MR seiz en lin trend

*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: Sat, 22 Nov 2008 04:09:40 -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/22/t1227352271id5xilueoyveq62.htm/, Retrieved Sat, 22 Nov 2008 11:11:11 +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/22/t1227352271id5xilueoyveq62.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}, }

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User-defined keywords:

Dataseries X:

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15859,4 0 15258,9 0 15498,6 0 15106,5 0 15023,6 0 12083 0 15761,3 0 16942,6 0 15070,3 0 13659,6 0 14768,9 0 14725,1 0 15998,1 0 15370,6 0 14956,9 0 15469,7 0 15101,8 0 11703,7 0 16283,6 0 16726,5 0 14968,9 0 14861 0 14583,3 0 15305,8 0 17903,9 0 16379,4 0 15420,3 0 17870,5 0 15912,8 0 13866,5 0 17823,2 0 17872 0 17422 0 16704,5 0 15991,2 0 16583,6 0 19123,5 0 17838,7 0 17209,4 0 18586,5 0 16258,1 0 15141,6 1 19202,1 1 17746,5 1 19090,1 1 18040,3 1 17515,5 1 17751,8 1 21072,4 1 17170 1 19439,5 1 19795,4 1 17574,9 1 16165,4 1 19464,6 1 19932,1 1 19961,2 1 17343,4 1 18924,2 1 18574,1 1 21350,6 1 18594,6 1 19823,1 1 20844,4 1 19640,2 1 17735,4 1 19813,6 1 22238,5 1 20682,2 1 17818,6 1 21872,1 1 22117 1 21865,9 1

