Multiple_Regression_2

*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: Tue, 29 Dec 2009 07:44:45 -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/29/t1262097916213vff6f06gdhwe.htm/, Retrieved Tue, 29 Dec 2009 15:45:28 +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/29/t1262097916213vff6f06gdhwe.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:

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Paper

Dataseries X:

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2529 314 2196 318 3202 320 2718 323 2728 325 2354 327 2697 330 2651 331 2067 332 2641 334 2539 334 2294 334 2712 339 2314 345 3092 346 2677 352 2813 355 2668 358 2939 361 2617 363 2231 364 2481 365 2421 366 2408 370 2560 371 2100 371 3315 372 2801 373 2403 373 3024 374 2507 375 2980 375 2211 376 2471 376 2594 377 2452 377 2232 378 2373 379 3127 380 2802 384 2641 389 2787 390 2619 391 2806 392 2193 393 2323 394 2529 394 2412 395 2262 396 2154 397 3230 398 2295 399 2715 400 2733 400 2317 401 2730 401 1913 406 2390 407 2484 423 1960 427

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] = + 2798.64582612754 -1.29649455104450X[t] + 126.573614428065M1[t] -101.914798649428M2[t] + 865.440994811826M3[t] + 334.730478464959M4[t] + 338.982766477257M5[t] + 393.997858848719M6[t] + 298.931549040599M7[t] + 440.968744681435M8[t] -190.497565126685M9[t] + 148.998929424360M10[t] + 205.866309808120M11[t] + 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) 2798.64582612754 310.55353 9.0118 0 0 X -1.29649455104450 0.792395 -1.6362 0.108484 0.054242 M1 126.573614428065 106.094938 1.193 0.238849 0.119424 M2 -101.914798649428 105.813332 -0.9632 0.340399 0.170199 M3 865.440994811826 105.685081 8.1889 0 0 M4 334.730478464959 105.401308 3.1758 0.002639 0.001319 M5 338.982766477257 105.226858 3.2214 0.002318 0.001159 M6 393.997858848719 105.130745 3.7477 0.000488 0.000244 M7 298.931549040599 105.024261 2.8463 0.006536 0.003268 M8 440.968744681435 104.983121 4.2004 0.000118 5.9e-05 M9 -190.497565126685 104.904503 -1.8159 0.075765 0.037883 M10 148.998929424360 104.869184 1.4208 0.161974 0.080987 M11 205.866309808120 104.791559 1.9645 0.055396 0.027698 Multiple Linear Regression - Regression Statistics Multiple R 0.880399109517796 R-squared 0.775102592039729 Adjusted R-squared 0.717681977241361 F-TEST (value) 13.4986815233781 F-TEST (DF numerator) 12 F-TEST (DF denominator) 47 p-value 1.89890325685838e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 165.674653926675 Sum Squared Residuals 1290060.27482500 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 2529 2518.12015152763 10.8798484723707 2 2196 2284.44576024596 -88.4457602459581 3 3202 3249.20856460512 -47.2085646051217 4 2718 2714.60856460512 3.3914353948774 5 2728 2716.26786351533 11.7321364846685 6 2354 2768.68996678470 -414.689966784705 7 2697 2669.73417332345 27.265826676549 8 2651 2810.47487441324 -159.474874413242 9 2067 2177.71207005408 -110.712070054078 10 2641 2514.61557550303 126.384424496967 11 2539 2571.48295588679 -32.4829558867934 12 2294 2365.61664607867 -71.6166460786734 13 2712 2485.70778775152 226.292212248483 14 2314 2249.44040736776 64.5595926322436 15 3092 3215.49970627797 -123.499706277965 16 2677 2677.01022262483 -0.0102226248318100 17 2813 2677.37302698400 135.626973016004 18 2668 2728.49863570232 -60.498635702325 19 2939 2629.54284224107 309.457157758928 20 2617 2768.98704877982 -151.987048779818 21 2231 2136.22424442065 94.775755579346 22 2481 2474.42424442065 6.575755579346 