*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: Fri, 10 Dec 2010 08:45:25 +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/10/t1291970613ha6vrmv0y6oh8n1.htm/, Retrieved Fri, 10 Dec 2010 09:43:44 +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/10/t1291970613ha6vrmv0y6oh8n1.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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9700 0 9081 0 9084 0 9743 0 8587 0 9731 0 9563 0 9998 0 9437 0 10038 0 9918 0 9252 0 9737 0 9035 0 9133 0 9487 0 8700 0 9627 0 8947 0 9283 0 8829 0 9947 0 9628 0 9318 0 9605 0 8640 0 9214 0 9567 0 8547 0 9185 0 9470 0 9123 0 9278 0 10170 0 9434 0 9655 0 9429 0 8739 0 9552 0 9687 1 9019 1 9672 1 9206 1 9069 1 9788 1 10312 1 10105 1 9863 1 9656 1 9295 1 9946 1 9701 1 9049 1 10190 1 9706 1 9765 1 9893 1 9994 1 10433 1 10073 1 10112 1 9266 1 9820 1 10097 1 9115 1 10411 1 9678 1 10408 1 10153 1 10368 1 10581 1 10597 1 10680 1 9738 1 9556 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 10 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation geboortes[t] = + 9430.3111111111 + 286.706944444440x[t] + 99.161855158722M1[t] -638.203273809523M2[t] -284.711259920635M3[t] -37.5551587301577M4[t] -920.277430555554M5[t] + 41.0002976190488M6[t] -338.555307539682M7[t] -164.444246031745M8[t] -214.333184523809M9[t] + 355.611210317461M10[t] + 228.722271825397M11[t] + 5.22227182539697t + 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) 9430.3111111111 140.713171 67.018 0 0 x 286.706944444440 134.583356 2.1303 0.037185 0.018593 M1 99.161855158722 158.573874 0.6253 0.534083 0.267042 M2 -638.203273809523 158.462983 -4.0275 0.000159 7.9e-05 M3 -284.711259920635 158.413321 -1.7973 0.077243 0.038622 M4 -37.5551587301577 166.197782 -0.226 0.821983 0.410991 M5 -920.277430555554 165.759024 -5.5519 1e-06 0 M6 41.0002976190488 165.377825 0.2479 0.80503 0.402515 M7 -338.555307539682 165.054585 -2.0512 0.044552 0.022276 M8 -164.444246031745 164.789644 -0.9979 0.322268 0.161134 M9 -214.333184523809 164.583284 -1.3023 0.197717 0.098859 M10 355.611210317461 164.435725 2.1626 0.034501 0.01725 M11 228.722271825397 164.347126 1.3917 0.169067 0.084533 t 5.22227182539697 3.116074 1.6759 0.098874 0.049437 Multiple Linear Regression - Regression Statistics Multiple R 0.857999753809147 R-squared 0.736163577536557 Adjusted R-squared 0.67993614324107 F-TEST (value) 13.0926048246813 F-TEST (DF numerator) 13 F-TEST (DF denominator) 61 p-value 3.89466237038505e-13 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 284.606401731326 Sum Squared Residuals 4941049.03829363 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 9700 9534.69523809529 165.304761904713 2 9081 8802.55238095238 278.447619047622 3 9084 9161.26666666666 -77.2666666666633 4 9743 9413.64503968254 329.354960317462 5 8587 8536.14503968254 50.854960317464 6 9731 9502.64503968254 228.354960317463 7 9563 9128.3117063492 434.688293650796 8 9998 9307.64503968254 690.354960317463 9 9437 9262.97837301587 174.02162698413 10 10038 9838.14503968254 199.854960317462 11 9918 9716.47837301587 201.521626984129 12 9252 9492.97837301587 -240.978373015871 13 9737 9597.36249999999 139.637500000010 14 9035 8865.21964285714 169.780357142859 15 9133 9223.93392857143 -90.9339285714269 16 9487 9476.3123015873 10.6876984126990 17 8700 8598.8123015873 101.187698412698 18 9627 9565.3123015873 61.6876984126988 19 8947 9190.97896825397 -243.978968253968 20 9283 9370.3123015873 -87.312301587301 21 8829 9325.64563492063 -496.645634920635 22 9947 9900.8123015873 46.1876984126991 23 9628 9779.14563492063 -151.145634920634 24 9318 9555.64563492063 -237.645634920634 25 9605 9660.02976190475 -55.0297619047533 26 8640 8927.8869047619 -287.886904761905 27 9214 9286.60119047619 -72.6011904761905 28 9567 9538.97956349206 28.0204365079354 29 8547 8661.47956349206 -114.479563492065 30 9185 9627.97956349206 -442.979563492065 31 9470 9253.64623015873 216.353769841269 32 9123 9432.97956349206 -309.979563492065 33 9278 9388.3128968254 -110.312896825398 34 10170 9963.47956349206 206.520436507935 35 9434 9841.8128968254 -407.812896825398 36 9655 9618.3128968254 36.6871031746021 37 9429 9722.69702380952 -293.697023809517 38 8739 