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 09:20:36 -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/t1229962912eh42f11cwbdwsxs.htm/, Retrieved Mon, 22 Dec 2008 17:22:01 +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/t1229962912eh42f11cwbdwsxs.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 1 0 137507 0 2 0 136919 0 3 0 136151 0 4 0 133001 0 5 0 125554 0 6 0 119647 0 7 0 114158 0 8 0 116193 0 9 0 152803 0 10 0 161761 0 11 0 160942 0 12 0 149470 0 13 0 139208 0 14 0 134588 0 15 0 130322 0 16 0 126611 0 17 0 122401 0 18 0 117352 0 19 0 112135 0 20 0 112879 0 21 0 148729 0 22 0 157230 0 23 0 157221 0 24 0 146681 0 25 0 136524 0 26 0 132111 0 27 0 125326 1 0 28 122716 1 0 29 116615 1 0 30 113719 1 0 31 110737 1 0 32 112093 1 0 33 143565 1 0 34 149946 1 0 35 149147 1 0 36 134339 1 0 37 122683 1 0 38 115614 1 0 39 116566 1 0 40 111272 1 0 41 104609 1 0 42 101802 1 0 43 94542 1 0 44 93051 1 0 45 124129 1 0 46 130374 1 0 47 123946 1 0 48 114971 1 0 49 105531 1 0 50 104919 1 0 51 104782 0 52 0 101281 0 53 0 94545 0 54 0 93248 0 55 0 84031 0 56 0 87486 0 57 0 115867 0 58 0 120327 0 59 0 117008 0 60 0 108811 0 61 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] = + 166884.834688186 + 27255.1891332781d[t] -702.060280641744t1[t] -1348.48529483192t2[t] -11267.2704959925M1[t] -19865.6627950653M2[t] -22365.4325087475M3[t] -26708.4422905425M4[t] -29401.0120042247M5[t] -34671.7817179069M6[t] -37302.3514315891M7[t] -42374.7211452712M8[t] -40194.2908589534M9[t] -6555.46057263563M10[t] + 1314.16971368219M11[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) 166884.834688186 2205.563236 75.6654 0 0 d 27255.1891332781 5407.211139 5.0405 8e-06 4e-06 t1 -702.060280641744 35.418691 -19.8217 0 0 t2 -1348.48529483192 131.304157 -10.2699 0 0 M1 -11267.2704959925 2565.321932 -4.3921 6.5e-05 3.3e-05 M2 -19865.6627950653 2703.223909 -7.3489 0 0 M3 -22365.4325087475 2703.016071 -8.2743 0 0 M4 -26708.4422905425 2711.010209 -9.8518 0 0 M5 -29401.0120042247 2702.279503 -10.8801 0 0 M6 -34671.7817179069 2694.69001 -12.8667 0 0 M7 -37302.3514315891 2688.251396 -13.8761 0 0 M8 -42374.7211452712 2682.971946 -15.7939 0 0 M9 -40194.2908589534 2678.858514 -15.0043 0 0 M10 -6555.46057263563 2675.916477 -2.4498 0.018159 0.00908 M11 1314.16971368219 2674.149701 0.4914 0.625456 0.312728 Multiple Linear Regression - Regression Statistics Multiple R 0.981063562928421 R-squared 0.962485714505809 Adjusted R-squared 0.951068323268446 F-TEST (value) 84.2999678732339 F-TEST (DF numerator) 14 F-TEST (DF denominator) 46 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4227.27034708779 Sum Squared Residuals 822011471.018915 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 147768 154915.503911552 -7147.50391155166 2 137507 145615.051331838 -8108.05133183763 3 136919 142413.221337514 -5494.2213375137 4 136151 137368.151275077 -1217.15127507692 5 133001 133973.521280753 -972.521280752997 6 125554 128000.691286429 -2446.69128642905 7 119647 124668.061292105 -5021.06129210516 8 114158 118893.631297781 -4735.63129778118 9 116193 120372.001303457 -4179.00130345726 10 152803 153308.771309133 -505.771309133354 11 161761 160476.341314809 1284.6586851906 12 160942 158460.111320485 2481.88867951452 13 149470 146490.780543851 2979.21945614880 14 139208 137190.327964137 2017.67203586331 15 134588 133988.497969813 599.502030187242 16 130322 128943.427907376 1378.57209262399 17 126611 125548.797913052 1062.20208694792 18 122401 119575.967918728 2825.03208127186 19 117352 116243.337924404 1108.66207559580 20 112135 