Multiple Lineair Regression

*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: Tue, 16 Dec 2008 09:18:01 -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/Dec/16/t1229444397sibckfw119372up.htm/, Retrieved Tue, 16 Dec 2008 17:20:07 +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/2008/Dec/16/t1229444397sibckfw119372up.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}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Multiple Lineair Regression

Dataseries X:

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147768 0 137507 0 136919 0 136151 0 133001 0 125554 0 119647 0 114158 0 116193 0 152803 0 161761 0 160942 0 149470 0 139208 0 134588 0 130322 0 126611 0 122401 0 117352 0 112135 0 112879 0 148729 0 157230 0 157221 0 146681 0 136524 0 132111 1 125326 1 122716 1 116615 1 113719 1 110737 1 112093 1 143565 1 149946 1 149147 1 134339 1 122683 1 115614 1 116566 1 111272 1 104609 1 101802 1 94542 1 93051 1 124129 1 130374 1 123946 1 114971 1 105531 1 104919 0 104782 0 101281 0 94545 0 93248 0 84031 0 87486 0 115867 0 120327 0 117008 0 108811 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 jonger_dan_25[t] = + 144165.981651376 -6282.95412844038plan[t] -8398.33027522928M1[t] -13362.2M2[t] -16822.6M3[t] -19023.4M4[t] -22676.6000000000M5[t] -28908M6[t] -32499.2M7[t] -38532.2M8[t] -37312.4M9[t] -4634.19999999999M10[t] + 2274.80000000000M11[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) 144165.981651376 6735.593741 21.4036 0 0 plan -6282.95412844038 3846.295072 -1.6335 0.108905 0.054453 M1 -8398.33027522928 8882.63798 -0.9455 0.349151 0.174575 M2 -13362.2 9273.746312 -1.4409 0.156115 0.078058 M3 -16822.6 9273.746312 -1.814 0.075931 0.037965 M4 -19023.4 9273.746312 -2.0513 0.045715 0.022857 M5 -22676.6000000000 9273.746312 -2.4452 0.018195 0.009097 M6 -28908 9273.746312 -3.1172 0.003082 0.001541 M7 -32499.2 9273.746312 -3.5044 0.001002 0.000501 M8 -38532.2 9273.746312 -4.155 0.000133 6.7e-05 M9 -37312.4 9273.746312 -4.0234 0.000202 0.000101 M10 -4634.19999999999 9273.746312 -0.4997 0.619561 0.309781 M11 2274.80000000000 9273.746312 0.2453 0.807274 0.403637 Multiple Linear Regression - Regression Statistics Multiple R 0.727331643237498 R-squared 0.529011319254558 Adjusted R-squared 0.411264149068198 F-TEST (value) 4.49277310373815 F-TEST (DF numerator) 12 F-TEST (DF denominator) 48 p-value 8.41828926807509e-05 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 14663.0803935306 Sum Squared Residuals 10320284478.1028 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 147768 135767.651376146 12000.3486238536 2 137507 130803.781651376 6703.21834862386 3 136919 127343.381651376 9575.61834862384 4 136151 125142.581651376 11008.4183486239 5 133001 121489.381651376 11511.6183486238 6 125554 115257.981651376 10296.0183486238 7 119647 111666.781651376 7980.2183486239 8 114158 105633.781651376 8524.21834862384 9 116193 106853.581651376 9339.41834862386 10 152803 139531.781651376 13271.2183486239 11 161761 146440.781651376 15320.2183486239 12 160942 144165.981651376 16776.0183486238 13 149470 135767.651376147 13702.3486238531 14 139208 130803.781651376 8404.21834862384 15 134588 127343.381651376 7244.61834862385 16 130322 125142.581651376 5179.41834862385 17 126611 121489.381651376 5121.61834862385 18 122401 115257.981651376 7143.01834862386 19 117352 111666.781651376 5685.21834862383 20 112135 105633.781651376 6501.21834862385 21 112879 106853.581651376 6025.41834862385 22 148729 139531.781651376 9197.21834862384 23 157230 146440.781651376 10789.2183486238 24 157221 144165.981651376 13055.0183486238 25 146681 135767.651376147 10913.3486238531 26 136524 130803.781651376 5720.21834862384 27 132111 