Multiple Regression analysis 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, 15 Dec 2009 12:17:15 -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/15/t12609047295e486ybasnfmbj2.htm/, Retrieved Tue, 15 Dec 2009 20:19:04 +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/15/t12609047295e486ybasnfmbj2.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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103.34 98.60 96.33 102.60 96.90 96.33 100.69 95.10 95.05 105.67 97.00 96.84 123.61 112.70 96.92 113.08 102.90 97.44 106.46 97.40 97.78 123.38 111.40 97.69 109.87 87.40 96.67 95.74 96.80 98.29 123.06 114.10 98.20 123.39 110.30 98.71 120.28 103.90 98.54 115.33 101.60 98.20 110.40 94.60 100.80 114.49 95.90 101.33 132.03 104.70 101.88 123.16 102.80 101.85 118.82 98.10 102.04 128.32 113.90 102.22 112.24 80.90 102.63 104.53 95.70 102.65 132.57 113.20 102.54 122.52 105.90 102.37 131.80 108.80 102.68 124.55 102.30 102.76 120.96 99.00 102.82 122.60 100.70 103.31 145.52 115.50 103.23 118.57 100.70 103.60 134.25 109.90 103.95 136.70 114.60 103.93 121.37 85.40 104.25 111.63 100.50 104.38 134.42 114.80 104.36 137.65 116.50 104.32 137.86 112.90 104.58 119.77 102.00 104.68 130.69 106.00 104.92 128.28 105.30 105.46 147.45 118.80 105.23 128.42 106.10 105.58 136.90 109.30 105.34 143.95 117.20 105.28 135.64 92.50 105.70 122.48 104.20 105.67 136.83 112.50 105.71 153.04 122.40 106.19 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 Uitvoer[t] = -209.936846753641 + 1.70732899709278TIP[t] + 1.46475451772423cons[t] + 3.84262135112876M1[t] + 4.97584082203382M2[t] + 7.75818751841094M3[t] + 6.43846429337343M4[t] + 4.03950933406176M5[t] + 4.92791824996914M6[t] + 6.84642000424656M7[t] + 1.04533165595581M8[t] + 32.4213266482419M9[t] + 2.89906337160993M10[t] -1.23736464838987M11[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) -209.936846753641 17.809277 -11.7881 0 0 TIP 1.70732899709278 0.109147 15.6424 0 0 cons 1.46475451772423 0.129884 11.2774 0 0 M1 3.84262135112876 3.212424 1.1962 0.236668 0.118334 M2 4.97584082203382 3.477148 1.431 0.157984 0.078992 M3 7.75818751841094 3.483103 2.2274 0.029959 0.014979 M4 6.43846429337343 3.416693 1.8844 0.064703 0.032352 M5 4.03950933406176 3.11295 1.2976 0.199729 0.099864 M6 4.92791824996914 3.285531 1.4999 0.139261 0.069631 M7 6.84642000424656 3.340859 2.0493 0.045128 0.022564 M8 1.04533165595581 3.096237 0.3376 0.736917 0.368458 M9 32.4213266482419 4.252464 7.6241 0 0 M10 2.89906337160993 3.582136 0.8093 0.421762 0.210881 M11 -1.23736464838987 3.228352 -0.3833 0.702963 0.351481 Multiple Linear Regression - Regression Statistics Multiple R 0.954508054745504 R-squared 0.911085626574047 Adjusted R-squared 0.890444789885879 F-TEST (value) 44.1399561625484 F-TEST (DF numerator) 13 F-TEST (DF denominator) 56 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5.10427813315091 Sum Squared Residuals 1459.00469459150 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 103.34 103.348216403211 -0.0082164032108234 2 102.6 101.578976579058 1.02102342094163 3 100.69 99.4132452979814 1.27675470201855 4 105.67 103.959357754147 1.71064224585335 5 123.61 128.482648410610 -4.87264841060958 6 113.08 113.400905504224 -0.320905504224309 7 106.46 106.427114310518 0.0328856894823335 8 123.38 124.396804014931 -1.01680401493068 9 109.87 113.302853468911 -3.43285346891128 10 95.74 102.202385083665 -6.46238508366476 11 123.06 127.470920806775 -4.41092080677485 12 123.39 122.967460070252 0.422539929748496 13 120.28 115.634167571973 4.64583242802663 14 115.33 112.342513813539 2.98748618646123 15 110.4 106.981919276349 3.41808072365058 16 114.49 108.658043641926 5.83195635807359 17 132.03 122.089198841780 9.94080115822048 18 123.16 119.689740027679 3.47025997232112 19 118.82 113.862098853988 4.95790114601216 20 128.32 135.300464472953 -6.9804644729534 21 112.24 110.935151913445 1.30484808655536 22 104.53 106.710652884140 -2.18065288414032 23 132.57 132.291359316315 0.278640683685455 24 122.52 120.816214017914 1.70378598208601 25 131.8 130.064163361106 1.73583663889371 26 124.55 120.216924712326 4.33307528767377 27 120.96 117.452970989361 3.50702901063938 28 122.6 119.753436773066 2.84656322693426 29 145.52 142.505770609309 3.01422939069074 30 118.57 118.667669539801 -0.0976695398014662 31 134.25 136.806262148536 -2.55626214853594 32 136.7 139.000324996227 -2.30032499622679 33 121.37 120.991034719075 0.378965280924589 