110468.907930080 1666.09206991971 21 112879 111947.277935756 931.72206424365 22 148729 144884.047941432 3844.95205856758 23 157230 152051.617947108 5178.38205289151 24 157221 150035.387952785 7185.61204721544 25 146681 138066.057176150 8614.9428238497 26 136524 128765.604596436 7758.39540356423 27 132111 125563.774602112 6547.22539788817 28 125326 129673.993275628 -4347.99327562840 29 122716 125632.938267114 -2916.93826711431 30 116615 119013.683258600 -2398.68325860021 31 113719 115034.628250086 -1315.62825008609 32 110737 108613.773241572 2123.22675842801 33 112093 109445.718233058 2647.28176694211 34 143565 141736.063224544 1828.93677545621 35 149946 148257.208216030 1688.79178397031 36 149147 145594.553207516 3552.44679248442 37 134339 132978.797416691 1360.20258330885 38 122683 123031.919822786 -348.919822786452 39 115614 119183.664814272 -3569.66481427235 40 116566 113492.169737645 3073.83026235457 41 111272 109451.114729131 1820.88527086868 42 104609 102831.859720617 1777.14027938278 43 101802 98852.8047121031 2949.19528789689 44 94542 92431.949703589 2110.05029641099 45 93051 93263.8946950749 -212.894695074905 46 124129 125554.239686561 -1425.23968656080 47 130374 132075.384678047 -1701.38467804670 48 123946 129412.729669533 -5466.72966953259 49 114971 116796.973878708 -1825.97387870816 50 105531 106850.096284803 -1319.09628480345 51 104919 103001.841276289 1917.15872371064 52 104782 103669.257804273 1112.74219572676 53 101281 100274.627809949 1006.37219005070 54 94545 94301.7978156254 243.202184374625 55 93248 90969.1678213014 2278.83217869856 56 84031 85194.7378269775 -1163.73782697752 57 87486 86673.1078326536 812.892167346413 58 115867 119609.877838330 -3742.87783832964 59 120327 126777.447844006 -6450.44784400572 60 117008 124761.217849682 -7753.21784968179 61 108811 112791.887073048 -3980.88707304753 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 18 0.551925360368338 0.896149279263324 0.448074639631662 19 0.425592774323083 0.851185548646165 0.574407225676917 20 0.334810066209041 0.669620132418083 0.665189933790959 21 0.337497560954425 0.674995121908849 0.662502439045575 22 0.285231307935773 0.570462615871546 0.714768692064227 23 0.227280013524598 0.454560027049196 0.772719986475402 24 0.149387634621635 0.298775269243271 0.850612365378365 25 0.113440110998598 0.226880221997196 0.886559889001402 26 0.0797902348364934 0.159580469672987 0.920209765163507 27 0.0653080945219418 0.130616189043884 0.934691905478058 28 0.0619637844248442 0.123927568849688 0.938036215575156 29 0.0540740053851485 0.108148010770297 0.945925994614851 30 0.0529003896917503 0.105800779383501 0.94709961030825 31 0.105641761549089 0.211283523098177 0.894358238450911 32 0.07919162919361 0.15838325838722 0.92080837080639 33 0.0511975614069331 0.102395122813866 0.948802438593067 34 0.0899720269821393 0.179944053964279 0.91002797301786 35 0.140519839888328 0.281039679776656 0.859480160111672 36 0.625910369334876 0.748179261330248 0.374089630665124 37 0.82455723763905 0.350885524721900 0.175442762360950 38 0.96447670928228 0.0710465814354384 0.0355232907177192 39 0.952550797556923 0.094898404886155 0.0474492024430775 40 0.918397875259629 0.163204249480742 0.0816021247403712 41 0.842037461277613 0.315925077444774 0.157962538722387 42 0.724691821794234 0.550616356411533 0.275308178205766 43 0.571790710233988 0.856418579532024 0.428209289766012 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 2 0.0769230769230769 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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