Multiple Regression 1xlag9

*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, 19 Dec 2009 15:25:18 -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/Dec/19/t1261261601j61qtb4013b2bpc.htm/, Retrieved Sat, 19 Dec 2009 23:26:53 +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/Dec/19/t1261261601j61qtb4013b2bpc.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:

kvn paper

Dataseries X:

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9605 3024 9487 8640 1887 8700 9214 2070 9627 9567 1351 8947 8547 2218 9283 9185 2461 8829 9470 3028 9947 9123 4784 9628 9278 4975 9318 10170 4607 9605 9434 6249 8640 9655 4809 9214 9429 3157 9567 8739 1910 8547 9552 2228 9185 9784 1594 9470 9089 2467 9123 9763 2222 9278 9330 3607 10170 9144 4685 9434 9895 4962 9655 10404 5770 9429 10195 5480 8739 9987 5000 9552 9789 3228 9784 9437 1993 9089 10096 2288 9763 9776 1580 9330 9106 2111 9144 10258 2192 9895 9766 3601 10404 9826 4665 10195 9957 4876 9987 10036 5813 9789 10508 5589 9437 10146 5331 10096 10166 3075 9776 9365 2002 9106 9968 2306 10258 10123 1507 9766 9144 1992 9826 10447 2487 9957 9699 3490 10036 10451 4647 10508 10192 5594 10146 10404 5611 10166 10597 5788 9365 10633 6204 9968 10727 3013 10123 9784 1931 9144 9667 2549 10447 10297 1504 9699 9426 2090 10451 10274 2702 10192 9598 2939 10404 10400 4500 10597 9985 6208 10633 10761 6415 10727 11081 5657 9784 10297 5964 9667 10751 3163 10297 9760 1 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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 8102.07795549649 -0.242111708219858X[t] + 0.294090165163183Y9[t] -601.166495294743M1[t] -1457.90238078569M2[t] -1173.69107251394M3[t] -926.983178052489M4[t] -1726.24499265077M5[t] -840.679042781025M6[t] -1061.93051395988M7[t] -578.819575933422M8[t] -315.3129403144M9[t] + 251.173734798207M10[t] + 471.831776534164M11[t] + 13.4944539023085t + 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) 8102.07795549649 1127.472859 7.1861 0 0 X -0.242111708219858 0.072502 -3.3394 0.001447 0.000724 Y9 0.294090165163183 0.119547 2.46 0.01679 0.008395 M1 -601.166495294743 208.800184 -2.8791 0.005519 0.00276 M2 -1457.90238078569 283.081064 -5.1501 3e-06 2e-06 M3 -1173.69107251394 260.035373 -4.5136 3e-05 1.5e-05 M4 -926.983178052489 309.354509 -2.9965 0.003967 0.001983 M5 -1726.24499265077 266.022189 -6.4891 0 0 M6 -840.679042781025 248.843876 -3.3783 0.001286 0.000643 M7 -1061.93051395988 214.382506 -4.9534 6e-06 3e-06 M8 -578.819575933422 156.019021 -3.7099 0.000455 0.000228 M9 -315.3129403144 138.117916 -2.2829 0.025992 0.012996 M10 251.173734798207 139.933477 1.795 0.077699 0.038849 M11 471.831776534164 155.947312 3.0256 0.003651 0.001825 t 13.4944539023085 2.416702 5.5838 1e-06 0 Multiple Linear Regression - Regression Statistics Multiple R 0.933000835040473 R-squared 0.87049055818622 Adjusted R-squared 0.840271688429672 F-TEST (value) 28.8061917999954 F-TEST (DF numerator) 14 F-TEST (DF denominator) 60 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 231.462914307378 Sum Squared Residuals 3214504.84197987 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 9605 9572.29350535034 32.7064946496555 2 8640 8772.88412602424 -132.884126024241 3 9214 9298.90502870034 -84.9050287003371 4 9567 9533.2043829632 33.7956170367939 5 8547 8636.34046673544 -89.3404667354413 6 9185 9343.05079042599 -158.050790425990 7 9470 9326.80923924122 143.190760758780 8 9123 9304.45170884886 -181.451708848865 9 9278 9444.04151089961 -166.041510899614 10 10170 10197.5236259413 -27.5236259412705 11 9434 9750.33168730006 -316.331687300058 12 9655 9809.44297930847 -154.442979308465 13 9429 9725.55330819784 -296.55330819784 14 8739 8884.25320829292 -145.253208292919 15 9552 9292.59697262717 259.403027372826 16 9784 9790.11384107383 -6.11384107382797 17 9089 8690.93367179029 398.06632820971 18 9763 9694.8954196765 68.1045803234928 19 9330 9414.14211384102 -84.1421138410144 20 9144 9433.30072274867 -289.300722748674 21 9895 9708.23079559417 186.769204405833 22 10404 10026.1212870406 377.878712959442 23 10195 10127.5639641000 67.4360359000147 24 9987 10024.5355656913 -37.5355656913302 25 9789 9934.11438958234 -145.114389582343 26 9437 9185.48825285682 251.511747143182 27 10096 9609.987832426 486.012167573995 28 9776 9914.26422869376 -138.264228693762 29 9106 8945.23478021269 160.765219787312 30 10258 10045.5458496565 212.454150343511 31 9766 9646.34532956622 119.654670433779 32 