*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: Sun, 23 Nov 2008 07:11:11 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/23/t1227449498ckomdtw3z7rcapb.htm/, Retrieved Sun, 23 Nov 2008 14:11:47 +0000

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/2008/Nov/23/t1227449498ckomdtw3z7rcapb.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

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Original text written by user:

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User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

299.63 0 305.945 0 382.252 0 348.846 0 335.367 0 373.617 0 312.612 0 312.232 0 337.161 0 331.476 0 350.103 0 345.127 0 297.256 0 295.979 0 361.007 0 321.803 0 354.937 0 349.432 0 290.979 0 349.576 0 327.625 0 349.377 0 336.777 0 339.134 0 323.321 0 318.86 0 373.583 0 333.03 0 408.556 0 414.646 0 291.514 0 348.857 0 349.368 0 375.765 0 364.136 0 349.53 0 348.167 1 332.856 1 360.551 1 346.969 1 392.815 1 372.02 1 371.027 1 342.672 1 367.343 1 390.786 1 343.785 1 362.6 1 349.468 1 340.624 1 369.536 1 407.782 1 392.239 1 404.824 1 373.669 1 344.902 1 396.7 1 398.911 1 366.009 1 392.484 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 3 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation x[t] = + 346.178416666667 + 28.9914583333334y[t] -34.2066000000002M1[t] -38.9222000000000M2[t] + 11.6108M3[t] -6.08899999999998M4[t] + 19.0078M5[t] + 25.1328000000000M6[t] -29.8148M7[t] -18.1272M8[t] -2.1356M9[t] + 11.488M10[t] -5.61299999999999M11[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) 346.178416666667 9.371336 36.9401 0 0 y 28.9914583333334 5.37483 5.3939 2e-06 1e-06 M1 -34.2066000000002 12.899592 -2.6518 0.010882 0.005441 M2 -38.9222000000000 12.899592 -3.0173 0.004108 0.002054 M3 11.6108 12.899592 0.9001 0.372661 0.18633 M4 -6.08899999999998 12.899592 -0.472 0.639089 0.319545 M5 19.0078 12.899592 1.4735 0.147277 0.073639 M6 25.1328000000000 12.899592 1.9483 0.057359 0.02868 M7 -29.8148 12.899592 -2.3113 0.02525 0.012625 M8 -18.1272 12.899592 -1.4053 0.166522 0.083261 M9 -2.1356 12.899592 -0.1656 0.869217 0.434608 M10 11.488 12.899592 0.8906 0.377696 0.188848 M11 -5.61299999999999 12.899592 -0.4351 0.66546 0.33273 Multiple Linear Regression - Regression Statistics Multiple R 0.806465254265892 R-squared 0.65038620633815 Adjusted R-squared 0.56112311008406 F-TEST (value) 7.28617125812901 F-TEST (DF numerator) 12 F-TEST (DF denominator) 47 p-value 2.64957100259977e-07 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 20.3960459594058 Sum Squared Residuals 19551.9384665750 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 299.63 311.971816666668 -12.3418166666675 2 305.945 307.256216666667 -1.31121666666669 3 382.252 357.789216666667 24.4627833333333 4 348.846 340.089416666667 8.75658333333342 5 335.367 365.186216666667 -29.8192166666667 6 373.617 371.311216666667 2.30578333333334 7 312.612 316.363616666667 -3.75161666666663 8 312.232 328.051216666667 -15.8192166666667 9 337.161 344.042816666667 -6.88181666666667 10 331.476 357.666416666667 -26.1904166666666 11 350.103 340.565416666667 9.53758333333334 12 345.127 346.178416666667 -1.05141666666664 13 297.256 311.971816666666 -14.7158166666665 14 295.979 307.256216666667 -11.2772166666667 15 361.007 357.789216666667 3.21778333333336 16 321.803 340.089416666667 -18.2864166666667 17 354.937 365.186216666667 -10.2492166666666 18 349.432 371.311216666667 -21.8792166666666 19 290.979 316.363616666667 -25.3846166666667 20 349.576 328.051216666667 