802721 2365.39931972788 61 56126 45987.1723356009 10138.8276643991 62 49231 49713.0011337869 -482.001133786857 63 59723 57115.8344671202 2607.16553287983 64 48103 49935.1678004535 -1832.16780045354 65 47472 43361.0011337868 4110.99886621317 66 50497 45097.8344671202 5399.16553287981 67 40059 35354.5011337868 4704.49886621315 68 34149 31243.1678004535 2905.83219954647 69 36860 34880.5011337869 1979.49886621314 70 46356 41024.5011337868 5331.49886621315 71 36577 33334.3344671202 3242.66553287981 72 149 18934.0011337869 -18785.0011337869 73 101.6 46076.5727891156 -45974.9727891156 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.00651426933225496 0.0130285386645099 0.993485730667745 17 0.00243186062312078 0.00486372124624156 0.997568139376879 18 0.0103285089861508 0.0206570179723016 0.98967149101385 19 0.00581197550570871 0.0116239510114174 0.994188024494291 20 0.00499848859810553 0.00999697719621106 0.995001511401894 21 0.00325472452770203 0.00650944905540406 0.996745275472298 22 0.00275048107161249 0.00550096214322498 0.997249518928388 23 0.00149963940163914 0.00299927880327828 0.99850036059836 24 0.00216507241084418 0.00433014482168836 0.997834927589156 25 0.00120193311936855 0.00240386623873711 0.998798066880631 26 0.000571891692336503 0.00114378338467301 0.999428108307663 27 0.00158340376823181 0.00316680753646361 0.998416596231768 28 0.00095363082342641 0.00190726164685282 0.999046369176574 29 0.000450020956893757 0.000900041913787513 0.999549979043106 30 0.00023942479979638 0.00047884959959276 0.999760575200204 31 0.000147168189647737 0.000294336379295474 0.999852831810352 32 6.43502356218172e-05 0.000128700471243634 0.999935649764378 33 2.57088879374220e-05 5.14177758748439e-05 0.999974291112063 34 1.09154163088839e-05 2.18308326177677e-05 0.999989084583691 35 5.68935757008592e-06 1.13787151401718e-05 0.99999431064243 36 2.24229530040657e-06 4.48459060081314e-06 0.9999977577047 37 9.57142901837103e-07 1.91428580367421e-06 0.999999042857098 38 5.9696565372247e-07 1.19393130744494e-06 0.999999403034346 39 3.72931286512296e-07 7.45862573024592e-07 0.999999627068713 40 1.39261866726125e-07 2.7852373345225e-07 0.999999860738133 41 7.55794011873506e-08 1.51158802374701e-07 0.999999924420599 42 1.02580824172305e-07 2.05161648344611e-07 0.999999897419176 43 5.61820263900014e-08 1.12364052780003e-07 0.999999943817974 44 2.92118287161743e-08 5.84236574323485e-08 0.999999970788171 45 1.1742590339579e-08 2.3485180679158e-08 0.99999998825741 46 1.5948828204549e-08 3.1897656409098e-08 0.999999984051172 47 1.28913237346034e-08 2.57826474692068e-08 0.999999987108676 48 4.89930029072237e-09 9.79860058144474e-09 0.9999999951007 49 1.50698287179668e-08 3.01396574359335e-08 0.999999984930171 50 6.8646345543837e-09 1.37292691087674e-08 0.999999993135365 51 9.68560320915057e-09 1.93712064183011e-08 0.999999990314397 52 2.62594834459250e-09 5.25189668918499e-09 0.999999997374052 53 2.32440241142746e-09 4.64880482285491e-09 0.999999997675598 54 1.01886003828271e-09 2.03772007656542e-09 0.99999999898114 55 6.04817804606374e-10 1.20963560921275e-09 0.999999999395182 56 2.92924952689094e-10 5.85849905378187e-10 0.999999999707075 57 2.87994152430392e-10 5.75988304860785e-10 0.999999999712006 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 39 0.928571428571429 NOK 5% type I error level 42 1 NOK 10% type I error level 42 1 NOK

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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