9826 9823.87901942995 2.1209805700446 33 9957 9988.62378416295 -31.6237841629539 34 10036 10283.5163898736 -247.516389873552 35 10508 10468.3821700156 39.6178299843749 36 10146 10266.3150869470 -120.315086947031 37 10166 10130.7382064464 35.2617935536225 38 9365 9350.24222711831 14.7577728816851 39 9968 9913.13790026152 54.8620997384746 40 10123 10222.0951422327 -99.0951422326619 41 9144 9336.54901295984 -192.549012959845 42 10447 10154.2899327995 292.710067200549 43 9699 9726.92799522628 -27.9279952262751 44 10451 10082.2206987017 368.779301298309 45 10192 10023.4813607497 168.518639250256 46 10404 10605.2283940282 -201.228394028185 47 10597 10560.9608950158 36.0391049841739 48 10633 10179.2414713579 453.758528642090 49 10727 10409.7318664953 317.268133504665 50 9784 9540.54103150583 243.458968494172 51 9667 10071.8212432076 -404.821243207643 52 10297 10365.0508831191 -68.0508831190898 53 9426 9658.5618656090 -232.56186560899 54 10274 10333.2805511732 -59.280551173231 55 9598 10130.4901740632 -532.49017406317 56 10400 10305.9185913372 94.0814086627643 57 9985 10179.9801291649 -194.980129164924 58 10761 10737.4886101037 23.5113898963325 59 11081 10877.8347548237 203.165245176297 60 10297 10310.7605884443 -13.7605884442593 61 10751 10586.5202458285 164.479754171547 62 9760 9769.42853216704 -9.42853216703677 63 10133 10213.6252784060 -80.6252784060365 64 10806 10528.2715219175 277.728478082548 65 9734 9778.38020269275 -44.3802026927457 66 10083 10438.9374562683 -355.937456268331 67 10691 10309.2851480621 381.7148519379 68 10446 10440.2292589336 5.77074106642149 69 10517 10479.6424194286 37.3575805714029 70 11353 11278.1216930128 74.8783069872328 71 10436 10465.9265287448 -29.9265287448018 72 10721 10848.704308251 -127.704308251004 73 10701 10809.0484780993 -108.048478099307 74 9793 10015.1626220348 -222.162622034843 75 10142 10371.9257443713 -229.925744371279 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 18 0.634341570867243 0.731316858265514 0.365658429132757 19 0.484760545950467 0.969521091900934 0.515239454049533 20 0.502848088704578 0.994303822590844 0.497151911295422 21 0.476438565750588 0.952877131501176 0.523561434249412 22 0.483694052612775 0.96738810522555 0.516305947387225 23 0.436237981242663 0.872475962485326 0.563762018757337 24 0.337126912403871 0.674253824807742 0.662873087596129 25 0.300294847457702 0.600589694915403 0.699705152542298 26 0.284690290637275 0.569380581274550 0.715309709362725 27 0.332525471567021 0.665050943134041 0.66747452843298 28 0.387585022589586 0.775170045179171 0.612414977410414 29 0.353932556570270 0.707865113140541 0.64606744342973 30 0.291007378787803 0.582014757575606 0.708992621212197 31 0.227905992236548 0.455811984473095 0.772094007763452 32 0.176076756254418 0.352153512508836 0.823923243745582 33 0.148216310404249 0.296432620808497 0.851783689595751 34 0.269263430262908 0.538526860525816 0.730736569737092 35 0.205431955327525 0.410863910655051 0.794568044672475 36 0.181460159728313 0.362920319456626 0.818539840271687 37 0.140418799180644 0.280837598361287 0.859581200819357 38 0.106325341543825 0.212650683087650 0.893674658456175 39 0.102905913875861 0.205811827751722 0.897094086124139 40 0.0930644479031534 0.186128895806307 0.906935552096847 41 0.125889961935903 0.251779923871807 0.874110038064097 42 0.140728280559883 0.281456561119766 0.859271719440117 43 0.107754335213474 0.215508670426949 0.892245664786526 44 0.136990577605091 0.273981155210182 0.863009422394909 45 0.10597476792601 0.21194953585202 0.89402523207399 46 0.122196174394322 0.244392348788643 0.877803825605678 47 0.089982999512396 0.179965999024792 0.910017000487604 48 0.198756758487661 0.397513516975322 0.801243241512339 49 0.180012985399925 0.36002597079985 0.819987014600075 50 0.182552613998559 0.365105227997119 0.81744738600144 51 0.258015999025125 0.51603199805025 0.741984000974875 52 0.229351703664753 0.458703407329506 0.770648296335247 53 0.192953756445517 0.385907512891033 0.807046243554483 54 0.158190635817446 0.316381271634891 0.841809364182554 55 0.98736216207352 0.025275675852959 0.0126378379264795 56 0.986558785252563 0.0268824294948742 0.0134412147474371 57 0.987337436236323 0.0253251275273532 0.0126625637636766 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 3 0.075 NOK 10% type I error level 3 0.075 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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