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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: Fri, 27 Nov 2009 08:58:30 -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/27/t1259337591a527iz0uvjcjs5h.htm/, Retrieved Fri, 27 Nov 2009 17:00:02 +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/27/t1259337591a527iz0uvjcjs5h.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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277026 1 277051 277838 276610 282965 274960 1 277026 277051 277838 276610 270073 1 274960 277026 277051 277838 267063 1 270073 274960 277026 277051 264916 1 267063 270073 274960 277026 287182 1 264916 267063 270073 274960 291109 1 287182 264916 267063 270073 292223 1 291109 287182 264916 267063 288109 1 292223 291109 287182 264916 281400 1 288109 292223 291109 287182 282579 1 281400 288109 292223 291109 280113 1 282579 281400 288109 292223 280331 1 280113 282579 281400 288109 276759 1 280331 280113 282579 281400 275139 1 276759 280331 280113 282579 274275 1 275139 276759 280331 280113 271234 1 274275 275139 276759 280331 289725 1 271234 274275 275139 276759 290649 1 289725 271234 274275 275139 292223 1 290649 289725 271234 274275 278429 0 292223 290649 289725 271234 269749 0 278429 292223 290649 289725 265784 0 269749 278429 292223 290649 268957 0 265784 269749 278429 292223 264099 0 268957 265784 269749 278429 255121 0 264099 268957 265784 269749 253276 0 255121 264099 268957 265784 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 Y[t] = + 23742.1551966182 + 6615.98887332214X[t] + 0.902769444396003Y1[t] + 0.187257523728878Y2[t] + 0.0782568056750277Y3[t] -0.261594494752365Y4[t] -4817.45387065382M1[t] -9797.82497078342M2[t] -7592.9204932169M3[t] -10990.3561951020M4[t] -7520.4387858831M5[t] + 15571.2127480332M6[t] -1051.92432274379M7[t] -10008.0686935439M8[t] -15844.4644416581M9[t] -10334.1572687118M10[t] -1324.53698797528M11[t] + 144.895467430072t + 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) 23742.1551966182 12205.578893 1.9452 0.059179 0.029589 X 6615.98887332214 2553.85907 2.5906 0.013514 0.006757 Y1 0.902769444396003 0.147766 6.1095 0 0 Y2 0.187257523728878 0.206373 0.9074 0.369928 0.184964 Y3 0.0782568056750277 0.20625 0.3794 0.706483 0.353241 Y4 -0.261594494752365 0.162849 -1.6064 0.116474 0.058237 M1 -4817.45387065382 2604.005125 -1.85 0.072099 0.036049 M2 -9797.82497078342 2998.209807 -3.2679 0.002303 0.001152 M3 -7592.9204932169 2926.792723 -2.5943 0.013392 0.006696 M4 -10990.3561951020 2565.546722 -4.2838 0.000121 6e-05 M5 -7520.4387858831 2775.472514 -2.7096 0.010049 0.005025 M6 15571.2127480332 2595.664252 5.9989 1e-06 0 M7 -1051.92432274379 3485.975333 -0.3018 0.764481 0.382241 M8 -10008.0686935439 4463.886007 -2.242 0.030877 0.015439 M9 -15844.4644416581 5372.774649 -2.949 0.005429 0.002714 M10 -10334.1572687118 3144.926122 -3.286 0.002191 0.001096 M11 -1324.53698797528 2822.16277 -0.4693 0.641513 0.320756 t 144.895467430072 82.529097 1.7557 0.0872 0.0436 Multiple Linear Regression - Regression Statistics Multiple R 0.987881224556706 R-squared 0.975909313831657 Adjusted R-squared 0.96513190159845 F-TEST (value) 90.5513580360972 F-TEST (DF numerator) 17 F-TEST (DF denominator) 38 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3444.73750487735 Sum Squared Residuals 450916226.145328 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 277026 275450.547694024 1575.45230597623 2 274960 272203.66352556 2756.33647443986 3 270073 272300.834214719 -2227.83421471922 4 267063 264453.504108705 2609.49589129474 5 264916 264280.714741103 635.285258896512 6 287182 285173.383815732 2008.61618426771 7 291109 289437.024068634 1671.97593136619 8 292223 288959.808864174 3263.19113582563 9 288109 287313.463455624 795.536544375801 10 281400 283945.928938919 -2545.92893891904 11 282579 285333.283532642 -2754.28353264171 12 280113 285997.405670592 -5884.4056705917 13 280331 279870.569280101 460.430719898766 14 276759 276617.422571949 141.577428050907 15 275139 275281.951009628 -142.951009628418 16 274275 270560.192408189 3714.80759181126 17 271234 272755.094386712 -1521.09438671162 18 289725 293892.16851721 -4167.16851720995 19 290649 293893.755781926 -3244.75578192557 20 292223 289367.283413856 2855.71658614362 21 278429 280896.334769534 -2467.33476953379 22 269749 269628.644522239 120.355477761316 23 265784 268245.554109713 -2461.55410971316 24 268957 263018.8862999 5938.11370009986 25 264099 263397.504649515 