121060.427522936 11050.5724770642 28 125326 118859.627522936 6466.37247706422 29 122716 115206.427522936 7509.57247706423 30 116615 108975.027522936 7639.97247706424 31 113719 105383.827522936 8335.17247706421 32 110737 99350.8275229358 11386.1724770642 33 112093 100570.627522936 11522.3724770642 34 143565 133248.827522936 10316.1724770642 35 149946 140157.827522936 9788.17247706423 36 149147 137883.027522936 11263.9724770642 37 134339 129484.697247706 4854.3027522935 38 122683 124520.827522936 -1837.82752293578 39 115614 121060.427522936 -5446.42752293577 40 116566 118859.627522936 -2293.62752293577 41 111272 115206.427522936 -3934.42752293577 42 104609 108975.027522936 -4366.02752293576 43 101802 105383.827522936 -3581.82752293578 44 94542 99350.8275229358 -4808.82752293577 45 93051 100570.627522936 -7519.62752293578 46 124129 133248.827522936 -9119.82752293578 47 130374 140157.827522936 -9783.82752293578 48 123946 137883.027522936 -13937.0275229358 49 114971 129484.697247706 -14513.6972477065 50 105531 124520.827522936 -18989.8275229358 51 104919 127343.381651376 -22424.3816513762 52 104782 125142.581651376 -20360.5816513761 53 101281 121489.381651376 -20208.3816513761 54 94545 115257.981651376 -20712.9816513761 55 93248 111666.781651376 -18418.7816513762 56 84031 105633.781651376 -21602.7816513762 57 87486 106853.581651376 -19367.5816513762 58 115867 139531.781651376 -23664.7816513762 59 120327 146440.781651376 -26113.7816513762 60 117008 144165.981651376 -27157.9816513761 61 108811 135767.651376147 -26956.6513761469 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.00882080797643045 0.0176416159528609 0.99117919202357 17 0.00482147106527009 0.00964294213054019 0.99517852893473 18 0.00127615961065138 0.00255231922130276 0.998723840389349 19 0.000295385128063292 0.000590770256126584 0.999704614871937 20 6.73515154025049e-05 0.000134703030805010 0.999932648484598 21 1.96526813697159e-05 3.93053627394317e-05 0.99998034731863 22 8.5769595937616e-06 1.71539191875232e-05 0.999991423040406 23 5.58460518281842e-06 1.11692103656368e-05 0.999994415394817 24 4.9765486545346e-06 9.9530973090692e-06 0.999995023451345 25 6.49648443493955e-06 1.29929688698791e-05 0.999993503515565 26 2.22007871263886e-05 4.44015742527772e-05 0.999977799212874 27 9.17698465049532e-06 1.83539693009906e-05 0.99999082301535 28 4.16061106652268e-06 8.32122213304537e-06 0.999995839388933 29 1.39350312557830e-06 2.78700625115660e-06 0.999998606496874 30 4.79244791480477e-07 9.58489582960954e-07 0.999999520755209 31 1.70147361902759e-07 3.40294723805518e-07 0.999999829852638 32 1.69571379731459e-07 3.39142759462919e-07 0.99999983042862 33 1.77895780806861e-07 3.55791561613722e-07 0.99999982210422 34 2.75979605388008e-07 5.51959210776016e-07 0.999999724020395 35 1.81743050074962e-06 3.63486100149924e-06 0.9999981825695 36 0.000273947628767452 0.000547895257534905 0.999726052371233 37 0.0577724033951669 0.115544806790334 0.942227596604833 38 0.98901784967621 0.0219643006475815 0.0109821503237908 39 0.996916656820567 0.00616668635886674 0.00308334317943337 40 0.998175449143404 0.00364910171319249 0.00182455085659625 41 0.997566107015021 0.00486778596995766 0.00243389298497883 42 0.99662692476336 0.00674615047327857 0.00337307523663929 43 0.990674382151434 0.0186512356971328 0.0093256178485664 44 0.990079898852772 0.0198402022944551 0.00992010114722757 45 0.982055474546954 0.0358890509060926 0.0179445254530463 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 24 0.8 NOK 5% type I error level 29 0.966666666666667 NOK 10% type I error level 29 0.966666666666667 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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