regressie 1

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

Title produced by software: Multiple Regression

Date of computation: Wed, 09 Jan 2008 05:06:38 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Jan/09/t11998807503p7gisgs84f793b.htm/, Retrieved Wed, 09 Jan 2008 13:12:40 +0100

User-defined keywords:

Dataseries X:

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1,0137 89,97 0,9834 99,8 0,9643 112,99 0,947 93,69 0,906 108,02 0,9492 99,11 0,9397 94,33 0,9041 83,75 0,8721 106,37 0,8552 109,63 0,8564 105,5 0,8973 96,13 0,9383 102,48 0,9217 101,37 0,9095 112,76 0,892 95,57 0,8742 102,81 0,8532 104,13 0,8607 97,52 0,9005 85,29 0,9111 101,01 0,9059 108,48 0,8883 101,33 0,8924 87,57 0,8833 97,44 0,87 96,06 0,8758 106,67 0,8858 102,67 0,917 104,54 0,9554 102,46 0,9922 103,35 0,9778 83,27 0,9808 108,22 0,9811 115,23 1,0014 103,7 1,0183 93,61 1,0622 100,25 1,0773 100,56 1,0807 108,86 1,0848 105,43 1,1582 104,77 1,1663 109,13 1,1372 106,13 1,1139 82,27 1,1222 113,6 1,1692 117,73 1,1702 104,83 1,2286 104,61 1,2613 102,93 1,2646 106,95 1,2262 123,45 1,1985 111,99 1,2007 103,95 1,2138 122,05 1,2266 108,04 1,2176 93,72 1,2218 119,61 1,249 118,29 1,2991 117,14 1,3408 112,76 1,3119 105,97 1,3014 107,96 1,3201 122,27 1,2938 114,54 1,2694 110,15 1,2165 120,02 1,2037 103,94 1,2292 96,18 1,2256 121,01 1,2015 110,55 1,1786 120,04 1,1856 114,19

Text written by user:

