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: Wed, 18 Nov 2009 11:59:07 -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/18/t1258570833z5audn932mo3jwx.htm/, Retrieved Wed, 18 Nov 2009 20:00:44 +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/18/t1258570833z5audn932mo3jwx.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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2863.36 99.9 2882.6 2767.63 2803.47 3030.29 2897.06 99.7 2863.36 2882.6 2767.63 2803.47 3012.61 99.5 2897.06 2863.36 2882.6 2767.63 3142.95 99.2 3012.61 2897.06 2863.36 2882.6 3032.93 99 3142.95 3012.61 2897.06 2863.36 3045.78 99 3032.93 3142.95 3012.61 2897.06 3110.52 99.3 3045.78 3032.93 3142.95 3012.61 3013.24 99.5 3110.52 3045.78 3032.93 3142.95 2987.1 99.7 3013.24 3110.52 3045.78 3032.93 2995.55 100 2987.1 3013.24 3110.52 3045.78 2833.18 100.4 2995.55 2987.1 3013.24 3110.52 2848.96 100.6 2833.18 2995.55 2987.1 3013.24 2794.83 100.7 2848.96 2833.18 2995.55 2987.1 2845.26 100.7 2794.83 2848.96 2833.18 2995.55 2915.02 100.6 2845.26 2794.83 2848.96 2833.18 2892.63 100.5 2915.02 2845.26 2794.83 2848.96 2604.42 100.6 2892.63 2915.02 2845.26 2794.83 2641.65 100.5 2604.42 2892.63 2915.02 2845.26 2659.81 100.4 2641.65 2604.42 2892.63 2915.02 2638.53 100.3 2659.81 2641.65 2604.42 2892.63 2720.25 100.4 2638.53 2659.81 2641.65 2604.42 2745.88 100.4 2720.25 2638.53 2659.81 2641.65 2735.7 100.4 2 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Bel20[t] = -884.525935938039 + 9.56064946708065G.indx[t] + 1.26039173545551Y1[t] -0.333457810230375Y2[t] + 0.215737728536247Y3[t] -0.173493002072184Y4[t] -0.0944078418962099t + 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) -884.525935938039 2177.753448 -0.4062 0.68639 0.343195 G.indx 9.56064946708065 21.439332 0.4459 0.657605 0.328803 Y1 1.26039173545551 0.137892 9.1404 0 0 Y2 -0.333457810230375 0.22167 -1.5043 0.138923 0.069462 Y3 0.215737728536247 0.218026 0.9895 0.327277 0.163638 Y4 -0.173493002072184 0.141721 -1.2242 0.226736 0.113368 t -0.0944078418962099 1.640201 -0.0576 0.954334 0.477167 Multiple Linear Regression - Regression Statistics Multiple R 0.972206501101255 R-squared 0.945185480783544 Adjusted R-squared 0.938473498838672 F-TEST (value) 140.820623259520 F-TEST (DF numerator) 6 F-TEST (DF denominator) 49 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 100.454706268188 Sum Squared Residuals 494466.252559967 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 2863.36 2859.88605584778 3.47394415222183 2 2897.06 2826.91157921939 70.1484207806061 3 3012.61 2904.81732708184 107.792672918157 4 3142.95 3012.15817688167 130.791823118332 5 3032.93 3146.50841478505 -113.578414785047 6 3045.78 2983.36459758544 62.4154024145609 7 3110.52 3047.09358581379 63.4264141862095 8 3013.24 3079.87559317359 -66.6355931735936 9 2987.1 2959.35427846536 27.745721534641 10 2995.55 2973.3576767468 22.1923232532003 11 2833.18 2964.2355228296 -131.055522829598 12 2848.96 2769.82373531640 79.1362646835963 13 2794.83 2851.07600953411 -56.2460095341083 14 2845.26 2740.99928195663 104.260718043371 15 2915.02 2853.13483575758 61.8851642424206 16 2892.63 2908.77741024607 -16.1474102460672 17 2604.42 2878.42770940461 -274.00770940461 18 2641.65 2527.88646675962 113.763533240381 19 2659.81 2652.93301420204 6.87698579796227 20 2638.53 2604.06335862939 34.4666413706074 21 2720.25 2630.08261953056 90.1673804694434 22 2745.88 2737.54205919486 8.33794080514238 23 2735.7 2734.75978749978 0.940212500221704 24 2811.7 2734.61008637482 77.0899136251818 25 2799.43 2825.05156078873 -25.6215607887314 26 2555.28 2778.46258200239 -223.182582002386 27 2304.98 2493.85335035711 -188.873350357112 28 2214.95 2243.86404541182 -28.914045411821 29 2065.81 2162.26138729412 -96.4513872941207 30 