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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: Thu, 26 Nov 2009 07:46:46 -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/26/t1259246856eyr3jio7t3eyp6l.htm/, Retrieved Thu, 26 Nov 2009 15:47:48 +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/26/t1259246856eyr3jio7t3eyp6l.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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13807 0 19169 22782 20366 29743 0 13807 19169 22782 25591 0 29743 13807 19169 29096 0 25591 29743 13807 26482 0 29096 25591 29743 22405 0 26482 29096 25591 27044 0 22405 26482 29096 17970 0 27044 22405 26482 18730 0 17970 27044 22405 19684 0 18730 17970 27044 19785 0 19684 18730 17970 18479 0 19785 19684 18730 10698 0 18479 19785 19684 31956 0 10698 18479 19785 29506 0 31956 10698 18479 34506 0 29506 31956 10698 27165 0 34506 29506 31956 26736 0 27165 34506 29506 23691 0 26736 27165 34506 18157 0 23691 26736 27165 17328 0 18157 23691 26736 18205 0 17328 18157 23691 20995 0 18205 17328 18157 17382 0 20995 18205 17328 9367 0 17382 20995 18205 31124 0 9367 17382 20995 26551 0 31124 9367 17382 30651 0 26551 31124 9367 25859 0 30651 26551 31124 25100 0 25859 30651 26551 25778 0 25100 25859 30651 20418 0 25778 25100 25859 18688 0 20418 25778 25100 20424 0 18688 20418 25778 24776 0 20424 18688 20418 19814 0 24776 20424 18688 12738 0 19814 24776 20424 31566 0 12738 19814 24776 30 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 Y[t] = + 4746.19129722464 -866.780609791573X[t] + 0.156995128968414Y1[t] + 0.442321422199032Y2[t] + 0.0364744218977145Y3[t] -6690.66593526214M1[t] + 14375.1133278374M2[t] + 11689.2387306921M3[t] + 7477.25242961239M4[t] + 4810.45819860558M5[t] + 506.153729263371M6[t] + 3289.15893096822M7[t] -1351.27077153871M8[t] -2032.54263674398M9[t] + 2664.83981479995M10[t] + 5242.33673357328M11[t] + 14.8885796963493t + 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) 4746.19129722464 3544.00355 1.3392 0.187877 0.093939 X -866.780609791573 879.708747 -0.9853 0.330254 0.165127 Y1 0.156995128968414 0.157787 0.995 0.32558 0.16279 Y2 0.442321422199032 0.141714 3.1212 0.003295 0.001648 Y3 0.0364744218977145 0.155503 0.2346 0.815719 0.40786 M1 -6690.66593526214 1475.642246 -4.5341 4.9e-05 2.5e-05 M2 14375.1133278374 2320.460748 6.1949 0 0 M3 11689.2387306921 2214.977542 5.2774 5e-06 2e-06 M4 7477.25242961239 2474.349367 3.0219 0.004315 0.002157 M5 4810.45819860558 2005.681778 2.3984 0.0211 0.01055 M6 506.153729263371 1962.268029 0.2579 0.797741 0.398871 M7 3289.15893096822 2169.03656 1.5164 0.137088 0.068544 M8 -1351.27077153871 1727.284386 -0.7823 0.438528 0.219264 M9 -2032.54263674398 1812.282349 -1.1215 0.268585 0.134292 M10 2664.83981479995 1925.060804 1.3843 0.173759 0.086879 M11 5242.33673357328 1345.082826 3.8974 0.000352 0.000176 t 14.8885796963493 23.781235 0.6261 0.534743 0.267371 Multiple Linear Regression - Regression Statistics Multiple R 0.96643382677579 R-squared 0.933994341536498 Adjusted R-squared 0.908236035794644 F-TEST (value) 36.2599291621446 F-TEST (DF numerator) 16 F-TEST (DF denominator) 41 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1769.04422157133 Sum Squared Residuals 128310215.772871 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 13807 11899.6582857616 1907.34171423840 2 29743 30628.5331519286 -885.533151928608 3 25591 27955.9119575727 -2364.91195757268 4 29096 29960.2287946607 -864.228794660664 5 26482 26603.3289127761 -121.328912776103 6 22405 23302.4225410951 -897.422541095091 7 