23 2421 2529.99513025337 -108.995130253370 24 2408 2318.94284224107 89.0571577589282 25 2560 2444.21996211809 115.780037881907 26 2100 2215.7315490406 -115.731549040599 27 3315 3181.79084795081 133.209152049191 28 2801 2649.78383705290 151.216162947103 29 2403 2654.03612506519 -251.036125065195 30 3024 2707.75472288561 316.245277114387 31 2507 2611.39191852645 -104.391918526449 32 2980 2753.42911416728 226.570885832716 33 2211 2120.66630980812 90.33369019188 34 2471 2460.16280435916 10.8371956408356 35 2594 2515.73369019188 78.2663098081199 36 2452 2309.86738038376 142.132619616240 37 2232 2435.14450026078 -203.144500260781 38 2373 2205.35959263224 167.640407367757 39 3127 3171.41889154245 -44.4188915424526 40 2802 2635.52239699141 166.477603008592 41 2641 2633.29221224848 7.70778775151669 42 2787 2687.0108100689 99.989189931099 43 2619 2590.64800570974 28.3519942902633 44 2806 2731.38870679953 74.611293200472 45 2193 2098.62590244036 94.3740975596365 46 2323 2436.82590244036 -113.825902440363 47 2529 2493.69328282412 35.3067171758764 48 2412 2286.53047846496 125.469521535041 49 2262 2411.80759834198 -149.807598341980 50 2154 2182.02269071344 -28.0226907134425 51 3230 3148.08198962365 81.9180103763483 52 2295 2616.07497872574 -321.074978725741 53 2715 2619.03077218699 95.9692278130061 54 2733 2674.04586455846 58.9541354415439 55 2317 2577.68306019929 -260.683060199292 56 2730 2719.72025584013 10.2797441598727 57 1913 2081.77147327678 -168.771473276785 58 2390 2419.97147327679 -29.971473276785 59 2484 2456.09494084383 27.9050591561669 60 1960 2245.04265283154 -285.042652831535 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.225067800411415 0.450135600822829 0.774932199588585 17 0.110570907755643 0.221141815511287 0.889429092244357 18 0.199867376175430 0.399734752350861 0.80013262382457 19 0.183440812248812 0.366881624497624 0.816559187751188 20 0.207608909084904 0.415217818169809 0.792391090915096 21 0.132826767258500 0.265653534517001 0.8671732327415 22 0.191980966159829 0.383961932319658 0.808019033840171 23 0.243210845217772 0.486421690435544 0.756789154782228 24 0.168795802250753 0.337591604501506 0.831204197749247 25 0.173660632442977 0.347321264885953 0.826339367557023 26 0.247439781394709 0.494879562789417 0.752560218605291 27 0.208980044580183 0.417960089160366 0.791019955419817 28 0.165478969068599 0.330957938137197 0.834521030931401 29 0.656544100657989 0.686911798684022 0.343455899342011 30 0.866721199215898 0.266557601568204 0.133278800784102 31 0.89224428396882 0.21551143206236 0.10775571603118 32 0.892820605546796 0.214358788906407 0.107179394453204 33 0.83803127993128 0.323937440137439 0.161968720068720 34 0.780603491946686 0.438793016106628 0.219396508053314 35 0.7399530848272 0.520093830345599 0.260046915172799 36 0.649845316391598 0.700309367216804 0.350154683608402 37 0.7185812261257 0.5628375477486 0.2814187738743 38 0.63459767466886 0.73080465066228 0.36540232533114 39 0.65510476137925 0.6897904772415 0.34489523862075 40 0.79922450057203 0.401550998855939 0.200775499427969 41 0.759763701652091 0.480472596695817 0.240236298347909 42 0.639582945924749 0.720834108150501 0.360417054075251 43 0.631530261318727 0.736939477362545 0.368469738681272 44 0.455156638330279 0.910313276660559 0.544843361669721 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):

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No 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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