21.5247833333334 21 327.625 344.042816666667 -16.4178166666666 22 349.377 357.666416666667 -8.28941666666665 23 336.777 340.565416666667 -3.78841666666668 24 339.134 346.178416666667 -7.04441666666664 25 323.321 311.971816666666 11.3491833333336 26 318.86 307.256216666667 11.6037833333334 27 373.583 357.789216666667 15.7937833333334 28 333.03 340.089416666667 -7.0594166666667 29 408.556 365.186216666667 43.3697833333333 30 414.646 371.311216666667 43.3347833333334 31 291.514 316.363616666667 -24.8496166666666 32 348.857 328.051216666667 20.8057833333334 33 349.368 344.042816666667 5.32518333333334 34 375.765 357.666416666667 18.0985833333333 35 364.136 340.565416666667 23.5705833333334 36 349.53 346.178416666667 3.35158333333332 37 348.167 340.963275 7.20372500000018 38 332.856 336.247675 -3.39167500000002 39 360.551 386.780675 -26.2296750000000 40 346.969 369.080875 -22.1118750000000 41 392.815 394.177675 -1.36267500000002 42 372.02 400.302675 -28.2826750000000 43 371.027 345.355075 25.6719250000000 44 342.672 357.042675 -14.370675 45 367.343 373.034275 -5.691275 46 390.786 386.657875 4.12812499999997 47 343.785 369.556875 -25.771875 48 362.6 375.169875 -12.569875 49 349.468 340.963275 8.50472500000023 50 340.624 336.247675 4.37632500000000 51 369.536 386.780675 -17.244675 52 407.782 369.080875 38.701125 53 392.239 394.177675 -1.93867500000005 54 404.824 400.302675 4.52132499999999 55 373.669 345.355075 28.313925 56 344.902 357.042675 -12.1406750000000 57 396.7 373.034275 23.665725 58 398.911 386.657875 12.2531250000000 59 366.009 369.556875 -3.54787500000002 60 392.484 375.169875 17.3141250000000 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.281924004071573 0.563848008143146 0.718075995928427 17 0.222568542634461 0.445137085268923 0.777431457365539 18 0.218553903002892 0.437107806005785 0.781446096997108 19 0.215189780450668 0.430379560901337 0.784810219549332 20 0.302887262491783 0.605774524983565 0.697112737508217 21 0.239756016472022 0.479512032944043 0.760243983527978 22 0.208457725783608 0.416915451567216 0.791542274216392 23 0.151747009229639 0.303494018459279 0.84825299077036 24 0.104032771327953 0.208065542655906 0.895967228672047 25 0.106879977967242 0.213759955934484 0.893120022032758 26 0.0840501955210208 0.168100391042042 0.91594980447898 27 0.0578957036266505 0.115791407253301 0.94210429637335 28 0.0429024095794565 0.085804819158913 0.957097590420543 29 0.276901721837122 0.553803443674244 0.723098278162878 30 0.545441832437977 0.909116335124047 0.454558167562023 31 0.780241351465593 0.439517297068814 0.219758648534407 32 0.757578181830383 0.484843636339234 0.242421818169617 33 0.720754896590753 0.558490206818494 0.279245103409247 34 0.704702613355269 0.590594773289461 0.295297386644731 35 0.713399750576395 0.573200498847211 0.286600249423605 36 0.61903783586496 0.76192432827008 0.38096216413504 37 0.512172155749655 0.97565568850069 0.487827844250345 38 0.41464102668148 0.82928205336296 0.58535897331852 39 0.383565584440818 0.767131168881636 0.616434415559182 40 0.7231283357608 0.553743328478401 0.276871664239200 41 0.604340336619154 0.791319326761692 0.395659663380846 42 0.682957337223057 0.634085325553886 0.317042662776943 43 0.618115973439998 0.763768053120004 0.381884026560002 44 0.448751524003623 0.897503048007246 0.551248475996377 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 1 0.0344827586206897 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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