*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: Thu, 19 Nov 2009 15:46:07 -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/Nov/19/t12586710075v46mdbjzvu1r4q.htm/, Retrieved Thu, 19 Nov 2009 23:50:19 +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/Nov/19/t12586710075v46mdbjzvu1r4q.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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6802.96 0 7132.68 0 7073.29 0 7264.5 0 7105.33 0 7218.71 0 7225.72 0 7354.25 0 7745.46 0 8070.26 0 8366.33 0 8667.51 0 8854.34 0 9218.1 0 9332.9 0 9358.31 0 9248.66 0 9401.2 0 9652.04 0 9957.38 0 10110.63 0 10169.26 0 10343.78 0 10750.21 0 11337.5 0 11786.96 0 12083.04 0 12007.74 0 11745.93 0 11051.51 0 11445.9 0 11924.88 0 12247.63 0 12690.91 0 12910.7 0 13202.12 0 13654.67 0 13862.82 0 13523.93 0 14211.17 0 14510.35 0 14289.23 0 14111.82 0 13086.59 0 13351.54 0 13747.69 0 12855.61 0 12926.93 0 12121.95 1 11731.65 1 11639.51 1 12163.78 1 12029.53 1 11234.18 1 9852.13 1 9709.04 1 9332.75 1 7108.6 1 6691.49 1 6143.05 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 Y[t] = + 5272.08916666666 -5964.88333333334X[t] + 2128.74684722222M1[t] + 2147.04786111111M2[t] + 1957.28287500000M3[t] + 2053.99188888889M4[t] + 1806.99490277778M5[t] + 1344.14391666667M6[t] + 988.842930555555M7[t] + 763.891944444445M8[t] + 741.208958333335M9[t] + 367.093972222224M10[t] + 69.474986111113M11[t] + 173.856986111111t + 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) 5272.08916666666 677.476199 7.782 0 0 X -5964.88333333334 556.882005 -10.7112 0 0 M1 2128.74684722222 785.030268 2.7117 0.009382 0.004691 M2 2147.04786111111 782.722481 2.7431 0.008647 0.004323 M3 1957.28287500000 780.628605 2.5073 0.015759 0.00788 M4 2053.99188888889 778.750365 2.6375 0.011354 0.005677 M5 1806.99490277778 777.089325 2.3253 0.024519 0.01226 M6 1344.14391666667 775.646879 1.7329 0.089808 0.044904 M7 988.842930555555 774.424249 1.2769 0.208055 0.104027 M8 763.891944444445 773.422478 0.9877 0.328478 0.164239 M9 741.208958333335 772.642425 0.9593 0.342414 0.171207 M10 367.093972222224 772.084762 0.4755 0.636711 0.318355 M11 69.474986111113 771.74997 0.09 0.92866 0.46433 t 173.856986111111 13.125835 13.2454 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.893031005209968 R-squared 0.797504376266327 Adjusted R-squared 0.74027735216768 F-TEST (value) 13.9358002417110 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 7.49089679175086e-12 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1220.06734362336 Sum Squared Residuals 68473958.8569033 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 6802.96 7574.693 -771.733000000007 2 7132.68 7766.85099999999 -634.17099999999 3 7073.29 7750.943 -677.653000000002 4 7264.5 8021.509 -757.009000000002 5 7105.33 7948.369 -843.038999999994 6 7218.71 7659.375 -440.664999999997 7 7225.72 7477.931 -252.211000000003 8 7354.25 7426.837 -72.587000000002 9 7745.46 7578.011 167.448999999999 10 8070.26 7377.753 692.507 11 8366.33 7253.991 1112.33900000000 12 8667.51 7358.373 1309.137 13 8854.34 9660.97683333333 -806.63683333333 14 9218.1 9853.13483333334 -635.034833333337 15 9332.9 9837.22683333333 -504.326833333334 16 9358.31 10107.7928333333 -749.482833333333 17 9248.66 10034.6528333333 -785.992833333336 18 9401.2 9745.65883333333 -344.458833333333 19 9652.04 9564.21483333333 87.8251666666692 20 9957.38 9513.12083333333 444.259166666666 21 10110.63 9664.29483333333 446.335166666666 22 10169.26 9464.03683333333 705.223166666666 