*Unverified author*

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

Title produced by software: Multiple Regression

Date of computation: Wed, 18 Nov 2009 11:48:31 -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/18/t1258570162z86d0i2j7nz8l90.htm/, Retrieved Wed, 18 Nov 2009 19:49:34 +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/18/t1258570162z86d0i2j7nz8l90.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:

» Textbox « » Textfile « » CSV «

902.2 0 891.9 0 874 0 930.9 0 944.2 0 935.9 0 937.1 0 885.1 0 892.4 0 987.3 0 946.3 0 799.6 0 875.4 0 846.2 0 880.6 0 885.7 0 868.9 0 882.5 0 789.6 0 773.3 0 804.3 0 817.8 0 836.7 0 721.8 0 760.8 0 841.4 0 1045.6 0 949.2 1 850.1 1 957.4 0 851.8 0 913.9 0 888 0 973.8 0 927.6 1 833 1 879.5 1 797.3 1 834.5 1 735.1 1 835 1 892.8 1 697.2 1 821.1 1 732.7 1 797.6 1 866.3 1 826.3 1 778.6 1 779.2 1 951 1 692.3 1 841.4 1 857.3 1 760.7 1 841.2 0 810.3 0 1007.4 1 931.3 0 931.2 0

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] = + 843.872352941176 -53.7308823529411X[t] + 16.9199999999996M1[t] + 8.82000000000004M2[t] + 94.76M3[t] + 27.0061764705882M4[t] + 56.2861764705882M5[t] + 82.8M6[t] -15.1000000000000M7[t] + 13.7938235294118M8[t] -7.58617647058824M9[t] + 94.4M10[t] + 79.26M11[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) 843.872352941176 31.331185 26.9339 0 0 X -53.7308823529411 18.462078 -2.9103 0.005502 0.002751 M1 16.9199999999996 43.060596 0.3929 0.696144 0.348072 M2 8.82000000000004 43.060596 0.2048 0.838591 0.419296 M3 94.76 43.060596 2.2006 0.032712 0.016356 M4 27.0061764705882 43.218617 0.6249 0.535076 0.267538 M5 56.2861764705882 43.218617 1.3024 0.19914 0.09957 M6 82.8 43.060596 1.9229 0.060567 0.030284 M7 -15.1000000000000 43.060596 -0.3507 0.727404 0.363702 M8 13.7938235294118 43.218617 0.3192 0.751016 0.375508 M9 -7.58617647058824 43.218617 -0.1755 0.861417 0.430709 M10 94.4 43.060596 2.1923 0.033348 0.016674 M11 79.26 43.060596 1.8407 0.071989 0.035995 Multiple Linear Regression - Regression Statistics Multiple R 0.607193134151411 R-squared 0.368683502160613 Adjusted R-squared 0.207496311222897 F-TEST (value) 2.28730025019839 F-TEST (DF numerator) 12 F-TEST (DF denominator) 47 p-value 0.021804366792741 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 68.0847799140522 Sum Squared Residuals 217870.251029412 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 902.2 860.792352941178 41.4076470588216 2 891.9 852.692352941176 39.2076470588236 3 874 938.632352941176 -64.6323529411764 4 930.9 870.878529411765 60.0214705882352 5 944.2 900.158529411765 44.0414705882353 6 935.9 926.672352941176 9.22764705882366 7 937.1 828.772352941176 108.327647058824 8 885.1 857.666176470588 27.4338235294118 9 892.4 836.286176470588 56.1138235294118 10 987.3 938.272352941176 49.0276470588235 11 946.3 923.132352941176 23.1676470588236 12 799.6 843.872352941176 -44.2723529411764 13 875.4 860.792352941176 14.607647058824 14 846.2 852.692352941176 -6.49235294117639 15 880.6 938.632352941176 -58.0323529411764 16 885.7 870.878529411765 14.8214705882354 17 868.9 900.158529411765 -31.2585294117646 18 882.5 926.672352941176 -44.1723529411764 19 789.6 828.772352941176 -39.1723529411764 20 773.3 857.666176470588 -84.3661764705883 21 804.3 836.286176470588 -31.9861764705883 22 817.8 938.272352941176 -120.472352941176 23 836.7 923.132352941176 -86.4323529411764 24 721.8 843.872352941176 -122.072352941176 