q3b

*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 08:51:08 -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/Nov/23/t1227455514bt1r1nw5d88bojb.htm/, Retrieved Sun, 23 Nov 2008 15:52:03 +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/t1227455514bt1r1nw5d88bojb.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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User-defined keywords:

Dataseries X:

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1515 0 1510 0 1225 0 1577 0 1417 0 1224 0 1693 0 1633 0 1639 0 1914 0 1586 0 1552 0 2081 0 1500 0 1437 0 1470 0 1849 0 1387 0 1592 0 1589 0 1798 0 1935 0 1887 0 2027 0 2080 0 1556 0 1682 0 1785 0 1869 0 1781 0 2082 0 2570 1 1862 1 1936 1 1504 1 1765 1 1607 1 1577 1 1493 1 1615 1 1700 1 1335 1 1523 1 1623 1 1540 1 1637 1 1524 1 1419 1 1821 1 1593 1 1357 1 1263 1 1750 1 1405 1 1393 1 1639 1 1679 1 1551 1 1744 1 1429 1 1784 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 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Gebouwen[t] = + 1623.98461538462 -198.804487179487Dummy[t] + 174.955395299147M1[t] -93.8225427350426M2[t] -205.936378205128M3[t] -106.450213675214M4[t] + 64.8359508547011M5[t] -229.477884615384M6[t] -2.99172008546989M7[t] + 187.255341880342M8[t] + 76.3415064102565M9[t] + 163.627670940171M10[t] + 14.3138354700856M11[t] + 3.71383547008545t + 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) 1623.98461538462 118.465123 13.7085 0 0 Dummy -198.804487179487 114.36748 -1.7383 0.088707 0.044353 M1 174.955395299147 132.951342 1.3159 0.194578 0.097289 M2 -93.8225427350426 139.615548 -0.672 0.50487 0.252435 M3 -205.936378205128 139.36197 -1.4777 0.146156 0.073078 M4 -106.450213675214 139.183192 -0.7648 0.448202 0.224101 M5 64.8359508547011 139.079503 0.4662 0.643241 0.32162 M6 -229.477884615384 139.051071 -1.6503 0.105547 0.052773 M7 -2.99172008546989 139.097942 -0.0215 0.982931 0.491466 M8 187.255341880342 139.183192 1.3454 0.184955 0.092478 M9 76.3415064102565 138.919593 0.5495 0.585239 0.292619 M10 163.627670940171 138.731002 1.1795 0.244151 0.122076 M11 14.3138354700856 138.617724 0.1033 0.918195 0.459098 t 3.71383547008545 3.236122 1.1476 0.256934 0.128467 Multiple Linear Regression - Regression Statistics Multiple R 0.587246615212185 R-squared 0.344858587078168 Adjusted R-squared 0.163649260099789 F-TEST (value) 1.90309512666153 F-TEST (DF numerator) 13 F-TEST (DF denominator) 47 p-value 0.0543609535741828 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 219.114131458971 Sum Squared Residuals 2256517.12243589 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1515 1802.65384615384 -287.65384615384 2 1510 1537.58974358974 -27.5897435897437 3 1225 1429.18974358974 -204.189743589744 4 1577 1532.38974358974 44.6102564102563 5 1417 1707.38974358974 -290.389743589744 6 1224 1416.78974358974 -192.789743589744 7 1693 1646.98974358974 46.0102564102561 8 1633 1840.95064102564 -207.950641025642 9 1639 1733.75064102564 -94.7506410256413 10 1914 1824.75064102564 89.2493589743588 11 1586 1679.15064102564 -93.1506410256412 12 1552 1668.55064102564 -116.550641025641 13 2081 1847.21987179487 233.780128205127 14 1500 1582.15576923077 -82.1557692307694 15 1437 1473.75576923077 -36.7557692307694 16 1470 1576.95576923077 -106.955769230769 17 1849 1751.95576923077 97.0442307692306 18 1387 1461.35576923077 -74.3557692307694 19 1592 1691.55576923077 -99.5557692307693 20 1589 1885.51666666667 -296.516666666667 21 1798 1778.31666666667 19.6833333333333 22 1935 1869.31666666667 65.6833333333333 