23 10343.78 9340.27483333333 1003.50516666667 24 10750.21 9444.65683333333 1305.55316666667 25 11337.5 11747.2606666667 -409.760666666666 26 11786.96 11939.4186666667 -152.458666666669 27 12083.04 11923.5106666667 159.529333333334 28 12007.74 12194.0766666667 -186.336666666666 29 11745.93 12120.9366666667 -375.006666666669 30 11051.51 11831.9426666667 -780.432666666666 31 11445.9 11650.4986666667 -204.598666666665 32 11924.88 11599.4046666667 325.475333333333 33 12247.63 11750.5786666667 497.051333333333 34 12690.91 11550.3206666667 1140.58933333333 35 12910.7 11426.5586666667 1484.14133333333 36 13202.12 11530.9406666667 1671.17933333334 37 13654.67 13833.5445 -178.874499999998 38 13862.82 14025.7025 -162.882500000002 39 13523.93 14009.7945 -485.864499999999 40 14211.17 14280.3605 -69.1904999999997 41 14510.35 14207.2205 303.129499999998 42 14289.23 13918.2265 371.003499999998 43 14111.82 13736.7825 375.037499999999 44 13086.59 13685.6885 -599.098499999999 45 13351.54 13836.8625 -485.322499999999 46 13747.69 13636.6045 111.085500000001 47 12855.61 13512.8425 -657.2325 48 12926.93 13617.2245 -690.294499999998 49 12121.95 9954.945 2167.005 50 11731.65 10147.103 1584.54700000000 51 11639.51 10131.195 1508.315 52 12163.78 10401.761 1762.019 53 12029.53 10328.621 1700.90900000000 54 11234.18 10039.627 1194.553 55 9852.13 9858.183 -6.05299999999912 56 9709.04 9807.089 -98.0489999999993 57 9332.75 9958.263 -625.513 58 7108.6 9758.005 -2649.405 59 6691.49 9634.243 -2942.753 60 6143.05 9738.625 -3595.575 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.000179765772587634 0.000359531545175267 0.999820234227412 18 9.20222302826022e-06 1.84044460565204e-05 0.999990797776972 19 8.10799139000903e-06 1.62159827800181e-05 0.99999189200861 20 8.69442663901354e-06 1.73888532780271e-05 0.99999130557336 21 1.01545632111591e-06 2.03091264223182e-06 0.999998984543679 22 1.18315219048744e-07 2.36630438097488e-07 0.99999988168478 23 2.31893599842789e-08 4.63787199685578e-08 0.99999997681064 24 2.82074966342616e-09 5.64149932685231e-09 0.99999999717925 25 6.07586489954362e-10 1.21517297990872e-09 0.999999999392414 26 1.84531909274842e-10 3.69063818549684e-10 0.999999999815468 27 3.21556725641831e-10 6.43113451283662e-10 0.999999999678443 28 9.07529960694118e-11 1.81505992138824e-10 0.999999999909247 29 2.40582355739146e-11 4.81164711478292e-11 0.999999999975942 30 1.15014333894896e-09 2.30028667789793e-09 0.999999998849857 31 1.51049312705473e-09 3.02098625410946e-09 0.999999998489507 32 5.40876349878247e-10 1.08175269975649e-09 0.999999999459124 33 2.17096364193548e-10 4.34192728387097e-10 0.999999999782904 34 5.72486400880437e-11 1.14497280176087e-10 0.999999999942751 35 1.08675399480315e-11 2.17350798960630e-11 0.999999999989132 36 1.62566723601535e-12 3.2513344720307e-12 0.999999999998374 37 1.04386890194342e-12 2.08773780388684e-12 0.999999999998956 38 4.43512258823131e-13 8.87024517646263e-13 0.999999999999556 39 3.46982349626026e-12 6.93964699252052e-12 0.99999999999653 40 1.07893202078003e-11 2.15786404156006e-11 0.99999999998921 41 5.43990873048885e-10 1.08798174609777e-09 0.99999999945601 42 9.44124944719725e-09 1.88824988943945e-08 0.99999999055875 43 4.66544290133591e-09 9.33088580267181e-09 0.999999995334557 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 27 1 NOK 5% type I error level 27 1 NOK 10% type I error level 27 1 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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