701.495350485206 26 255121 256730.89515868 -1609.89515868026 27 253276 251351.464997715 1924.53500228535 28 245980 243541.906196493 2438.09380350746 29 235295 240792.859529705 -5497.85952970512 30 258479 255221.295691971 3257.70430802932 31 260916 257583.694435071 3332.30556492931 32 254586 256386.292562900 -1800.29256289958 33 250566 250046.051243715 519.948756285099 34 243345 245012.685661507 -1667.68566150673 35 247028 245762.656642665 1265.34335733471 36 248464 250546.103175904 -2082.10317590375 37 244962 248346.108629851 -3384.10862985125 38 237003 242795.229868860 -5792.22986885955 39 237008 236453.036206586 554.963793413793 40 225477 231064.922160057 -5587.92216005662 41 226762 224564.094865249 2197.90513475080 42 247857 248883.855964289 -1026.85596428925 43 248256 250786.474509755 -2530.47450975508 44 246892 249402.634192042 -2510.63419204164 45 245021 243869.150531127 1151.84946887290 46 246186 242092.740877336 4093.25912266446 47 255688 251737.50571498 3950.49428502015 48 264242 262213.604853604 2028.39514639559 49 268270 267623.269746509 646.73025349105 50 272969 268464.788874951 4504.21112504904 51 273886 273994.713571351 -108.713571351506 52 267353 270527.475126557 -3174.47512655684 53 271916 267730.236477231 4185.76352276943 54 292633 292705.296010798 -72.296010797836 55 295804 295033.051204615 770.948795385147 56 293222 295029.980967028 -1807.98096702804 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.0159090960208824 0.0318181920417649 0.984090903979118 22 0.00507123410633958 0.0101424682126792 0.99492876589366 23 0.00691439417928566 0.0138287883585713 0.993085605820714 24 0.00581956533953463 0.0116391306790693 0.994180434660465 25 0.00679766566135662 0.0135953313227132 0.993202334338643 26 0.0243805013900334 0.0487610027800668 0.975619498609967 27 0.039658552566596 0.079317105133192 0.960341447433404 28 0.154894411149358 0.309788822298717 0.845105588850642 29 0.379746894393111 0.759493788786223 0.620253105606889 30 0.425199915033964 0.850399830067927 0.574800084966036 31 0.612230812247546 0.775538375504908 0.387769187752454 32 0.601476233291617 0.797047533416766 0.398523766708383 33 0.531993929152655 0.936012141694691 0.468006070847345 34 0.376202130715717 0.752404261431435 0.623797869284283 35 0.358006088671413 0.716012177342825 0.641993911328587 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 6 0.4 NOK 10% type I error level 7 0.466666666666667 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259337591a527iz0uvjcjs5h/10e2gz1259337506.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259337591a527iz0uvjcjs5h/10e2gz1259337506.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259337591a527iz0uvjcjs5h/19wkr1259337506.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259337591a527iz0uvjcjs5h/19wkr1259337506.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259337591a527iz0uvjcjs5h/2umfe1259337506.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259337591a527iz0uvjcjs5h/2umfe1259337506.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259337591a527iz0uvjcjs5h/3pn0o1259337506.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259337591a527iz0uvjcjs5h/3pn0o1259337506.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259337591a527iz0uvjcjs5h/4g50s1259337506.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259337591a527iz0uvjcjs5h/4g50s1259337506.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259337591a527iz0uvjcjs5h/529bl1259337506.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259337591a527iz0uvjcjs5h/529bl1259337506.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259337591a527iz0uvjcjs5h/6q51f1259337506.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259337591a527iz0uvjcjs5h/6q51f1259337506.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259337591a527iz0uvjcjs5h/7i6981259337506.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259337591a527iz0uvjcjs5h/7i6981259337506.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259337591a527iz0uvjcjs5h/8vkf81259337506.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259337591a527iz0uvjcjs5h/8vkf81259337506.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259337591a527iz0uvjcjs5h/9drlv1259337506.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259337591a527iz0uvjcjs5h/9drlv1259337506.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; 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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