model 4

*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: Mon, 30 Nov 2009 15:55:12 -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/Nov/30/t1259621749uai5wbc3e0fkhsp.htm/, Retrieved Mon, 30 Nov 2009 23:56:01 +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/Nov/30/t1259621749uai5wbc3e0fkhsp.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:

Dataseries X:

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10723.78 3080.58 10539.51 10673.38 10411.75 10001.60 10682.06 3106.22 10723.78 10539.51 10673.38 10411.75 10283.19 3119.31 10682.06 10723.78 10539.51 10673.38 10377.18 3061.26 10283.19 10682.06 10723.78 10539.51 10486.64 3097.31 10377.18 10283.19 10682.06 10723.78 10545.38 3161.69 10486.64 10377.18 10283.19 10682.06 10554.27 3257.16 10545.38 10486.64 10377.18 10283.19 10532.54 3277.01 10554.27 10545.38 10486.64 10377.18 10324.31 3295.32 10532.54 10554.27 10545.38 10486.64 10695.25 3363.99 10324.31 10532.54 10554.27 10545.38 10827.81 3494.17 10695.25 10324.31 10532.54 10554.27 10872.48 3667.03 10827.81 10695.25 10324.31 10532.54 10971.19 3813.06 10872.48 10827.81 10695.25 10324.31 11145.65 3917.96 10971.19 10872.48 10827.81 10695.25 11234.68 3895.51 11145.65 10971.19 10872.48 10827.81 11333.88 3801.06 11234.68 11145.65 10971.19 10872.48 10997.97 3570.12 11333.88 11234.68 11145.65 10971.19 11036.89 3701.61 10997.97 11333.88 11234.68 11145.65 11257.35 3862.27 11036.89 10997.97 11333.88 11234.68 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 6 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 R Framework error message The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'. Multiple Linear Regression - Estimated Regression Equation X[t] = -999.997265120483 + 0.564526605850022Y[t] -0.0123080270622791`Yt-1`[t] + 0.029081352446026`Yt-2`[t] -0.0827779579897504`Yt-3`[t] -0.0652551152233573`Yt-4 `[t] -87.0424548307653M1[t] -1.31472901234750M2[t] -35.8724720751150M3[t] -180.493075859543M4[t] -233.770413585435M5[t] -241.721782476039M6[t] -240.130841473458M7[t] -210.279668566981M8[t] -103.591023428529M9[t] -107.571987999933M10[t] -139.295890813598M11[t] -9.13867789192095t + 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) -999.997265120483 287.492303 -3.4783 0.001281 0.000641 Y 0.564526605850022 0.085075 6.6356 0 0 `Yt-1` -0.0123080270622791 0.134495 -0.0915 0.927566 0.463783 `Yt-2` 0.029081352446026 0.136414 0.2132 0.832322 0.416161 `Yt-3` -0.0827779579897504 0.135677 -0.6101 0.54542 0.27271 `Yt-4 ` -0.0652551152233573 0.088219 -0.7397 0.464029 0.232014 M1 -87.0424548307653 166.077139 -0.5241 0.603247 0.301623 M2 -1.31472901234750 165.272061 -0.008 0.993695 0.496847 M3 -35.8724720751150 167.817992 -0.2138 0.831878 0.415939 M4 -180.493075859543 163.893165 -1.1013 0.2777 0.13885 M5 -233.770413585435 162.897906 -1.4351 0.159446 0.079723 M6 -241.721782476039 172.246312 -1.4033 0.168632 0.084316 M7 -240.130841473458 169.612838 -1.4158 0.164991 0.082495 M8 -210.279668566981 161.063394 -1.3056 0.199548 0.099774 M9 -103.591023428529 168.786037 -0.6137 0.543043 0.271521 M10 -107.571987999933 174.960958 -0.6148 0.542329 0.271164 M11 -139.295890813598 174.583954 -0.7979 0.429902 0.214951 t -9.13867789192095 2.1489 -4.2527 0.000132 6.6e-05 Multiple Linear Regression - Regression Statistics Multiple R 0.974162571371517 R-squared 0.948992715461167 Adjusted R-squared 0.926173667114847 F-TEST (value) 41.587742882985 F-TEST (DF numerator) 17 F-TEST (DF denominator) 38 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 235.970880547297 Sum Squared Residuals 2115925.74571814 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 3080.58 