*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, 15 Dec 2009 03:24:05 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/15/t1260872712ztlh17ggcm9g7sm.htm/, Retrieved Tue, 15 Dec 2009 11:25:25 +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/2009/Dec/15/t1260872712ztlh17ggcm9g7sm.htm/}, year = {2009}, } @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 = {2009}, 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:

Dataseries X:

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89.1 0 82.6 0 102.7 0 91.8 0 94.1 0 103.1 0 93.2 0 91 0 94.3 0 99.4 0 115.7 0 116.8 0 99.8 0 96 0 115.9 0 109.1 0 117.3 0 109.8 0 112.8 0 110.7 0 100 0 113.3 0 122.4 0 112.5 0 104.2 0 92.5 0 117.2 0 109.3 0 106.1 0 118.8 0 105.3 0 106 0 102 0 112.9 0 116.5 0 114.8 0 100.5 0 85.4 0 114.6 0 109.9 0 100.7 0 115.5 0 100.7 1 99 1 102.3 1 108.8 1 105.9 1 113.2 1 95.7 1 80.9 1 113.9 1 98.1 1 102.8 1 104.7 1 95.9 1 94.6 1 101.6 1 103.9 1 110.3 1 114.1 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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 105.371428571429 -2.79365079365078X[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) 105.371428571429 1.48447 70.9825 0 0 X -2.79365079365078 2.71026 -1.0308 0.306929 0.153464 Multiple Linear Regression - Regression Statistics Multiple R 0.134123649770878 R-squared 0.0179891534278611 Adjusted R-squared 0.00105793193523807 F-TEST (value) 1.06248408809128 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 0.306928587854473 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 9.6204674284218 Sum Squared Residuals 5368.09682539684 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 89.1 105.371428571429 -16.2714285714289 2 82.6 105.371428571429 -22.7714285714286 3 102.7 105.371428571429 -2.67142857142856 4 91.8 105.371428571429 -13.5714285714286 5 94.1 105.371428571429 -11.2714285714286 6 103.1 105.371428571429 -2.27142857142857 7 93.2 105.371428571429 -12.1714285714286 8 91 105.371428571429 -14.3714285714286 9 94.3 105.371428571429 -11.0714285714286 10 99.4 105.371428571429 -5.97142857142856 11 115.7 105.371428571429 10.3285714285714 12 116.8 105.371428571429 11.4285714285714 13 99.8 105.371428571429 -5.57142857142856 14 96 105.371428571429 -9.37142857142856 15 115.9 105.371428571429 10.5285714285714 16 109.1 105.371428571429 3.72857142857143 17 117.3 105.371428571429 11.9285714285714 18 109.8 105.371428571429 4.42857142857144 19 112.8 105.371428571429 7.42857142857144 20 110.7 105.371428571429 5.32857142857144 21 100 105.371428571429 -5.37142857142856 22 113.3 105.371428571429 7.92857142857144 23 122.4 105.371428571429 17.0285714285714 24 112.5 105.371428571429 7.12857142857144 25 104.2 105.371428571429 -1.17142857142856 26 92.5 105.371428571429 -12.8714285714286 27 117.2 105.371428571429 11.8285714285714 28 109.3 105.371428571429 3.92857142857144 29 106.1 105.371428571429 0.728571428571433 30 118.8 105.371428571429 13.4285714285714 31 105.3 105.371428571429 -0.0714285714285638 32 106 105.371428571429 0.628571428571439 33 102 105.371428571429 -3.37142857142856 34 112.9 105.371428571429 7.52857142857144 35 116.5 105.371428571429 11.1285714285714 36 114.8 105.371428571429 9.42857142857144 37 100.5 105.371428571429 -4.87142857142856 38 85.4 105.371428571429 -19.9714285714286 39 114.6 105.371428571429 9.22857142857143 40 109.9 105.371428571429 4.52857142857144 41 100.7 105.371428571429 -4.67142857142856 42 115.5 105.371428571429 10.1285714285714 43 100.7 102.577777777778 -1.87777777777777 44 99 102.577777777778 -3.57777777777778 45 102.3 102.577777777778 -0.277777777777781 46 108.8 102.577777777778 6.22222222222222 47 105.9 102.577777777778 3.32222222222223 