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R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Mon, 21 Dec 2009 07:16:30 -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/21/t1261405057qw9o2x7mp1sdv5y.htm/, Retrieved Mon, 21 Dec 2009 15:17:48 +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/21/t1261405057qw9o2x7mp1sdv5y.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:

» Textbox « » Textfile « » CSV «

2350.44 0 1 0 2440.25 0 2 0 2408.64 0 3 0 2472.81 0 4 0 2407.6 0 5 0 2454.62 0 6 0 2448.05 0 7 0 2497.84 0 8 0 2645.64 0 9 0 2756.76 0 10 0 2849.27 0 11 0 2921.44 0 12 0 2981.85 0 13 0 3080.58 0 14 0 3106.22 0 15 0 3119.31 0 16 0 3061.26 0 17 0 3097.31 0 18 0 3161.69 0 19 0 3257.16 0 20 0 3277.01 0 21 0 3295.32 0 22 0 3363.99 0 23 0 3494.17 0 24 0 3667.03 0 25 0 3813.06 0 26 0 3917.96 0 27 0 3895.51 0 28 0 3801.06 0 29 0 3570.12 0 30 0 3701.61 0 31 0 3862.27 0 32 0 3970.1 0 33 0 4138.52 0 34 0 4199.75 0 35 0 4290.89 0 36 0 4443.91 0 37 0 4502.64 1 38 38 4356.98 1 39 39 4591.27 1 40 40 4696.96 1 41 41 4621.4 1 42 42 4562.84 1 43 43 4202.52 1 44 44 4296.49 1 45 45 4435.23 1 46 46 4105.18 1 47 47 4116.68 1 48 48 3844.49 1 49 49 3720.98 1 50 50 3674.4 1 51 51 3857.62 1 52 52 3801.06 1 53 53 3504.37 1 54 54 3032.6 1 55 55 3047.03 1 56 56 2962.34 1 57 57 2197.82 1 58 58 2014.45 1 59 59