34 111.63 117.439857385849 -5.80985738584858 35 134.42 137.688938933921 -3.26893893392108 36 137.65 141.770172696660 -4.12017269665968 37 137.86 139.847245832863 -1.98724583286274 38 119.77 122.517054687229 -2.74705468722893 39 130.69 132.480258456231 -1.79025845623098 40 128.28 130.756372372800 -2.4763723727996 41 147.45 151.069465335164 -3.61946533516393 42 128.42 130.787460069196 -2.36746006919646 43 136.9 137.817873529917 -0.917873529916937 44 143.95 145.416798987596 -1.46679898759574 45 135.64 135.236964649134 0.403035350865702 46 122.48 125.646508002956 -3.16650800295614 47 136.83 135.739500839535 1.09049916046463 48 153.04 154.582504727651 -1.54250472765144 49 142.71 143.972350548352 -1.2623505483518 50 123.46 123.145119161962 0.314880838037761 51 144.37 144.796435479499 -0.426435479499037 52 146.15 148.321792033599 -2.17179203359921 53 147.61 141.694350338821 5.91564966117904 54 158.51 155.636735000937 2.87326499906265 55 147.4 144.595114686638 2.80488531336185 56 165.05 151.019060416023 14.0309395839775 57 154.64 149.298061076797 5.34193892320321 58 126.2 125.765631453091 0.434368546908863 59 157.36 151.049280103454 6.31071989654584 60 154.15 150.613648487523 3.53635151247661 61 123.21 126.333856282495 -3.12385628249497 62 113.07 118.979411045885 -5.90941104588546 63 110.45 116.435170500578 -5.9851705005785 64 113.57 119.310997424462 -5.7409974244624 65 122.44 132.818566464317 -10.3785664643168 66 114.93 118.487489858162 -3.55748985816153 67 111.85 116.171536470403 -4.32153647040346 68 126.04 128.306547112271 -2.26654711227089 69 121.34 125.335934172638 -3.99593417263758 70 124.36 107.174965190299 17.1850348097009 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.285895877146033 0.571791754292065 0.714104122853967 18 0.157092600922101 0.314185201844201 0.8429073990779 19 0.082251088359825 0.16450217671965 0.917748911640175 20 0.183248168713256 0.366496337426511 0.816751831286744 21 0.134497953879458 0.268995907758916 0.865502046120542 22 0.0780434185708931 0.156086837141786 0.921956581429107 23 0.0424290472116658 0.0848580944233315 0.957570952788334 24 0.0302901436800674 0.0605802873601348 0.969709856319933 25 0.0163960261989907 0.0327920523979813 0.98360397380101 26 0.00982618435020305 0.0196523687004061 0.990173815649797 27 0.0064641676083446 0.0129283352166892 0.993535832391655 28 0.00521311071625534 0.0104262214325107 0.994786889283745 29 0.00365659600388016 0.00731319200776032 0.99634340399612 30 0.00555326186545139 0.0111065237309028 0.994446738134549 31 0.00290555574246025 0.00581111148492050 0.99709444425754 32 0.00141749977344974 0.00283499954689948 0.99858250022655 33 0.000822401376581322 0.00164480275316264 0.999177598623419 34 0.000637308032896476 0.00127461606579295 0.999362691967103 35 0.000426813035258339 0.000853626070516678 0.999573186964742 36 0.000243783682364577 0.000487567364729153 0.999756216317635 37 0.000116914787163447 0.000233829574326893 0.999883085212837 38 0.000369763281717808 0.000739526563435616 0.999630236718282 39 0.000185119164179939 0.000370238328359877 0.99981488083582 40 0.000149737027148096 0.000299474054296193 0.999850262972852 41 8.73834682991561e-05 0.000174766936598312 0.9999126165317 42 4.62164317165252e-05 9.24328634330505e-05 0.999953783568283 43 2.01383786536878e-05 4.02767573073756e-05 0.999979861621346 44 1.35242148484791e-05 2.70484296969582e-05 0.999986475785152 45 1.01902340829507e-05 2.03804681659013e-05 0.999989809765917 46 3.72435365625322e-05 7.44870731250644e-05 0.999962756463437 47 1.41410888181369e-05 2.82821776362738e-05 0.999985858911182 48 1.40811641983079e-05 2.81623283966159e-05 0.999985918835802 49 6.26365696234096e-06 1.25273139246819e-05 0.999993736343038 50 3.24862273949219e-06 6.49724547898437e-06 0.99999675137726 51 1.11947960245031e-06 2.23895920490061e-06 0.999998880520398 52 7.86659273637073e-07 1.57331854727415e-06 0.999999213340726 53 1.25818192145017e-06 2.51636384290035e-06 0.999998741818079 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 24 0.648648648648649 NOK 5% type I error level 29 0.783783783783784 NOK 10% type I error level 31 0.837837837837838 NOK

Charts produced by software:

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Parameters (Session):

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

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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