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R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Sat, 04 Dec 2010 10:28:08 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/04/t12914584281vvew4jmkm0gbi8.htm/, Retrieved Sat, 04 Dec 2010 11:27:08 +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/2010/Dec/04/t12914584281vvew4jmkm0gbi8.htm/}, year = {2010}, } @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 = {2010}, 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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14731798.37 0 16471559.62 0 15213975.95 0 17637387.4 0 17972385.83 0 16896235.55 0 16697955.94 0 19691579.52 0 15930700.75 0 17444615.98 0 17699369.88 0 15189796.81 0 15672722.75 0 17180794.3 0 17664893.45 0 17862884.98 0 16162288.88 0 17463628.82 0 16772112.17 0 19106861.48 0 16721314.25 0 18161267.85 0 18509941.2 0 17802737.97 0 16409869.75 0 17967742.04 0 20286602.27 0 19537280.81 0 18021889.62 0 20194317.23 0 19049596.62 0 20244720.94 0 21473302.24 0 19673603.19 0 21053177.29 0 20159479.84 0 18203628.31 0 21289464.94 0 20432335.71 1 17180395.07 1 15816786.32 1 15071819.75 1 14521120.61 1 15668789.39 1 14346884.11 1 13881008.13 1 15465943.69 1 14238232.92 1 13557713.21 1 16127590.29 1 16793894.2 1 16014007.43 1 16867867.15 1 16014583.21 1 15878594.85 1 18664899.14 1 17962530.06 1 17332692.2 1 19542066.35 1 17203555.19 1

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 5 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 17654549.7169412 -1839472.92735294X[t] -1571508.65347059M1[t] + 520775.106529412M2[t] + 1159579.77M3[t] + 727630.592M4[t] + 49483.014M5[t] + 209356.366000001M6[t] -334884.508M7[t] + 1756609.548M8[t] + 368185.735999999M9[t] + 379876.924000001M10[t] + 1535339.136M11[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) 17654549.7169412 791300.81047 22.3108 0 0 X -1839472.92735294 466278.474202 -3.945 0.000265 0.000132 M1 -1571508.65347059 1091529.923072 -1.4397 0.156572 0.078286 M2 520775.106529412 1091529.923072 0.4771 0.635498 0.317749 M3 1159579.77 1087538.941069 1.0662 0.291761 0.14588 M4 727630.592 1087538.941069 0.6691 0.506729 0.253365 M5 49483.014 1087538.941069 0.0455 0.963902 0.481951 M6 209356.366000001 1087538.941069 0.1925 0.848176 0.424088 M7 -334884.508 1087538.941069 -0.3079 0.759497 0.379749 M8 1756609.548 1087538.941069 1.6152 0.112958 0.056479 M9 368185.735999999 1087538.941069 0.3385 0.736457 0.368228 M10 379876.924000001 1087538.941069 0.3493 0.728425 0.364212 M11 1535339.136 1087538.941069 1.4118 0.164608 0.082304 Multiple Linear Regression - Regression Statistics Multiple R 0.61198741386414 R-squared 0.374528594728118 Adjusted R-squared 0.214833767850191 F-TEST (value) 2.34527693883543 F-TEST (DF numerator) 12 F-TEST (DF denominator) 47 p-value 0.0187656331272622 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1719550.04895249 Sum Squared Residuals 138972061430068 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 14731798.37 16083041.0634706 -1351242.69347061 2 16471559.62 18175324.8234706 -1703765.20347059 3 15213975.95 18814129.4869412 -3600153.53694118 4 17637387.4 18382180.3089412 -744792.908941177 5 17972385.83 17704032.7309412 268353.099058822 6 16896235.55 17863906.0829412 -967670.532941176 7 16697955.94 17319665.2089412 -621709.268941176 8 19691579.52 19411159.2649412 280420.255058822 9 15930700.75 18022735.4529412 -2092034.70294118 10 17444615.98 18034426.6409412 -589810.660941177 11 17699369.88 19189888.8529412 -1490518.97294118 12 15189796.81 17654549.7169412 -2464752.90694118 13 15672722.75 16083041.0634706 -410318.313470583 14 17180794.3 18175324.8234706 -994530.523470587 15 17664893.45 18814129.4869412 -1149236.03694118 16 17862884.98 18382180.3089412 -519295.328941175 17 16162288.88 17704032.7309412 -1541743.85094118 18 17463628.82 17863906.0829412 -400277.262941176 19 16772112.17 17319665.2089412 -547553.038941176 20 19106861.48 19411159.2649412 -304297.784941176 21 16721314.25 18022735.4529412 -1301421.20294118 22 18161267.85 18034426.6409412 126841.209058824 23 18509941.2 19189888.8529412 -679947.652941177 24 17802737.97 17654549.7169412 148188.253058822 25 16409869.75 16083041.0634706 326828.686529417 26 17967742.04 18175324.8234706 -207582.783470589 27 20286602.27 18814129.4869412 1472472.78305882 28 19537280.81 18382180.3089412 1155100.50105882 29 18021889.62 17704032.7309412 317856.889058825 30 20194317.23 17863906.0829412 2330411.14705882 31 19049596.62 17319665.2089412 1729931.41105882 32 20244720.94 19411159.2649412 833561.675058825 33 21473302.24 18022735.4529412 3450566.78705882 34 19673603.19 18034426.6409412 1639176.54905882 35 21053177.29 19189888.8529412 1863288.43705882 36 20159479.84 17654549.7169412 2504930.12305882 37 18203628.31 16083041.0634706 2120587.24652941 38 21289464.94 18175324.8234706 3114140.11652941 39 20432335.71 16974656.5595882 3457679.15041176 40 17180395.07 16542707.3815882 637687.688411765 41 15816786.32 15864559.8035882 -47773.4835882354 42 15071819.75 16024433.1555882 -952613.405588236 43 14521120.61 15480192.2815882 -959071.671588236 44 15668789.39 17571686.3375882 -1902896.94758824 45 14346884.11 16183262.5255882 -1836378.41558824 46 13881008.13 16194953.7135882 -2313945.58358823 47 15465943.69 17350415.9255882 -1884472.23558824 48 14238232.92 15815076.7895882 -1576843.86958824 49 13557713.21 14243568.1361176 -685854.926117641 50 16127590.29 16335851.8961176 -208261.606117648 51 16793894.2 16974656.5595882 -180762.359588236 52 16014007.43 16542707.3815882 -528699.951588235 53 16867867.15 15864559.8035882 1003307.34641176 54 16014583.21 16024433.1555882 -9849.94558823517 55 15878594.85 15480192.2815882 398402.568411764 56 18664899.14 17571686.3375882 1093212.80241176 57 17962530.06 16183262.5255882 1779267.53441176 58 17332692.2 16194953.7135882 1137738.48641176 59 19542066.35 17350415.9255882 2191650.42441177 60 17203555.19 15815076.7895882 1388478.40041177 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.301331064069983 0.602662128139965 0.698668935930017 17 0.28902424451173 0.57804848902346 0.71097575548827 18 0.180771016615290 0.361542033230580 0.81922898338471 19 0.103325426111989 0.206650852223978 0.896674573888011 20 0.0580449651091736 0.116089930218347 0.941955034890826 21 0.0465192451673856 0.0930384903347712 0.953480754832614 22 0.0267803470574853 0.0535606941149707 0.973219652942515 23 0.0196407136732036 0.0392814273464072 0.980359286326796 24 0.0499196996722279 0.0998393993444557 0.950080300327772 25 0.0408439449637583 0.0816878899275165 0.959156055036242 26 0.0412322784614852 0.0824645569229704 0.958767721538515 27 0.223201854978901 0.446403709957801 0.7767981450211 28 0.210355786129538 0.420711572259077 0.789644213870462 29 0.204475249591487 0.408950499182973 0.795524750408513 30 0.265586603232438 0.531173206464875 0.734413396767562 31 0.259206771690627 0.518413543381253 0.740793228309373 32 0.208891909361914 0.417783818723828 0.791108090638086 33 0.421682335948256 0.843364671896512 0.578317664051744 34 0.359093527440682 0.718187054881363 0.640906472559318 35 0.350277704097373 0.700555408194747 0.649722295902627 36 0.354960308361630 0.709920616723259 0.64503969163837 37 0.308260247553751 0.616520495107501 0.69173975244625 38 0.314098943567352 0.628197887134704 0.685901056432648 39 0.332893834181616 0.665787668363233 0.667106165818384 40 0.280017416767602 0.560034833535204 0.719982583232398 41 0.207595726209381 0.415191452418762 0.792404273790619 42 0.151835552230888 0.303671104461776 0.848164447769112 43 0.0990481622854388 0.198096324570878 0.900951837714561 44 0.086598930068725 0.17319786013745 0.913401069931275 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 1 0.0344827586206897 OK 10% type I error level 6 0.206896551724138 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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