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 8 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation X[t] = + 2265.76895251738 + 6702.57359475699Dummy[t] + 56.2740308416929Trend[t] -160.319856371451Extradummy[t] + 15.5441499291209M1[t] -76.7917201666513M2[t] -87.5998084597628M3[t] + 14.7181032471253M4[t] -11.1439850459874M5[t] -107.3140733391M6[t] -167.666161632212M7[t] -167.806249925324M8[t] -103.000338218437M9[t] -160.732426511549M10[t] -211.080514804662M11[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) 2265.76895251738 137.974357 16.4217 0 0 Dummy 6702.57359475699 385.111397 17.4042 0 0 Trend 56.2740308416929 3.524242 15.9677 0 0 Extradummy -160.319856371451 8.380617 -19.1298 0 0 M1 15.5441499291209 150.075395 0.1036 0.917977 0.458988 M2 -76.7917201666513 152.300485 -0.5042 0.616628 0.308314 M3 -87.5998084597628 151.713518 -0.5774 0.56661 0.283305 M4 14.7181032471253 151.22283 0.0973 0.922909 0.461454 M5 -11.1439850459874 150.829361 -0.0739 0.941437 0.470718 M6 -107.3140733391 150.533872 -0.7129 0.479678 0.239839 M7 -167.666161632212 150.336942 -1.1153 0.270789 0.135395 M8 -167.806249925324 150.238958 -1.1169 0.270087 0.135043 M9 -103.000338218437 150.240113 -0.6856 0.49658 0.24829 M10 -160.732426511549 150.340406 -1.0691 0.290844 0.145422 M11 -211.080514804662 150.539638 -1.4022 0.167884 0.083942 Multiple Linear Regression - Regression Statistics Multiple R 0.96331215525516 R-squared 0.927970308462342 Adjusted R-squared 0.905051770245815 F-TEST (value) 40.4899431061072 F-TEST (DF numerator) 14 F-TEST (DF denominator) 44 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 222.805240997540 Sum Squared Residuals 2184255.71830277 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 2350.44 2337.58713328820 12.852866711805 2 2440.25 2301.52529403412 138.724705965879 3 2408.64 2346.99123658270 61.6487634173034 4 2472.81 2505.58317913128 -32.7731791312767 5 2407.6 2535.99512167986 -128.395121679859 6 2454.62 2496.09906422844 -41.4790642284385 7 2448.05 2492.02100677702 -43.971006777019 8 2497.84 2548.1549493256 -50.3149493255997 9 2645.64 2669.23489187418 -23.5948918741802 10 2756.76 2667.77683442276 88.9831655772394 11 2849.27 2673.70277697134 175.567223028659 12 2921.44 2941.05732261770 -19.6173226176957 13 2981.85 3012.87550338851 -31.0255033885097 14 3080.58 2976.81366413443 103.766335865570 15 3106.22 3022.27960668301 83.9403933169882 16 3119.31 3180.87154923159 -61.5615492315926 17 3061.26 3211.28349178017 -150.023491780172 18 3097.31 3171.38743432875 -74.0774343287531 19 3161.69 3167.30937687733 -5.61937687733370 20 3257.16 3223.44331942591 33.7166805740856 21 3277.01 3344.52326197449 -67.5132619744944 22 3295.32 3343.06520452307 -47.745204523075 23 3363.99 3348.99114707166 14.9988529283441 24 3494.17 3616.34569271801 -122.17569271801 25 3667.03 3688.16387348882 -21.1338734888238 26 3813.06 3652.10203423474 160.957965765255 27 3917.96 3697.56797678333 220.392023216674 28 3895.51 3856.15991933191 39.3500806680933 29 3801.06 3886.57186188049 -85.5118618804872 30 3570.12 3846.67580442907 -276.555804429068 31 3701.61 3842.59774697765 -140.987746977648 32 3862.27 3898.73168952623 -36.4616895262287 33 3970.1 4019.81163207481 -49.7116320748092 34 4138.52 4018.35357462339 120.166425376611 35 4199.75 4024.27951717197 175.47048282803 36 4290.89 4291.63406281832 -0.744062818324361 37 4443.91 4363.45224358914 80.4577564108615 38 4502.64 4937.8094569769 -435.169456976902 39 4356.98 4822.95554315403 -465.975543154033 40 4591.27 4821.22762933116 -229.957629331162 41 4696.96 4691.31971550829 5.64028449170894 42 4621.4 4491.10380168542 130.296198314579 43 4562.84 4326.70588786255 236.13411213745 44 4202.52 4222.51997403968 -19.9999740396787 45 4296.49 4183.28006021681 113.209939783192 46 4435.23 4021.50214639394 413.727853606062 47 4105.18 3867.10823257107 238.071767428933 48 4116.68 3974.14292184597 142.537078154030 49 3844.49 3885.64124624533 -41.1512462453329 50 3720.98 3689.2595506198 31.7204493801979 51 3674.4 3574.40563679693 99.9943632030678 52 3857.62 3572.67772297406 284.942277025938 53 3801.06 3442.76980915119 358.290190848809 54 3504.37 3242.55389532832 261.81610467168 55 3032.6 3078.15598150545 -45.5559815054496 56 3047.03 2973.97006768258 73.0599323174215 57 2962.34 2934.73015385971 27.6098461402922 58 2197.82 2772.95224003684 -575.132240036837 59 2014.45 2618.55832621397 -604.108326213966 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 18 0.000666355895927517 0.00133271179185503 0.999333644104073 19 0.000193146210495616 0.000386292420991231 0.999806853789504 20 0.000137792357539975 0.000275584715079951 0.99986220764246 21 2.10584594415713e-05 4.21169188831426e-05 0.999978941540558 22 2.24137812100874e-05 4.48275624201749e-05 0.99997758621879 23 1.84343245107032e-05 3.68686490214063e-05 0.99998156567549 24 4.5195309058326e-06 9.0390618116652e-06 0.999995480469094 25 8.6537854185872e-07 1.73075708371744e-06 0.999999134621458 26 3.60956966126119e-07 7.21913932252237e-07 0.999999639043034 27 1.63215390134351e-06 3.26430780268702e-06 0.999998367846099 28 7.69669899563964e-07 1.53933979912793e-06 0.9999992303301 29 1.80100132401275e-07 3.60200264802549e-07 0.999999819899868 30 7.38530195790277e-07 1.47706039158055e-06 0.999999261469804 31 2.73111936025378e-07 5.46223872050757e-07 0.999999726888064 32 5.68598719859657e-08 1.13719743971931e-07 0.999999943140128 33 1.48086595428652e-08 2.96173190857304e-08 0.99999998519134 34 6.10595251552454e-09 1.22119050310491e-08 0.999999993894047 35 2.33602538147325e-09 4.67205076294651e-09 0.999999997663975 36 5.34928924784169e-10 1.06985784956834e-09 0.99999999946507 37 1.40124018066601e-10 2.80248036133202e-10 0.999999999859876 38 5.43811403237742e-11 1.08762280647548e-10 0.999999999945619 39 5.90718616341904e-11 1.18143723268381e-10 0.999999999940928 40 7.27372675911688e-10 1.45474535182338e-09 0.999999999272627 41 5.09055983828414e-09 1.01811196765683e-08 0.99999999490944 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 24 1 NOK 5% type I error level 24 1 NOK 10% type I error level 24 1 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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