27044 24431.8618328153 2612.13816718472 8 17970 18635.9325361431 -665.932536143107 9 18730 18448.1983098791 281.80169012088 10 19684 19435.3658972849 248.634102715128 11 19785 22182.7201253618 -2397.72012536183 12 18479 17420.8236769308 1058.17632306917 13 10698 10619.4817450648 78.5182549351743 14 31956 29904.5826285772 2051.41737142279 15 29506 27081.6604816098 2424.33951839024 16 34506 31618.9860105747 2887.01398942533 17 27165 29443.7417804203 -2278.74178042027 18 26736 26124.0694263630 611.93057363697 19 23691 25789.9028465623 -2098.90284656226 20 18157 20228.7969347683 -2071.79693476835 21 17328 17331.0863479581 -3.08634795805432 22 18205 19354.3370521555 -1149.33705215553 23 20995 21515.8733689456 -520.873368945564 24 17382 17084.1202164058 297.879783594151 25 9367 11107.1842958168 -1740.18429581677 26 31124 29433.1925186203 1690.80748137966 27 26551 26500.9612368955 50.038763104476 28 30651 30917.1694820137 -266.169482013737 29 25859 27679.7819929862 -1820.78199298618 30 25100 24284.7657450015 815.234254998543 31 25778 24993.4410981185 784.558901881504 32 20418 19963.8352835656 454.164716434412 33 18688 18728.1679448165 -40.1679448165498 34 20424 20822.7242380013 -398.724238001302 35 24776 22726.9343185841 2049.06568141592 36 19814 18887.4982050322 926.50179496784 37 12738 13421.0134453497 -683.013445349716 38 31566 31354.7215427124 211.278457287635 39 30111 28328.7873485439 1782.21265145607 40 30019 31973.1964423267 -1954.19644232665 41 31934 28483.2293755501 3450.77062444989 42 25826 24400.6953031753 1425.30469682473 43 26835 27083.3527135339 -248.352713533948 44 20205 19984.3689469949 220.631053005066 45 17789 18500.624502473 -711.624502473013 46 20520 19937.8069646408 582.193035359192 47 22518 21648.4721871085 869.527812891474 48 15572 17854.5579016312 -2282.55790163116 49 11509 11071.6622280071 437.337771992913 50 25447 28514.9701581615 -3067.97015816147 51 24090 25981.6789753781 -1891.67897537811 52 27786 27588.4192704243 197.580729575718 53 26195 25424.9179382673 770.082061732657 54 20516 22471.0469843652 -1955.04698436515 55 22759 23808.44150897 -1049.44150897002 56 19028 16965.0662985280 2062.93370147198 57 16971 16497.9228948733 473.077105126737 58 20036 19318.7658479175 717.23415208251 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 20 0.915576281154959 0.168847437690083 0.0844237188450413 21 0.868811896232415 0.262376207535169 0.131188103767585 22 0.883955485594838 0.232089028810324 0.116044514405162 23 0.839305196106945 0.321389607786111 0.160694803893055 24 0.779658720368048 0.440682559263904 0.220341279631952 25 0.807150769569582 0.385698460860835 0.192849230430418 26 0.801279744455446 0.397440511089109 0.198720255544554 27 0.711264860995648 0.577470278008705 0.288735139004352 28 0.673042009947973 0.653915980104053 0.326957990052027 29 0.852816115334931 0.294367769330138 0.147183884665069 30 0.805890788902268 0.388218422195463 0.194109211097732 31 0.714408606342331 0.571182787315337 0.285591393657669 32 0.692072141768938 0.615855716462124 0.307927858231062 33 0.57747841605572 0.845043167888559 0.422521583944279 34 0.500615407230609 0.998769185538782 0.499384592769391 35 0.482259852586103 0.964519705172206 0.517740147413897 36 0.384326924612248 0.768653849224496 0.615673075387752 37 0.274026711949665 0.548053423899330 0.725973288050335 38 0.329334520858637 0.658669041717275 0.670665479141363 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):

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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