8990.55416666667 -251.554166666668 39 9552 9349.26845238095 202.731547619046 40 9687 9888.35376984127 -201.353769841269 41 9019 9010.85376984127 8.1462301587311 42 9672 9977.35376984127 -305.353769841269 43 9206 9603.02043650794 -397.020436507935 44 9069 9782.35376984127 -713.353769841269 45 9788 9737.6871031746 50.3128968253978 46 10312 10312.8537698413 -0.853769841268381 47 10105 10191.1871031746 -86.187103174602 48 9863 9967.6871031746 -104.687103174602 49 9656 10072.0712301587 -416.071230158721 50 9295 9339.92837301587 -44.9283730158724 51 9946 9698.64265873016 247.357341269842 52 9701 9951.02103174603 -250.021031746032 53 9049 9073.52103174603 -24.5210317460325 54 10190 10040.0210317460 149.978968253968 55 9706 9665.6876984127 40.3123015873011 56 9765 9845.02103174603 -80.0210317460321 57 9893 9800.35436507937 92.6456349206342 58 9994 10375.5210317460 -381.521031746032 59 10433 10253.8543650794 179.145634920634 60 10073 10030.3543650794 42.6456349206345 61 10112 10134.7384920635 -22.7384920634845 62 9266 9402.59563492064 -136.595634920636 63 9820 9761.30992063492 58.6900793650783 64 10097 10013.6882936508 83.3117063492042 65 9115 9136.1882936508 -21.1882936507961 66 10411 10102.6882936508 308.311706349204 67 9678 9728.35496031746 -50.3549603174625 68 10408 9907.6882936508 500.311706349204 69 10153 9863.02162698413 289.978373015871 70 10368 10438.1882936508 -70.1882936507957 71 10581 10316.5216269841 264.478373015871 72 10597 10093.0216269841 503.97837301587 73 10680 10197.4057539682 482.594246031752 74 9738 9465.2628968254 272.737103174600 75 9556 9823.97718253969 -267.977182539686 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.128704094160690 0.257408188321380 0.87129590583931 18 0.058526104950631 0.117052209901262 0.941473895049369 19 0.332367614469385 0.66473522893877 0.667632385530615 20 0.550884107448716 0.898231785102568 0.449115892551284 21 0.586756671353634 0.826486657292732 0.413243328646366 22 0.513449018504325 0.97310196299135 0.486550981495675 23 0.407871981551802 0.815743963103603 0.592128018448198 24 0.370593804769151 0.741187609538303 0.629406195230849 25 0.319036561008133 0.638073122016266 0.680963438991867 26 0.249508717541666 0.499017435083332 0.750491282458334 27 0.280486322768490 0.560972645536981 0.71951367723151 28 0.242372334677351 0.484744669354702 0.757627665322649 29 0.182497335099524 0.364994670199047 0.817502664900476 30 0.197747143157021 0.395494286314041 0.80225285684298 31 0.299959030274243 0.599918060548485 0.700040969725757 32 0.287707852601751 0.575415705203503 0.712292147398249 33 0.288768577780515 0.57753715556103 0.711231422219485 34 0.382424533003743 0.764849066007487 0.617575466996257 35 0.374207099953586 0.748414199907172 0.625792900046414 36 0.44291566149623 0.88583132299246 0.55708433850377 37 0.384864629026903 0.769729258053805 0.615135370973097 38 0.359014037214079 0.718028074428158 0.640985962785921 39 0.446307393782848 0.892614787565697 0.553692606217152 40 0.375181631546514 0.750363263093028 0.624818368453486 41 0.364361540384441 0.728723080768882 0.635638459615559 42 0.316459530508156 0.632919061016311 0.683540469491844 43 0.282369215667827 0.564738431335654 0.717630784332173 44 0.5455371596092 0.9089256807816 0.4544628403908 45 0.562852318887968 0.874295362224064 0.437147681112032 46 0.627185925495232 0.745628149009536 0.372814074504768 47 0.564436560349907 0.871126879300186 0.435563439650093 48 0.503167450735586 0.993665098528827 0.496832549264414 49 0.559425109492356 0.881149781015288 0.440574890507644 50 0.48379018640313 0.96758037280626 0.51620981359687 51 0.783017429210445 0.43396514157911 0.216982570789555 52 0.705302666891452 0.589394666217095 0.294697333108548 53 0.648188520995924 0.703622958008152 0.351811479004076 54 0.584657412834871 0.830685174330258 0.415342587165129 55 0.580366115387948 0.839267769224104 0.419633884612052 56 0.558480063448771 0.883039873102457 0.441519936551229 57 0.429348480632675 0.85869696126535 0.570651519367325 58 0.29345967342011 0.58691934684022 0.70654032657989 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 = 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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