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: Wed, 26 Nov 2008 10:31:29 -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/26/t12277207473ue967v2vp2r1ew.htm/, Retrieved Wed, 26 Nov 2008 17:32:36 +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/26/t12277207473ue967v2vp2r1ew.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:

IsPrivate?

No (this computation is public)

User-defined keywords:

multiple lineair regression

Dataseries X:

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159129 0 157928 0 147768 0 137507 1 136919 1 136151 1 133001 0 125554 0 119647 0 114158 0 116193 0 152803 0 161761 0 160942 0 149470 0 139208 1 134588 1 130322 1 126611 0 122401 0 117352 0 112135 0 112879 0 148729 0 157230 0 157221 0 146681 0 136524 1 132111 1 125326 1 122716 0 116615 0 113719 0 110737 0 112093 0 143565 0 149946 0 149147 0 134339 0 122683 1 115614 1 116566 1 111272 0 104609 0 101802 0 94542 0 93051 0 124129 0 130374 0 123946 0 114971 0 105531 1 104919 1 104782 1 101281 0 94545 0 93248 0 84031 0 87486 0 115867 0 120327 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 6 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation jonger_dan_25[t] = + 124955.456521739 + 294.610144927525winter[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) 124955.456521739 2971.58222 42.0501 0 0 winter 294.610144927525 5992.486152 0.0492 0.960955 0.480478 Multiple Linear Regression - Regression Statistics Multiple R 0.00640037996695919 R-squared 4.09648637214525e-05 Adjusted R-squared -0.0169074933589273 F-TEST (value) 0.00241702597270528 F-TEST (DF numerator) 1 F-TEST (DF denominator) 59 p-value 0.960955245791588 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 20154.2511873085 Sum Squared Residuals 23965436614.3464 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 159129 124955.456521739 34173.5434782613 2 157928 124955.456521739 32972.5434782609 3 147768 124955.456521739 22812.5434782609 4 137507 125250.066666667 12256.9333333333 5 136919 125250.066666667 11668.9333333333 6 136151 125250.066666667 10900.9333333333 7 133001 124955.456521739 8045.54347826086 8 125554 124955.456521739 598.54347826086 9 119647 124955.456521739 -5308.45652173914 10 114158 124955.456521739 -10797.4565217391 11 116193 124955.456521739 -8762.45652173914 12 152803 124955.456521739 27847.5434782609 13 161761 124955.456521739 36805.5434782609 14 160942 124955.456521739 35986.5434782609 15 149470 124955.456521739 24514.5434782609 16 139208 125250.066666667 13957.9333333333 17 134588 125250.066666667 9337.93333333333 18 130322 125250.066666667 5071.93333333334 19 126611 124955.456521739 1655.54347826086 20 122401 124955.456521739 -2554.45652173914 21 117352 124955.456521739 -7603.45652173914 22 112135 124955.456521739 -12820.4565217391 23 112879 124955.456521739 -12076.4565217391 24 148729 124955.456521739 23773.5434782609 25 157230 124955.456521739 32274.5434782609 26 157221 124955.456521739 32265.5434782609 27 146681 124955.456521739 21725.5434782609 28 136524 125250.066666667 11273.9333333333 29 132111 125250.066666667 6860.93333333334 30 125326 125250.066666667 75.9333333333352 31 122716 124955.456521739 -2239.45652173914 32 116615 124955.456521739 -8340.45652173914 33 113719 124955.456521739 -11236.4565217391 34 110737 124955.456521739 -14218.4565217391 35 112093 124955.456521739 -12862.4565217391 36 143565 124955.456521739 18609.5434782609 37 149946 124955.456521739 24990.5434782609 38 149147 124955.456521739 24191.5434782609 39 134339 124955.456521739 9383.54347826086 40 122683 125250.066666667 -2567.06666666666 41 115614 125250.066666667 -9636.06666666667 42 116566 125250.066666667 -8684.06666666667 43 111272 124955.456521739 -13683.4565217391 44 104609 124955.456521739 -20346.4565217391 45 101802 124955.456521739 -23153.4565217391 46 94542 124955.456521739 -30413.4565217391 47 93051 124955.456521739 -31904.4565217391 48 124129 124955.456521739 -826.45652173914 49 130374 124955.456521739 5418.54347826086 50 123946 124955.456521739 -1009.45652173914 51 114971 124955.456521739 -9984.45652173914 52 105531 125250.066666667 -19719.0666666667 53 104919 125250.066666667 -20331.0666666667 54 104782 125250.066666667 -20468.0666666667 55 101281 124955.456521739 -23674.4565217391 56 94545 124955.456521739 -30410.4565217391 57 93248 124955.456521739 -31707.4565217391 58 84031 124955.456521739 -40924.4565217391 59 87486 124955.456521739 -37469.4565217391 60 115867 124955.456521739 -9088.45652173914 61 120327 124955.456521739 -4628.45652173914 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.0232987668625943 0.0465975337251886 0.976701233137406 6 0.00501366051289739 0.0100273210257948 0.994986339487103 7 0.0496335768654423 0.0992671537308846 0.950366423134558 8 0.107889640137469 0.215779280274937 0.892110359862532 9 0.168133027540014 0.336266055080028 0.831866972459986 10 0.233075430209996 0.466150860419991 0.766924569790004 11 0.232308759928239 0.464617519856478 0.767691240071761 12 0.240095298622594 0.480190597245189 0.759904701377406 13 0.335521919164751 0.671043838329502 0.664478080835249 14 0.41553475966587 0.83106951933174 0.58446524033413 15 0.386504737024095 0.77300947404819 0.613495262975905 16 0.318802228116385 0.63760445623277 0.681197771883615 17 0.254182837030278 0.508365674060556 0.745817162969722 18 0.19998605437512 0.39997210875024 0.80001394562488 19 0.175547395735426 0.351094791470851 0.824452604264574 20 0.163667747823082 0.327335495646164 0.836332252176918 21 0.167961676457428 0.335923352914856 0.832038323542572 22 0.191247316054161 0.382494632108322 0.808752683945839 23 0.197490228564901 0.394980457129801 0.8025097714351 24 0.208026173985283 0.416052347970567 0.791973826014717 25 0.302966313804946 0.605932627609891 0.697033686195054 26 0.437129397382381 0.874258794764762 0.562870602617619 27 0.482681161301226 0.965362322602452 0.517318838698774 28 0.450417346296477 0.900834692592954 0.549582653703523 29 0.41302033023196 0.82604066046392 0.58697966976804 30 0.372039389463604 0.744078778927207 0.627960610536396 31 0.341341955653345 0.68268391130669 0.658658044346655 32 0.325850570309529 0.651701140619058 0.674149429690471 33 0.316433156843089 0.632866313686179 0.68356684315691 34 0.314330630224069 0.628661260448137 0.685669369775932 35 0.296772549591692 0.593545099183383 0.703227450408308 36 0.351642364282915 0.70328472856583 0.648357635717085 37 0.537389123739539 0.925221752520921 0.462610876260461 38 0.782147269077803 0.435705461844395 0.217852730922197 39 0.856536012879858 0.286927974240284 0.143463987120142 40 0.839206985187983 0.321586029624034 0.160793014812017 41 0.810763504209441 0.378472991581118 0.189236495790559 42 0.784222125328229 0.431555749343543 0.215777874671771 43 0.760702900958444 0.478594198083111 0.239297099041556 44 0.743888016495028 0.512223967009944 0.256111983504972 45 0.729654214521672 0.540691570956655 0.270345785478328 46 0.75694356632125 0.4861128673575 0.24305643367875 47 0.787732217997141 0.424535564005717 0.212267782002859 48 0.777159795120569 0.445680409758863 0.222840204879431 49 0.85144775429702 0.297104491405959 0.148552245702979 50 0.893212033004865 0.213575933990270 0.106787966995135 51 0.889517973260318 0.220964053479363 0.110482026739682 52 0.831413188772604 0.337173622454791 0.168586811227396 53 0.748398976748735 0.50320204650253 0.251601023251265 54 0.636576637491457 0.726846725017086 0.363423362508543 55 0.509961288792002 0.980077422415995 0.490038711207998 56 0.381972419907955 0.763944839815909 0.618027580092045 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 2 0.0384615384615385 OK 10% type I error level 3 0.0576923076923077 OK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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