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: Mon, 22 Dec 2008 09:07:08 -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/22/t1229962069wytn5tji6wyu391.htm/, Retrieved Mon, 22 Dec 2008 17:07:49 +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/22/t1229962069wytn5tji6wyu391.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:

» Textbox « » Textfile « » CSV «

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 0 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 1 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 5 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation jonger_dan_25[t] = + 167690.964705882 + 2367.82608695652plan[t] -11569.5692526286M1[t] -20858.1153168514M2[t] -23568.9237851662M3[t] -25020.1322534811M4[t] -27923.7407217960M5[t] -33405.5491901108M6[t] -36247.1576584257M7[t] -41530.5661267406M8[t] -39561.1745950554M9[t] -6133.38306337028M10[t] + 1525.20846831486M11[t] -749.591531685138t + 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) 167690.964705882 2650.696505 63.263 0 0 plan 2367.82608695652 1454.930568 1.6274 0.110328 0.055164 M1 -11569.5692526286 3091.377983 -3.7425 0.000496 0.000248 M2 -20858.1153168514 3248.70855 -6.4204 0 0 M3 -23568.9237851662 3243.804918 -7.2658 0 0 M4 -25020.1322534811 3239.411166 -7.7237 0 0 M5 -27923.7407217960 3235.529372 -8.6303 0 0 M6 -33405.5491901108 3232.161379 -10.3354 0 0 M7 -36247.1576584257 3229.308795 -11.2244 0 0 M8 -41530.5661267406 3226.972987 -12.8698 0 0 M9 -39561.1745950554 3225.155078 -12.2664 0 0 M10 -6133.38306337028 3223.855944 -1.9025 0.063243 0.031621 M11 1525.20846831486 3223.076212 0.4732 0.63825 0.319125 t -749.591531685138 40.934411 -18.312 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.971752807351331 R-squared 0.944303518595193 Adjusted R-squared 0.928898108844928 F-TEST (value) 61.2968777788535 F-TEST (DF numerator) 13 F-TEST (DF denominator) 47 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5095.71992960273 Sum Squared Residuals 1220418995.24467 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 147768 155371.803921569 -7603.80392156853 2 137507 145333.666325661 -7826.6663256607 3 136919 141873.266325661 -4954.2663256607 4 136151 139672.466325661 -3521.46632566071 5 133001 136019.266325661 -3018.26632566070 6 125554 129787.866325661 -4233.86632566071 7 119647 126196.666325661 -6549.6663256607 8 114158 120163.666325661 -6005.66632566072 9 116193 121383.466325661 -5190.46632566072 10 152803 154061.666325661 -1258.66632566071 11 161761 160970.666325661 790.3336743393 12 160942 158695.866325661 2246.1336743393 13 149470 146376.705541347 3093.29445865301 14 139208 136338.567945439 2869.43205456096 15 134588 132878.167945439 1709.83205456095 16 130322 130677.367945439 -355.367945439043 17 126611 127024.167945439 -413.167945439047 18 122401 120792.767945439 1608.23205456095 19 117352 117201.567945439 150.432054560950 20 112135 111168.567945439 966.432054560955 21 112879 112388.367945439 490.632054560954 22 148729 145066.567945439 3662.43205456095 23 157230 151975.567945439 5254.43205456095 24 157221 149700.767945439 7520.23205456095 25 146681 137381.607161125 9299.39283887466 26 136524 127343.469565217 9180.5304347826 27 132111 123883.069565217 8227.93043478261 28 125326 124050.095652174 1275.90434782609 29 122716 120396.895652174 2319.10434782609 30 116615 114165.495652174 2449.50434782609 31 113719 110574.295652174 3144.70434782609 32 110737 104541.295652174 6195.70434782609 33 112093 105761.095652174 6331.9043478261 34 143565 138439.295652174 5125.70434782609 35 149946 145348.295652174 4597.70434782608 36 149147 143073.495652174 6073.50434782609 37 134339 130754.334867860 3584.66513213979 38 122683 120716.197271952 1966.80272804774 39 115614 117255.797271952 -1641.79727195226 40 116566 115054.997271952 1511.00272804775 41 111272 111401.797271952 -129.797271952260 42 104609 105170.397271952 -561.397271952254 43 101802 101579.197271952 222.802728047744 44 94542 95546.1972719523 -1004.19727195225 45 93051 96765.9972719522 -3714.99727195225 46 124129 129444.197271952 -5315.19727195226 47 130374 136353.197271952 -5979.19727195226 48 123946 134078.397271952 -10132.3972719523 49 114971 121759.236487639 -6788.23648763855 50 105531 111721.098891731 -6190.09889173061 51 104919 108260.698891731 -3341.6988917306 52 104782 103692.072804774 1089.92719522591 53 101281 100038.872804774 1242.12719522592 54 94545 93807.472804774 737.527195225917 55 93248 90216.272804774 3031.72719522592 56 84031 84183.272804774 -152.272804774075 57 87486 85403.072804774 2082.92719522592 58 115867 118081.272804774 -2214.27280477407 59 120327 124990.272804774 -4663.27280477407 60 117008 122715.472804774 -5707.47280477408 61 108811 110396.312020460 -1585.31202046038 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.389088067430114 0.778176134860228 0.610911932569886 18 0.247173860583097 0.494347721166195 0.752826139416903 19 0.175730177711434 0.351460355422869 0.824269822288566 20 0.135262978257245 0.270525956514490 0.864737021742755 21 0.152836104192132 0.305672208384265 0.847163895807868 22 0.139088554996016 0.278177109992032 0.860911445003984 23 0.119048055886207 0.238096111772414 0.880951944113793 24 0.0763757008697813 0.152751401739563 0.923624299130219 25 0.0621907621989514 0.124381524397903 0.937809237801049 26 0.0474033047545847 0.0948066095091693 0.952596695245415 27 0.0462168224554195 0.092433644910839 0.95378317754458 28 0.0497561515216036 0.0995123030432071 0.950243848478396 29 0.046951252264413 0.093902504528826 0.953048747735587 30 0.0460911338209782 0.0921822676419563 0.953908866179022 31 0.110678655847818 0.221357311695637 0.889321344152182 32 0.152060418781207 0.304120837562414 0.847939581218793 33 0.153197147195204 0.306394294390409 0.846802852804796 34 0.113551485004692 0.227102970009383 0.886448514995308 35 0.128411996156129 0.256823992312257 0.871588003843871 36 0.5601607115935 0.879678576812999 0.439839288406499 37 0.757429934949183 0.485140130101634 0.242570065050817 38 0.934481469058337 0.131037061883326 0.0655185309416628 39 0.959686343525713 0.0806273129485749 0.0403136564742874 40 0.971842684506204 0.0563146309875922 0.0281573154937961 41 0.96498944555339 0.0700211088932202 0.0350105544466101 42 0.955807264507587 0.0883854709848265 0.0441927354924132 43 0.905981565630574 0.188036868738851 0.0940184343694256 44 0.901862535464264 0.196274929071473 0.0981374645357363 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 9 0.321428571428571 NOK

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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