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 13846.4670804369 + 413.989821251241x[t] + 1956.27363908986M1[t] + 151.013702495232M2[t] + 357.992162599896M3[t] + 1163.23728937123M4[t] -279.317583857442M5[t] -2566.57076062798M6[t] + 959.941032810013M7[t] + 1395.95282624801M8[t] + 603.081286352674M9[t] -940.423586875995M10[t] -151.411793437997M11[t] + 82.2882065620025t + 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) 13846.4670804369 389.942744 35.509 0 0 x 413.989821251241 365.726852 1.132 0.262229 0.131115 M1 1956.27363908986 435.512683 4.4919 3.3e-05 1.7e-05 M2 151.013702495232 453.551856 0.333 0.740346 0.370173 M3 357.992162599896 452.99701 0.7903 0.432532 0.216266 M4 1163.23728937123 452.604833 2.5701 0.012712 0.006356 M5 -279.317583857442 452.375749 -0.6174 0.539316 0.269658 M6 -2566.57076062798 454.178133 -5.651 0 0 M7 959.941032810013 453.282096 2.1178 0.038419 0.01921 M8 1395.95282624801 452.547656 3.0847 0.003099 0.00155 M9 603.081286352674 451.975599 1.3343 0.187225 0.093613 M10 -940.423586875995 451.566543 -2.0826 0.041634 0.020817 M11 -151.411793437997 451.320932 -0.3355 0.738449 0.369224 t 82.2882065620025 8.597663 9.571 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.95331137265489 R-squared 0.908802573233149 Adjusted R-squared 0.888708224962487 F-TEST (value) 45.2267752599871 F-TEST (DF numerator) 13 F-TEST (DF denominator) 59 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 781.568929508545 Sum Squared Residuals 36040149.5028148 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 15859.4 15885.0289260888 -25.6289260888120 2 15258.9 14162.0571960562 1096.84280394382 3 15498.6 14451.3238627228 1047.27613727716 4 15106.5 15338.8571960562 -232.357196056179 5 15023.6 13978.5905293895 1045.00947061049 6 12083 11773.6255591810 309.374440819029 7 15761.3 15382.4255591810 378.874440819029 8 16942.6 15900.7255591810 1041.87444081903 9 15070.3 15190.1422258476 -119.842225847638 10 13659.6 13728.9255591810 -69.3255591809702 11 14768.9 14600.2255591810 168.674440819028 12 14725.1 14833.9255591810 -108.825559180970 13 15998.1 16872.4874048328 -874.387404832836 14 15370.6 15149.5156748002 221.084325199793 15 14956.9 15438.7823414669 -481.882341466875 16 15469.7 16326.3156748002 -856.615674800207 17 15101.8 14966.0490081335 135.750991866458 18 11703.7 12761.084037925 -1057.384037925 19 16283.6 16369.884037925 -86.2840379250002 20 16726.5 16888.184037925 -161.684037925001 21 14968.9 16177.6007045917 -1208.70070459167 22 14861 14716.384037925 144.615962074999 23 14583.3 15587.684037925 -1004.38403792500 24 15305.8 15821.384037925 -515.584037925002 25 17903.9 17859.9458835769 43.9541164231352 26 16379.4 16136.9741535442 242.425846455762 27 15420.3 16426.2408202109 -1005.94082021091 28 17870.5 17313.7741535442 556.725846455761 29 15912.8 15953.5074868776 -40.7074868775725 30 13866.5 13748.5425166690 117.957483330968 31 17823.2 17357.3425166690 465.85748333097 32 17872 17875.6425166690 -3.64251666903095 33 17422 17165.0591833357 256.940816664302 34 16704.5 15703.8425166690 1000.65748333097 35 15991.2 16575.1425166690 -583.942516669031 36 16583.6 16808.8425166690 -225.242516669032 37 19123.5 18847.4043623209 276.095637679103 38 17838.7 17124.4326322883 714.267367711733 39 17209.4 17413.6992989549 -204.299298954932 40 18586.5 18301.2326322883 285.267367711731 41 16258.1 16940.9659656216 -682.865965621601 42 15141.6 15149.9908166643 -8.39081666430192 43 19202.1 18758.7908166643 443.309183335698 44 17746.5 19277.0908166643 -1530.5908166643 45 19090.1 18566.5074833310 523.59251666903 46 18040.3 17105.2908166643 935.009183335698 47 17515.5 17976.5908166643 -461.090816664302 48 17751.8 18210.2908166643 -458.490816664302 49 21072.4 20248.8526623162 823.547337683835 50 17170 18525.8809322835 -1355.88093228354 51 19439.5 18815.1475989502 624.352401049795 52 19795.4 19702.6809322835 92.7190677164617 53 17574.9 18342.4142656169 -767.514265616871 54 16165.4 16137.4492954083 27.9507045916671 55 19464.6 19746.2492954083 -281.649295408333 56 19932.1 20264.5492954083 -332.449295408334 57 19961.2 19553.965962075 407.234037925002 58 17343.4 18092.7492954083 -749.349295408331 59 18924.2 18964.0492954083 -39.8492954083312 60 18574.1 19197.7492954083 -623.649295408333 61 21350.6 21236.3111410602 114.288858939802 62 18594.6 19513.3394110276 -918.73941102757 63 19823.1 19802.6060776942 20.4939223057624 64 20844.4 20690.1394110276 154.260588972431 65 19640.2 19329.8727443609 310.327255639098 66 17735.4 17124.9077741524 610.492225847638 67 19813.6 20733.7077741524 -920.107774152364 68 22238.5 21252.0077741524 986.492225847639 69 20682.2 20541.4244408190 140.775559180971 70 17818.6 19080.2077741524 -1261.60777415236 71 21872.1 19951.5077741524 1920.59222584764 72 22117 20185.2077741524 1931.79222584764 73 21865.9 22223.7696198042 -357.869619804226 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.0546448242552287 0.109289648510457 0.945355175744771 18 0.0262845285897373 0.0525690571794746 0.973715471410263 19 0.0177096455468283 0.0354192910936566 0.982290354453172 20 0.00671060195379929 0.0134212039075986 0.9932893980462 21 0.00251739328370882 0.00503478656741765 0.997482606716291 22 0.0150689148706050 0.0301378297412100 0.984931085129395 23 0.00820114012471066 0.0164022802494213 0.99179885987529 24 0.00501073046345308 0.0100214609269062 0.994989269536547 25 0.0584632235502177 0.116926447100435 0.941536776449782 26 0.0430205439955411 0.0860410879910821 0.956979456004459 27 0.0330957993115901 0.0661915986231802 0.96690420068841 28 0.151159346125365 0.302318692250731 0.848840653874635 29 0.103721693023674 0.207443386047348 0.896278306976326 30 0.111158463883803 0.222316927767607 0.888841536116197 31 0.100566401269365 0.201132802538730 0.899433598730635 32 0.0666119044832681 0.133223808966536 0.933388095516732 33 0.083913288487668 0.167826576975336 0.916086711512332 34 0.124476280081392 0.248952560162783 0.875523719918608 35 0.100476673173214 0.200953346346427 0.899523326826786 36 0.0742596425675968 0.148519285135194 0.925740357432403 37 0.0620699393998405 0.124139878799681 0.93793006060016 38 0.0786915199221346 0.157383039844269 0.921308480077865 39 0.0528723949779035 0.105744789955807 0.947127605022096 40 0.0399544496490638 0.0799088992981276 0.960045550350936 41 0.0339801533913646 0.0679603067827293 0.966019846608635 42 0.0205882591938121 0.0411765183876243 0.979411740806188 43 0.0197142173972610 0.0394284347945220 0.98028578260274 44 0.0552806565990819 0.110561313198164 0.944719343400918 45 0.0543265367659009 0.108653073531802 0.9456734632341 46 0.173015561319240 0.346031122638479 0.82698443868076 47 0.147184958682372 0.294369917364743 0.852815041317628 48 0.115586516132019 0.231173032264038 0.884413483867981 49 0.183540574389874 0.367081148779748 0.816459425610126 50 0.210953711882248 0.421907423764497 0.789046288117752 51 0.212678326143094 0.425356652286188 0.787321673856906 52 0.152428953539522 0.304857907079043 0.847571046460478 53 0.109615783429428 0.219231566858857 0.890384216570572 54 0.0629897238769494 0.125979447753899 0.93701027612305 55 0.0598072863736378 0.119614572747276 0.940192713626362 56 0.0316401356718871 0.0632802713437742 0.968359864328113 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 1 0.025 NOK 5% type I error level 8 0.2 NOK 10% type I error level 14 0.35 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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