*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, 21 Dec 2010 15:29:01 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/21/t129294524594fbbik8c4o5ul4.htm/, Retrieved Tue, 21 Dec 2010 16:27:36 +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/2010/Dec/21/t129294524594fbbik8c4o5ul4.htm/}, year = {2010}, } @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 = {2010}, 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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3010 2910 3840 3580 3140 3550 3250 2820 2260 2060 2120 2210 2190 2180 2350 2440 2370 2440 2610 3040 3190 3120 3170 3600 3420 3650 4180 2960 2710 2950 3030 3770 4740 4450 5550 5580 5890 7480 10450 6360 6710 6200 4490 3480 2520 1920 2010 1950 2240 2370 2840 2700 2980 3290 3300 3000 2330 2190 1970 2170 2830 3190 3550 3240 3450 3570 3230 3260 2700

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 10 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Garnalen[t] = + 3102 + 161.333333333333M1[t] + 528.000000000001M2[t] + 1433.00000000000M3[t] + 444.666666666666M4[t] + 458M5[t] + 564.666666666667M6[t] + 216.333333333334M7[t] + 126.333333333334M8[t] -145.333333333333M9[t] -354M10[t] -138M11[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) 3102 686.905418 4.5159 3.2e-05 1.6e-05 M1 161.333333333333 930.074332 0.1735 0.862902 0.431451 M2 528.000000000001 930.074332 0.5677 0.57247 0.286235 M3 1433.00000000000 930.074332 1.5407 0.128914 0.064457 M4 444.666666666666 930.074332 0.4781 0.634409 0.317205 M5 458 930.074332 0.4924 0.624304 0.312152 M6 564.666666666667 930.074332 0.6071 0.546182 0.273091 M7 216.333333333334 930.074332 0.2326 0.816907 0.408453 M8 126.333333333334 930.074332 0.1358 0.892433 0.446217 M9 -145.333333333333 930.074332 -0.1563 0.87638 0.43819 M10 -354 971.430958 -0.3644 0.7169 0.35845 M11 -138 971.430958 -0.1421 0.887535 0.443767 Multiple Linear Regression - Regression Statistics Multiple R 0.304904330702794 R-squared 0.0929666508813186 Adjusted R-squared -0.0820748726328129 F-TEST (value) 0.531111984259056 F-TEST (DF numerator) 11 F-TEST (DF denominator) 57 p-value 0.874056566975166 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1535.96720770917 Sum Squared Residuals 134474130 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 3010 3263.33333333333 -253.333333333332 2 2910 3630 -719.999999999999 3 3840 4535 -695 4 3580 3546.66666666667 33.333333333331 5 3140 3560 -420 6 3550 3666.66666666667 -116.666666666666 7 3250 3318.33333333333 -68.333333333333 8 2820 3228.33333333333 -408.333333333334 9 2260 2956.66666666667 -696.666666666667 10 2060 2748 -688 11 2120 2964 -844 12 2210 3102 -892 13 2190 3263.33333333333 -1073.33333333333 14 2180 3630 -1450 15 2350 4535 -2185 16 2440 3546.66666666667 -1106.66666666667 17 2370 3560 -1190 18 2440 3666.66666666667 -1226.66666666667 19 2610 3318.33333333333 -708.333333333333 20 3040 3228.33333333333 -188.333333333333 21 3190 2956.66666666667 233.333333333333 22 3120 2748 372 23 3170 2964 206.000000000000 24 3600 3102 498 25 3420 3263.33333333333 156.666666666666 26 3650 3630 19.9999999999999 27 4180 4535 -355 28 2960 3546.66666666667 -586.666666666666 29 2710 3560 -850 30 2950 3666.66666666667 -716.666666666667 31 3030 3318.33333333333 -288.333333333333 32 3770 3228.33333333333 541.666666666667 33 4740 2956.66666666667 1783.33333333333 34 4450 2748 1702 35 5550 2964 2586 36 5580 3102 2478 37 5890 3263.33333333333 2626.66666666667 38 7480 3630 3850 39 10450 4535 5915 40 6360 3546.66666666667 2813.33333333333 41 6710 3560 3150 42 6200 3666.66666666667 2533.33333333333 43 4490 3318.33333333333 