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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, 19 Nov 2007 03:15:52 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2007/Nov/19/t1195467182ipwg5hhfzejfbki.htm/, Retrieved Mon, 19 Nov 2007 11:13:28 +0100

User-defined keywords:

ws 6 vraag 3 groep 1

Dataseries X:

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97,3 0 101 0 113,2 0 101 0 105,7 0 113,9 0 86,4 0 96,5 0 103,3 0 114,9 0 105,8 0 94,2 0 98,4 0 99,4 0 108,8 0 112,6 0 104,4 0 112,2 0 81,1 0 97,1 0 112,6 0 113,8 0 107,8 0 103,2 0 103,3 0 101,2 0 107,7 0 110,4 0 101,9 0 115,9 0 89,9 0 88,6 0 117,2 0 123,9 0 100 1 103,6 1 94,1 1 98,7 1 119,5 1 112,7 1 104,4 1 124,7 1 89,1 1 97 1 121,6 1 118,8 1 114 1 111,5 1 97,2 1 102,5 1 113,4 1 109,8 1 104,9 1 126,1 1 80 1 96,8 1 117,2 1 112,3 1 117,3 1 111,1 1 102,2 1 104,3 1 122,9 1 107,6 1 121,3 1 131,5 1 89 1 104,4 1 128,9 1 135,9 1 133,3 1 121,3 1 120,5 1 120,4 1 137,9 1 126,1 1 133,2 1 146,6 1 103,4 1 117,2 1

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 y[t] = + 94.4683808553971 -8.64511201629328x[t] -4.21401537193293M1[t] -2.58969062166619M2[t] + 10.6632055571719M3[t] + 4.04467316458152M4[t] + 2.96899791484821M5[t] + 16.1076083794006M6[t] -20.3394954417612M7[t] -9.54374212006597M8[t] + 9.21712612743672M9[t] + 11.9033556396082M10[t] + 5.99710382116186M11[t] + 0.447103821161866t + 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) 94.4683808553971 2.735923 34.5289 0 0 x -8.64511201629328 2.66331 -3.246 0.00184 0.00092 M1 -4.21401537193293 3.319798 -1.2694 0.208771 0.104385 M2 -2.58969062166619 3.319146 -0.7802 0.438046 0.219023 M3 10.6632055571719 3.319471 3.2123 0.002037 0.001018 M4 4.04467316458152 3.320775 1.218 0.227564 0.113782 M5 2.96899791484821 3.323055 0.8935 0.37486 0.18743 M6 16.1076083794006 3.326311 4.8425 8e-06 4e-06 M7 -20.3394954417612 3.330538 -6.107 0 0 M8 -9.54374212006597 3.335733 -2.8611 0.00565 0.002825 M9 9.21712612743672 3.455681 2.6672 0.009611 0.004805 M10 11.9033556396082 3.459633 3.4406 0.001011 0.000505 M11 5.99710382116186 3.442297 1.7422 0.086135 0.043068 t 0.447103821161866 0.056984 7.8461 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.910883692866785 R-squared 0.829709101930632 Adjusted R-squared 0.796166955341211 F-TEST (value) 24.7363149439076 F-TEST (DF numerator) 13 F-TEST (DF denominator) 66 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5.96141569664024 Sum Squared Residuals 2345.53948913781 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 97.3 90.7014693046264 6.59853069537361 2 101 92.7728978760547 8.22710212394531 3 113.2 106.472897876055 6.72710212394528 4 101 100.301469304626 0.698530695373892 5 105.7 99.6728978760547 6.02710212394534 6 113.9 113.258612161769 0.641387838231008 7 86.4 77.258612161769 9.14138783823105 8 96.5 88.5014693046262 7.99853069537385 9 103.3 107.709441373291 -4.40944137329064 10 114.9 110.842774706624 4.05722529337604 11 105.8 105.383626709340 0.416373290660460 12 94.2 99.8336267093395 -5.63362670933954 13 98.4 96.0667151585685 2.33328484143154 14 99.4 98.138143729997 1.26185627000294 15 108.8 111.838143729997 -3.03814372999709 16 112.6 105.666715158569 6.93328484143148 17 104.4 105.038143729997 -0.638143729997084 18 112.2 118.623858015711 -6.42385801571137 19 81.1 82.6238580157114 -1.52385801571138 20 97.1 93.8667151585685 3.23328484143149 21 112.6 113.074687227233 -0.474687227233058 22 113.8 116.208020560566 -2.40802056056639 23 107.8 110.748872563282 -2.94887256328193 24 103.2 105.198872563282 -1.99887256328194 25 103.3 101.431961012511 1.86803898748913 26 101.2 103.503389583939 -2.30338958393948 27 107.7 117.203389583939 -9.50338958393948 28 110.4 111.031961012511 -0.631961012510907 29 101.9 110.403389583939 -8.50338958393948 30 115.9 123.989103869654 -8.08910386965376 31 89.9 87.9891038696538 1.91089613034623 32 88.6 99.231961012511 -10.6319610125109 33 117.2 118.439933081175 -1.23993308117545 34 123.9 121.573266414509 2.32673358549123 35 100 107.469006400931 -7.46900640093104 36 103.6 101.919006400931 1.68099359906895 37 94.1 98.15209485016 -4.05209485015998 38 98.7 100.223523421589 -1.52352342158859 39 119.5 113.923523421589 5.57647657841141 40 112.7 107.75209485016 4.94790514983999 41 104.4 107.123523421589 -2.72352342158859 42 124.7 120.709237707303 3.99076229269713 43 89.1 84.7092377073029 4.39076229269711 44 97 95.95209485016 1.04790514983999 45 121.6 115.160066918825 6.43993308117544 46 118.8 118.293400252158 0.506599747842102 47 114 112.834252254873 1.16574774512657 48 111.5 107.284252254873 4.21574774512656 49 97.2 103.517340704102 -6.31734070410237 50 102.5 105.588769275531 -3.08876927553099 51 113.4 119.288769275531 -5.88876927553098 52 109.8 113.117340704102 -3.31734070410242 53 104.9 112.488769275531 -7.58876927553099 54 126.1 126.074483561245 0.0255164387547245 55 80 90.0744835612453 -10.0744835612453 56 96.8 101.317340704102 -4.51734070410241 57 117.2 120.525312772767 -3.32531277276695 58 112.3 123.658646106100 -11.3586461061003 59 117.3 118.199498108816 -0.899498108815835 60 111.1 112.649498108816 -1.54949810881584 61 102.2 108.882586558045 -6.68258655804476 62 104.3 110.954015129473 -6.65401512947339 63 122.9 124.654015129473 -1.75401512947337 64 107.6 118.482586558045 -10.8825865580448 65 121.3 117.854015129473 3.44598487052661 66 131.5 131.439729415188 0.0602705848123345 67 89 95.4397294151877 -6.43972941518768 68 104.4 106.682586558045 -2.2825865580448 69 128.9 125.890558626709 3.00944137329066 70 135.9 129.023891960043 6.87610803995732 71 133.3 123.564743962758 9.73525603724178 72 121.3 118.014743962758 3.28525603724176 73 120.5 114.247832411987 6.25216758801284 74 120.4 116.319260983416 4.08073901658422 75 137.9 130.019260983416 7.88073901658422 76 126.1 123.847832411987 2.25216758801279 77 133.2 123.219260983416 9.98073901658421 78 146.6 136.80497526913 9.79502473086993 79 103.4 100.80497526913 2.59502473086993 80 117.2 112.047832411987 5.1521675880128

Charts produced by software:

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Parameters:

par1 = 1 ; 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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This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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