48 113.2 102.577777777778 10.6222222222222 49 95.7 102.577777777778 -6.87777777777777 50 80.9 102.577777777778 -21.6777777777778 51 113.9 102.577777777778 11.3222222222222 52 98.1 102.577777777778 -4.47777777777778 53 102.8 102.577777777778 0.222222222222219 54 104.7 102.577777777778 2.12222222222222 55 95.9 102.577777777778 -6.67777777777777 56 94.6 102.577777777778 -7.97777777777778 57 101.6 102.577777777778 -0.977777777777784 58 103.9 102.577777777778 1.32222222222223 59 110.3 102.577777777778 7.72222222222222 60 114.1 102.577777777778 11.5222222222222 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.561901519407667 0.876196961184665 0.438098480592333 6 0.58329479627284 0.833410407454319 0.416705203727159 7 0.462511286580751 0.925022573161502 0.537488713419249 8 0.382483184937962 0.764966369875924 0.617516815062038 9 0.296910158257785 0.593820316515571 0.703089841742214 10 0.257340915368894 0.514681830737788 0.742659084631106 11 0.700262327422885 0.59947534515423 0.299737672577115 12 0.881675528934525 0.236648942130949 0.118324471065475 13 0.84280817105334 0.314383657893321 0.157191828946661 14 0.817235835526786 0.365528328946427 0.182764164473214 15 0.895715932514559 0.208568134970882 0.104284067485441 16 0.882992895688787 0.234014208622425 0.117007104311213 17 0.927775467034802 0.144449065930397 0.0722245329651986 18 0.91240573671284 0.175188526574319 0.0875942632871597 19 0.90792306815967 0.18415386368066 0.09207693184033 20 0.889083243334919 0.221833513330162 0.110916756665081 21 0.862498610159961 0.275002779680077 0.137501389840039 22 0.853847034724158 0.292305930551685 0.146152965275842 23 0.927179054238842 0.145641891522317 0.0728209457611584 24 0.913364432384614 0.173271135230773 0.0866355676153863 25 0.88082699407911 0.238346011841779 0.119173005920890 26 0.914161686826558 0.171676626346884 0.085838313173442 27 0.92382460284808 0.152350794303841 0.0761753971519206 28 0.897076595901155 0.20584680819769 0.102923404098845 29 0.859855672057919 0.280288655884162 0.140144327942081 30 0.88745711595181 0.225085768096379 0.112542884048190 31 0.847213192452242 0.305573615095516 0.152786807547758 32 0.797974616820931 0.404050766358138 0.202025383179069 33 0.753537894513923 0.492924210972154 0.246462105486077 34 0.718415276179155 0.563169447641691 0.281584723820845 35 0.728400153582833 0.543199692834334 0.271599846417167 36 0.725593477356854 0.548813045286292 0.274406522643146 37 0.671251858154618 0.657496283690763 0.328748141845382 38 0.898460350433269 0.203079299133462 0.101539649566731 39 0.878249899176306 0.243500201647387 0.121750100823694 40 0.834541291548775 0.33091741690245 0.165458708451225 41 0.835622424598799 0.328755150802402 0.164377575401201 42 0.79258247162964 0.414835056740721 0.207417528370360 43 0.726186284852414 0.547627430295173 0.273813715147586 44 0.657198396114554 0.685603207770892 0.342801603885446 45 0.570794661859996 0.858410676280008 0.429205338140004 46 0.515675554791535 0.968648890416931 0.484324445208465 47 0.431131000785578 0.862262001571156 0.568868999214422 48 0.450776251476783 0.901552502953566 0.549223748523217 49 0.391813150026088 0.783626300052176 0.608186849973912 50 0.823842449372578 0.352315101254844 0.176157550627422 51 0.862401981176716 0.275196037646567 0.137598018823284 52 0.80780749683412 0.38438500633176 0.19219250316588 53 0.695035213699574 0.609929572600852 0.304964786300426 54 0.550633306698725 0.89873338660255 0.449366693301275 55 0.497744030132347 0.995488060264695 0.502255969867653 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 0 0 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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