1171.66666666667 44 3480 3228.33333333333 251.666666666667 45 2520 2956.66666666667 -436.666666666667 46 1920 2748 -828 47 2010 2964 -954 48 1950 3102 -1152 49 2240 3263.33333333333 -1023.33333333333 50 2370 3630 -1260 51 2840 4535 -1695 52 2700 3546.66666666667 -846.666666666666 53 2980 3560 -580 54 3290 3666.66666666667 -376.666666666667 55 3300 3318.33333333333 -18.3333333333332 56 3000 3228.33333333333 -228.333333333333 57 2330 2956.66666666667 -626.666666666667 58 2190 2748 -558 59 1970 2964 -994 60 2170 3102 -932 61 2830 3263.33333333333 -433.333333333334 62 3190 3630 -440 63 3550 4535 -985 64 3240 3546.66666666667 -306.666666666666 65 3450 3560 -110.000000000000 66 3570 3666.66666666667 -96.6666666666667 67 3230 3318.33333333333 -88.3333333333332 68 3260 3228.33333333333 31.6666666666668 69 2700 2956.66666666667 -256.666666666667 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 15 0.106170150533232 0.212340301066464 0.893829849466768 16 0.0672170860164741 0.134434172032948 0.932782913983526 17 0.0335715771546941 0.0671431543093882 0.966428422845306 18 0.0218209630156606 0.0436419260313212 0.97817903698434 19 0.0099507357192419 0.0199014714384838 0.990049264280758 20 0.00366910882049493 0.00733821764098986 0.996330891179505 21 0.00195273464208684 0.00390546928417369 0.998047265357913 22 0.00116976178286777 0.00233952356573555 0.998830238217132 23 0.000683137074204905 0.00136627414840981 0.999316862925795 24 0.000567725322503642 0.00113545064500728 0.999432274677496 25 0.000295200799917545 0.000590401599835091 0.999704799200082 26 0.000208201093524620 0.000416402187049241 0.999791798906475 27 0.000149783260001223 0.000299566520002445 0.999850216739999 28 5.59996729415587e-05 0.000111999345883117 0.999944000327058 29 2.17278885222635e-05 4.34557770445271e-05 0.999978272111478 30 7.87689177179518e-06 1.57537835435904e-05 0.999992123108228 31 2.5477086634943e-06 5.0954173269886e-06 0.999997452291337 32 1.26146726199123e-06 2.52293452398245e-06 0.999998738532738 33 5.64143185876742e-06 1.12828637175348e-05 0.99999435856814 34 1.33016038686965e-05 2.66032077373929e-05 0.999986698396131 35 0.000190966161178837 0.000381932322357675 0.999809033838821 36 0.000983491084208296 0.00196698216841659 0.999016508915792 37 0.00553558692855845 0.0110711738571169 0.994464413071442 38 0.0989454447093192 0.197890889418638 0.901054555290681 39 0.970404100324327 0.0591917993513452 0.0295958996756726 40 0.995952593482285 0.00809481303542908 0.00404740651771454 41 0.999954664997884 9.06700042326692e-05 4.53350021163346e-05 42 0.999999969199247 6.16015055246975e-08 3.08007527623488e-08 43 0.999999996893907 6.21218563017334e-09 3.10609281508667e-09 44 0.999999986734953 2.65300938295595e-08 1.32650469147797e-08 45 0.99999991877516 1.62449678629251e-07 8.12248393146255e-08 46 0.99999960869528 7.82609441062796e-07 3.91304720531398e-07 47 0.999997918621292 4.16275741672268e-06 2.08137870836134e-06 48 0.999990473006845 1.90539863104926e-05 9.5269931552463e-06 49 0.999974390512296 5.12189754082503e-05 2.56094877041252e-05 50 0.999968436470224 6.31270595521697e-05 3.15635297760849e-05 51 0.999958090398168 8.3819203664554e-05 4.1909601832277e-05 52 0.999900712790417 0.000198574419165814 9.92872095829069e-05 53 0.9997306521782 0.000538695643599951 0.000269347821799975 54 0.99832031652668 0.0033593669466389 0.00167968347331945 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 32 0.8 NOK 5% type I error level 35 0.875 NOK 10% type I error level 37 0.925 NOK

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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