23 1887 1723.71666666667 163.283333333333 24 2027 1713.11666666667 313.883333333333 25 2080 1891.7858974359 188.214102564101 26 1556 1626.72179487179 -70.7217948717949 27 1682 1518.32179487179 163.678205128205 28 1785 1621.52179487179 163.478205128205 29 1869 1796.52179487179 72.4782051282052 30 1781 1505.92179487179 275.078205128205 31 2082 1736.12179487179 345.878205128205 32 2570 1731.27820512821 838.721794871795 33 1862 1624.07820512821 237.921794871795 34 1936 1715.07820512821 220.921794871795 35 1504 1569.47820512821 -65.4782051282053 36 1765 1558.87820512821 206.121794871795 37 1607 1737.54743589744 -130.547435897437 38 1577 1472.48333333333 104.516666666667 39 1493 1364.08333333333 128.916666666667 40 1615 1467.28333333333 147.716666666667 41 1700 1642.28333333333 57.7166666666666 42 1335 1351.68333333333 -16.6833333333334 43 1523 1581.88333333333 -58.8833333333333 44 1623 1775.84423076923 -152.844230769231 45 1540 1668.64423076923 -128.644230769231 46 1637 1759.64423076923 -122.644230769231 47 1524 1614.04423076923 -90.0442307692307 48 1419 1603.44423076923 -184.444230769231 49 1821 1782.11346153846 38.8865384615373 50 1593 1517.04935897436 75.9506410256412 51 1357 1408.64935897436 -51.6493589743588 52 1263 1511.84935897436 -248.849358974359 53 1750 1686.84935897436 63.1506410256412 54 1405 1396.24935897436 8.75064102564123 55 1393 1626.44935897436 -233.449358974359 56 1639 1820.41025641026 -181.410256410256 57 1679 1713.21025641026 -34.2102564102561 58 1551 1804.21025641026 -253.210256410256 59 1744 1658.61025641026 85.389743589744 60 1429 1648.01025641026 -219.010256410256 61 1784 1826.67948717949 -42.6794871794881 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.641515422076526 0.716969155846948 0.358484577923474 18 0.501835273570395 0.99632945285921 0.498164726429605 19 0.491314605039223 0.982629210078445 0.508685394960777 20 0.561280078282179 0.87743984343564 0.43871992171782 21 0.456658302759554 0.913316605519108 0.543341697240446 22 0.361167128299487 0.722334256598974 0.638832871700513 23 0.289074375123823 0.578148750247646 0.710925624876177 24 0.308133310808388 0.616266621616776 0.691866689191612 25 0.217980032456807 0.435960064913613 0.782019967543193 26 0.230618053728380 0.461236107456760 0.76938194627162 27 0.174632193100977 0.349264386201953 0.825367806899023 28 0.115870680894781 0.231741361789562 0.884129319105219 29 0.095024253815862 0.190048507631724 0.904975746184138 30 0.087889347090556 0.175778694181112 0.912110652909444 31 0.0647036397170956 0.129407279434191 0.935296360282904 32 0.484608966376283 0.969217932752565 0.515391033623717 33 0.77489250157485 0.450214996850299 0.225107498425150 34 0.90174629499766 0.196507410004680 0.0982537050023398 35 0.939043071619004 0.121913856761992 0.0609569283809961 36 0.975652509429295 0.0486949811414101 0.0243474905707051 37 0.987442386920966 0.0251152261580674 0.0125576130790337 38 0.973907285835226 0.0521854283295485 0.0260927141647743 39 0.95627109667311 0.0874578066537818 0.0437289033268909 40 0.992271212808337 0.0154575743833259 0.00772878719166293 41 0.979626816889945 0.0407463662201097 0.0203731831100549 42 0.95394937525568 0.0921012494886408 0.0460506247443204 43 0.944112509545543 0.111774980908914 0.0558874904544569 44 0.877100394707206 0.245799210585587 0.122899605292794 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 4 0.142857142857143 NOK 10% type I error level 7 0.25 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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