3623.83751418869 -543.257514188694 2 3106.22 3622.29180866268 -516.071808662677 3 3119.31 3353.30376157706 -233.993761577058 4 3061.26 3249.78257227101 -188.522572271015 5 3097.31 3227.83206474094 -130.522064740940 6 3161.69 3281.0285179707 -119.338517970700 7 3257.16 3299.20770147416 -42.0477014741554 8 3277.01 3294.05765006429 -17.0476500642849 9 3295.32 3262.57702666131 32.7429733386929 10 3363.99 3456.22486454377 -92.2348645437679 11 3494.17 3480.79342818412 13.3765718158770 12 3667.03 3663.97877724408 3.05122275591673 13 3813.06 3609.70970720247 203.350292797532 14 3917.96 3749.69142689593 168.268573104068 15 3895.51 3744.63026210132 150.879737898676 16 3801.06 3639.76381059348 161.296189406521 17 3570.12 3368.20304435369 201.916955646312 18 3701.61 3361.34950360229 340.260496397713 19 3862.27 3453.98832038432 408.281679615683 20 3970.1 3650.39670002811 319.703299971888 21 4138.52 4012.13721347969 126.382786520313 22 4199.75 4106.31722154596 93.4327784540413 23 4290.89 4146.6149129186 144.2750870814 24 4443.91 4303.64195720389 140.268042796114 25 4502.64 4231.93219609917 270.707803900827 26 4356.98 4075.67967124113 281.300328758866 27 4591.27 4290.65453251765 300.61546748235 28 4696.96 4470.31909946695 226.640900533054 29 4621.4 4477.21920043068 144.180799569318 30 4562.84 4570.65104131696 -7.8110413169625 31 4202.52 4232.29095539348 -29.7709553934827 32 4296.49 4394.85633022535 -98.3663302253485 33 4435.23 4649.13915955244 -213.909159552437 34 4105.18 4268.7653319519 -163.585331951902 35 4116.68 4365.00261910298 -248.32261910298 36 3844.49 3932.56183304313 -88.0718330431305 37 3720.98 3821.73351096514 -100.753510965144 38 3674.4 3775.74604924036 -101.346049240355 39 3857.62 4051.06814500642 -193.44814500642 40 3801.06 4039.54165867668 -238.481658676682 41 3504.37 3588.40813016654 -84.038130166543 42 3032.6 3147.04862758206 -114.448627582061 43 3047.03 3201.09123443071 -154.061234430710 44 2962.34 3015.05805741985 -52.7180574198503 45 2197.82 2143.03660030657 54.7833996934314 46 2014.45 1852.06258195837 162.387418041628 47 1862.83 1772.15903979430 90.6709602057027 48 1905.41 1960.6574325089 -55.2474325089004 49 1810.99 1641.03707154452 169.952928455480 50 1670.07 1502.2210439599 167.848956040099 51 1864.44 1888.49329879755 -24.0532987975484 52 2052.02 2012.95285899188 39.0671410081221 53 2029.6 2161.13756030815 -131.537560308147 54 2070.83 2169.49230952799 -98.662309527989 55 2293.41 2475.81178831734 -182.401788317335 56 2443.27 2594.84126226240 -151.571262262404 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.118370347929680 0.236740695859360 0.88162965207032 22 0.462008788190391 0.924017576380783 0.537991211809609 23 0.556326800470946 0.88734639905811 0.443673199529054 24 0.526104519208253 0.947790961583495 0.473895480791747 25 0.414746365643973 0.829492731287946 0.585253634356027 26 0.318588855657229 0.637177711314458 0.681411144342771 27 0.293754527124568 0.587509054249135 0.706245472875432 28 0.302504929634989 0.605009859269979 0.697495070365010 29 0.442805785766651 0.885611571533302 0.557194214233349 30 0.653126926372902 0.693746147254196 0.346873073627098 31 0.827516110172539 0.344967779654922 0.172483889827461 32 0.829517105969025 0.340965788061949 0.170482894030975 33 0.87684388002442 0.24631223995116 0.12315611997558 34 0.843980912666062 0.312038174667877 0.156019087333938 35 0.80933120846437 0.38133758307126 0.19066879153563 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 Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 2 ; 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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