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 compuational 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 uit[t] = + 76.9448945475292 + 17.9272790802276wk[t] -0.0729373360848385M1[t] + 2.24275774771011M2[t] + 14.6337467597814M3[t] + 4.22137035214254M4[t] + 5.75861868890598M5[t] + 9.33169792914856M6[t] + 1.93242931516801M7[t] -12.9390144262923M8[t] + 11.1954660667304M9[t] + 12.6753380348809M10[t] + 7.90052272628074M11[t] + 0.117237698854330t + 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) 76.9448945475292 6.513144 11.8138 0 0 wk 17.9272790802276 7.609508 2.3559 0.021879 0.010939 M1 -0.0729373360848385 2.600614 -0.028 0.977722 0.488861 M2 2.24275774771011 2.580354 0.8692 0.388339 0.194169 M3 14.6337467597814 2.566722 5.7013 0 0 M4 4.22137035214254 2.555891 1.6516 0.104016 0.052008 M5 5.75861868890598 2.553427 2.2553 0.027907 0.013953 M6 9.33169792914856 2.551497 3.6573 0.000551 0.000275 M7 1.93242931516801 2.549741 0.7579 0.451584 0.225792 M8 -12.9390144262923 2.549667 -5.0748 4e-06 2e-06 M9 11.1954660667304 2.5514 4.388 4.9e-05 2.4e-05 M10 12.6753380348809 2.551645 4.9675 6e-06 3e-06 M11 7.90052272628074 2.551923 3.0959 0.00302 0.00151 t 0.117237698854330 0.057249 2.0479 0.045111 0.022556 Multiple Linear Regression - Regression Statistics Multiple R 0.910125143298849 R-squared 0.82832777646475 Adjusted R-squared 0.78984951946547 F-TEST (value) 21.5271647174726 F-TEST (DF numerator) 13 F-TEST (DF denominator) 58 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.41081407999703 Sum Squared Residuals 1128.40628920140 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 89.97 95.1620777139252 -5.1920777139252 2 99.8 97.0518139404438 2.74818605955620 3 112.99 109.217629620937 3.77237037906297 4 93.69 98.6123489840646 -4.92234898406459 5 108.02 99.531816577393 8.48818342260697 6 99.11 103.996591972756 -4.88659197275576 7 94.33 96.5442519063674 -2.21425190636739 8 83.75 81.1518347285053 2.59816527149473 9 106.37 104.829879989815 1.540120010185 10 109.63 106.124018640364 3.50598135963589 11 105.5 101.487953765514 4.01204623448553 12 96.13 94.4378944524694 1.69210554753064 13 102.48 95.2172132575282 7.2627867424718 14 101.37 97.3525532074457 4.0174467925543 15 112.76 109.642067113593 3.1179328864075 16 95.57 99.033201020904 -3.46320102090404 17 102.81 100.368581488894 2.44141851110625 18 104.13 103.682425567306 0.447574432694119 19 97.52 96.5348492452814 0.985150754718628 20 85.29 82.4941489100684 2.79585108993161 21 101.01 106.935896260196 -5.92589626019584 22 108.48 108.439784075984 0.0402159240164185 23 101.33 103.466686354426 -2.1366863544257 24 87.57 95.7569031712282 -8.18690317122823 25 97.44 95.6380652943676 1.80193470563236 26 96.06 97.83256526525 -1.7725652652499 27 106.67 110.444770194841 -3.77477019484081 28 102.67 100.328904276859 2.34109572314142 29 104.54 102.542721419779 1.99727858022055 30 102.46 106.921445875557 -4.4614458755571 31 103.35 100.299138830583 3.05086116941675 32 83.27 85.286779969222 -2.01677996922196 33 108.22 109.592279998340 -1.37227999833967 34 115.23 111.194767849069 4.03523215093135 35 103.7 106.901114004651 -3.20111400465140 36 93.61 99.4207999936808 -5.81079999368084 37 100.25 100.252107908072 -0.00210790807231687 38 100.56 102.955742604833 -2.39574260483303 39 108.86 115.524922064631 -6.6649220646314 40 105.43 105.303285200076 0.126714799924179 41 104.77 108.273633520182 -3.50363352018231 42 109.13 112.109161419829 -2.97916141982905 43 106.13 104.305446683468 1.82455331653179 44 82.27 89.1335350382929 -6.86353503829289 45 113.6 113.534049646536 0.0659503534641888 46 117.73 115.973741430311 1.75625856968858 47 104.83 111.334091099646 -6.50409109964577 48 104.61 104.597759170505 0.0122408294953484 49 102.93 105.228281559198 -2.29828155919758 50 106.95 107.720374362812 -0.770374362811615 51 123.45 119.540193557056 3.90980644294354 52 111.99 108.748469217750 3.24153078225034 53 103.95 110.442395267344 -6.49239526734394 54 122.05 114.367559562392 7.68244043760818 55 108.04 107.314997819493 0.725002180507494 56 93.72 92.3994462651644 1.32055373483555 57 119.61 116.726459029178 2.88354097082157 58 118.29 118.811190687166 -0.521190687165538 59 117.14 115.051769759339 2.08823024066094 60 112.76 108.016052269558 4.74394773044186 61 105.97 107.542254266909 -1.57225426690906 62 107.96 109.786950619216 -1.82695061921596 63 122.27 122.630417448942 -0.360417448941798 64 114.54 111.863791300347 2.67620869965269 65 110.15 113.080851726408 -2.93085172640753 66 120.02 115.822815602160 4.19718439783961 67 103.94 108.311315514807 -4.37131551480727 68 96.18 94.014255088747 2.16574491125296 69 121.01 118.201435075935 2.80856492406475 70 110.55 119.366497317107 -8.8164973171067 71 120.04 114.298385016424 5.7416149835764 72 114.19 106.640590942559 7.54940905744121

Charts produced by software:

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Parameters (Session):

par1 = 2 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 2 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

R code (references can be found in the software module):

library(lattice) 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)) 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$resid, main='Residual Normal Q-Q Plot') grid() dev.off() (myerror <- as.ts(mysum$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() 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')

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Software written by Ed van Stee & Patrick Wessa

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