1940.49 1992.57252568473 -52.082525684731 31 2042 1910.17228398527 131.827716014726 32 1995.37 2067.07788391703 -71.7078839170322 33 1946.81 1977.02486111008 -30.2148611100752 34 1765.9 1978.74090791573 -212.840907915734 35 1635.25 1741.06274744879 -105.812747448792 36 1833.42 1634.23776640732 199.182233592684 37 1910.43 1896.87715939837 13.5528406016298 38 1959.67 1933.83286446229 25.8371355377083 39 1969.6 2039.36442587997 -69.764425879975 40 2061.41 2020.46729448946 40.9427055105359 41 2093.48 2130.04044548770 -36.5604454876966 42 2120.88 2131.43938937352 -10.5593893735226 43 2174.56 2168.48949372182 6.07050627818473 44 2196.72 2213.12616193923 -16.4061619392286 45 2350.44 2217.67292320705 132.767076792951 46 2440.25 2405.02721119547 35.2227888045307 47 2408.64 2461.38102929264 -52.7410292926396 48 2472.81 2424.64065124771 48.1693487522908 49 2407.6 2513.45256830622 -105.85256830622 50 2454.62 2391.19341138449 63.4265886155146 51 2448.05 2493.34754047792 -45.2975404779186 52 2497.84 2446.00399936964 51.8360006303567 53 2645.64 2534.22491040361 111.415089596392 54 2756.76 2698.06275864358 58.6972413564192 55 2849.27 2807.31190124784 41.9580987521573 56 2921.44 2916.70277531158 4.73722468842403 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.0142685346242040 0.0285370692484079 0.985731465375796 11 0.0122891218151616 0.0245782436303233 0.987710878184838 12 0.0098628888932249 0.0197257777864498 0.990137111106775 13 0.0537065770902238 0.107413154180448 0.946293422909776 14 0.0271494355524729 0.0542988711049458 0.972850564447527 15 0.0147350039426511 0.0294700078853021 0.985264996057349 16 0.00618801916156715 0.0123760383231343 0.993811980838433 17 0.201245694419110 0.402491388838221 0.79875430558089 18 0.458102959788076 0.916205919576151 0.541897040211924 19 0.463655687292821 0.927311374585643 0.536344312707179 20 0.376575631809865 0.75315126361973 0.623424368190135 21 0.383117811471137 0.766235622942275 0.616882188528863 22 0.323382052846669 0.646764105693337 0.676617947153331 23 0.27839450660146 0.55678901320292 0.72160549339854 24 0.433361227609475 0.86672245521895 0.566638772390525 25 0.560323182360009 0.879353635279982 0.439676817639991 26 0.661180313981429 0.677639372037143 0.338819686018572 27 0.825556329502085 0.348887340995829 0.174443670497915 28 0.842512878389045 0.31497424322191 0.157487121610955 29 0.821305375758547 0.357389248482906 0.178694624241453 30 0.778670274007628 0.442659451984745 0.221329725992372 31 0.909467814365641 0.181064371268718 0.0905321856343589 32 0.921329390567138 0.157341218865724 0.078670609432862 33 0.964498806037617 0.0710023879247667 0.0355011939623834 34 0.969560861689977 0.0608782766200458 0.0304391383100229 35 0.971054159547774 0.0578916809044516 0.0289458404522258 36 0.994304562556316 0.0113908748873683 0.00569543744368413 37 0.99331849638329 0.0133630072334195 0.00668150361670974 38 0.988272843137501 0.0234543137249978 0.0117271568624989 39 0.996995687826855 0.00600862434629073 0.00300431217314537 40 0.993529325296356 0.0129413494072888 0.0064706747036444 41 0.985324028129405 0.0293519437411901 0.0146759718705951 42 0.968699065104754 0.0626018697904919 0.0313009348952459 43 0.947639885123096 0.104720229753808 0.0523601148769042 44 0.972927593198988 0.054144813602023 0.0270724068010115 45 0.959818143053823 0.0803637138923539 0.0401818569461769 46 0.96244165361814 0.0751166927637192 0.0375583463818596 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 1 0.0270270270270270 NOK 5% type I error level 11 0.297297297297297 NOK 10% type I error level 19 0.513513513513513 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 = Do not include Seasonal 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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