25 760.8 860.792352941176 -99.992352941176 26 841.4 852.692352941176 -11.2923529411765 27 1045.6 938.632352941176 106.967647058823 28 949.2 817.147647058824 132.052352941176 29 850.1 846.427647058823 3.6723529411765 30 957.4 926.672352941176 30.7276470588235 31 851.8 828.772352941176 23.0276470588235 32 913.9 857.666176470588 56.2338235294118 33 888 836.286176470588 51.7138235294118 34 973.8 938.272352941176 35.5276470588236 35 927.6 869.401470588235 58.1985294117647 36 833 790.141470588235 42.8585294117647 37 879.5 807.061470588235 72.4385294117651 38 797.3 798.961470588235 -1.66147058823541 39 834.5 884.901470588235 -50.4014705882353 40 735.1 817.147647058824 -82.0476470588236 41 835 846.427647058823 -11.4276470588235 42 892.8 872.941470588235 19.8585294117646 43 697.2 775.041470588235 -77.8414705882353 44 821.1 803.935294117647 17.1647058823529 45 732.7 782.555294117647 -49.8552941176471 46 797.6 884.541470588235 -86.9414705882353 47 866.3 869.401470588235 -3.10147058823541 48 826.3 790.141470588235 36.1585294117646 49 778.6 807.061470588235 -28.4614705882348 50 779.2 798.961470588235 -19.7614705882353 51 951 884.901470588235 66.0985294117646 52 692.3 817.147647058824 -124.847647058824 53 841.4 846.427647058823 -5.02764705882355 54 857.3 872.941470588235 -15.6414705882354 55 760.7 775.041470588235 -14.3414705882353 56 841.2 857.666176470588 -16.4661764705882 57 810.3 836.286176470588 -25.9861764705883 58 1007.4 884.541470588235 122.858529411765 59 931.3 923.132352941176 8.16764705882352 60 931.2 843.872352941176 87.3276470588236 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.0743657932428761 0.148731586485752 0.925634206757124 17 0.0883837929747112 0.176767585949422 0.911616207025289 18 0.0589700038770608 0.117940007754122 0.94102999612294 19 0.203068258093843 0.406136516187687 0.796931741906157 20 0.24663122436106 0.49326244872212 0.75336877563894 21 0.219251829658915 0.438503659317829 0.780748170341085 22 0.411867417265358 0.823734834530716 0.588132582734642 23 0.439610287654928 0.879220575309855 0.560389712345072 24 0.539561611629406 0.920876776741188 0.460438388370594 25 0.693607232847625 0.61278553430475 0.306392767152375 26 0.612505866542982 0.774988266914036 0.387494133457018 27 0.734734153222431 0.530531693555138 0.265265846777569 28 0.934069785530427 0.131860428939146 0.0659302144695728 29 0.909458175475335 0.181083649049329 0.0905418245246647 30 0.869470674959029 0.261058650081943 0.130529325040971 31 0.822515363808901 0.354969272382197 0.177484636191099 32 0.798889060163967 0.402221879672066 0.201110939836033 33 0.790034075570535 0.41993184885893 0.209965924429465 34 0.732543220867845 0.53491355826431 0.267456779132155 35 0.687834120425771 0.624331759148457 0.312165879574229 36 0.605620845644724 0.788758308710553 0.394379154355276 37 0.597828636085239 0.804342727829522 0.402171363914761 38 0.523288549425629 0.953422901148742 0.476711450574371 39 0.603199825400994 0.793600349198012 0.396800174599006 40 0.621912380126392 0.756175239747216 0.378087619873608 41 0.497406092626499 0.994812185252999 0.502593907373501 42 0.375404025421419 0.750808050842837 0.624595974578581 43 0.323955427074311 0.647910854148622 0.676044572925689 44 0.215230776050855 0.430461552101709 0.784769223949145 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 = 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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