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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: Sat, 15 Dec 2007 15:45:06 -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/Dec/15/t1197758034etvzemokz475bzu.htm/, Retrieved Sat, 15 Dec 2007 23:34:04 +0100

User-defined keywords:

Dataseries X:

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85.6 92.81 88 75.6 89 59.04 88.4 48.7 97.5 72.81 95 111.7 104 91.81 101.8 119.5 99.4 68.07 107.6 103.4 103.2 49.16 118.9 96.3 103 124.61 126.9 96.6 91.2 109.89 106.3 110.4 85.9 110.51 109.2 104.4 80.7 114.77 104.6 110.7 86.7 92.37 100.8 93.6 80.7 103.63 92.1 114.8 81.5 90.43 86.4 74.9 83.4 65.86 96 69.8 83.5 83.33 98.5 104.2 89.5 94.49 112 109.3 85.8 68.98 113.9 92.7 77.4 55.46 120 91.7 67.5 132.89 126.7 84.4 63.7 121.71 112.8 94.5 59.4 127.01 116.2 103.6 62 134.04 110.6 105.9 62.4 106.48 105 108 58.1 117.55 101.2 119.9 58 101.61 99.3 84.5 56.3 82.66 101.9 76.7 61.4 89.28 106.4 120.5 59.8 109.24 118.9 119.6 54.3 88.16 121.9 102.3 47 59.23 132 101.7 50.5 164.21 121.4 86.9 48.1 125.13 117 93.6 58.8 152.68 122.7 113.6 70.4 132.96 113 106.7 71.9 112.42 104 96.1 73.3 136.43 101.2 124.6 83.5 107.32 100.8 72.5 90.1 87.61 98.9 89 101.3 97.86 103 115.3 98.3 106.60 117.8 119.1 106.7 92.17 126.6 104.4 109.9 65.31 127.6 104.9 111.1 161.49 115.8 76.9 119 162.25 114.8 95.3 120.7 175.13 119.2 114.9 104.5 147.28 109.9 98.9 121.6 144.48 98.9 102.9 129.6 122.67 98.6 90 124.5 102.27 96.6 81 130.1 88.64 96.7 66.2 142.3 89.59 103.5 86.7 140 112.20 115.3 86.7 143.3 91.98 122.5 103.4 113.4 57.85 125.3 89.5 113.8 160.49 111.2 113.7 120.7 128.33 110.7 120.2 112.9 140.69 114.2 137.8 115.5 126.61 105.6 99.1 121.9 129.27 95.5 110.4 119.3 124.27 97.3 112.3 111 112.90 95.5 82.2 114.2 92.54 96.3 72.2 113.5 85.70 100.2 106.7 94 116.72 113.4 106.4 83.2 92.08 121.4 110 82.8 58.98 122.1 87.5 85.8 154.50 119.3 79.7 88.7 145.55 110.8 83.3 105.3 146.60 110.1 91.8 113.1 143.51 99.7 89.2 113.8 113.52 104.8 90.6 109.4 104.80 105.4 92.6

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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation olie[t] = + 266.990447890280 + 0.0738268262780373auto[t] -1.94100985624765electric[t] -0.140847432036701vervoer[t] -9.69338508432732M1[t] -2.94497280317953M2[t] + 16.3592288303806M3[t] + 35.8549981526060M4[t] + 44.8296305047298M5[t] + 48.893937994268M6[t] + 32.3703754437297M7[t] + 18.5310130663871M8[t] + 26.9018041142079M9[t] + 10.5413368531085M10[t] + 5.13864638469737M11[t] + 0.653509189796642t + 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) 266.990447890280 59.374346 4.4967 3.5e-05 1.8e-05 auto 0.0738268262780373 0.262954 0.2808 0.77993 0.389965 electric -1.94100985624765 0.55603 -3.4908 0.000947 0.000473 vervoer -0.140847432036701 0.254161 -0.5542 0.581672 0.290836 M1 -9.69338508432732 14.705934 -0.6591 0.512502 0.256251 M2 -2.94497280317953 17.124992 -0.172 0.864082 0.432041 M3 16.3592288303806 14.507954 1.1276 0.264295 0.132148 M4 35.8549981526060 15.117273 2.3718 0.021165 0.010582 M5 44.8296305047298 19.403066 2.3104 0.024572 0.012286 M6 48.893937994268 25.532501 1.915 0.060609 0.030305 M7 32.3703754437297 19.619087 1.6499 0.104553 0.052277 M8 18.5310130663871 14.926831 1.2415 0.219612 0.109806 M9 26.9018041142079 15.917039 1.6901 0.096564 0.048282 M10 10.5413368531085 13.776977 0.7651 0.4474 0.2237 M11 5.13864638469737 12.55453 0.4093 0.683876 0.341938 t 0.653509189796642 0.162906 4.0116 0.000181 9e-05 Multiple Linear Regression - Regression Statistics Multiple R 0.640211545029573 R-squared 0.409870822389154 Adjusted R-squared 0.251800506957677 F-TEST (value) 2.59296517040755 F-TEST (DF numerator) 15 F-TEST (DF denominator) 56 p-value 0.00510596940206898 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 21.2585706020548 Sum Squared Residuals 25307.9021463827 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 85.6 83.3455065308451 2.25449346915486 2 89 91.2666880576695 -2.26668805766948 3 97.5 90.5569410093282 6.9430589906718 4 104 97.8114522282626 6.18854777173742 5 99.4 96.696731403897 2.70326859610300 6 103.2 79.0850881901762 24.1149118098238 7 103 53.2149357925202 49.7850642074798 8 91.2 76.9834601987568 14.2165398012432 9 85.9 81.2696890777685 4.63031092223150 10 80.7 73.9185398033182 6.78146019668178 11 86.7 77.2999661576444 9.4000338423556 12 80.7 87.546939216811 -6.84693921681092 13 81.5 94.2161179342861 -12.7161179342861 14 83.4 81.8887415669889 1.51125843301116 15 83.5 93.4385307427412 -9.93853074274125 16 89.5 87.4897616732957 2.01023832670432 17 85.8 93.8847295218022 -8.0847295218022 18 77.4 85.905094818784 -8.50509481878397 19 67.5 63.7748728337593 3.72512716624068 20 63.7 75.3211136666966 -11.6211136666966 21 59.4 76.8555509408117 -17.4555509408117 22 62 72.213301559546 -10.2133015595460 23 62.4 76.0033285364186 -13.6033285364185 24 58.1 78.03520732092 -19.9352073209200 25 58 76.4924496364872 -18.4924496364872 26 56.3 78.5473370931052 -22.2473370931052 27 61.4 84.0901196301006 -22.6901196301006 28 59.8 81.5771210803696 -21.7771210803696 29 54.3 86.2626241298411 -31.9626241298411 30 47 69.324939636073 -22.3249396360730 31 50.5 83.864472968368 -33.364472968368 32 48.1 75.3902329827201 -27.2902329827201 33 58.8 72.5677574629518 -13.7677574629518 34 70.4 75.2045772641017 -4.80457726410166 35 71.9 87.9010644595542 -16.0010644595542 36 73.3 86.6091851480366 -13.3091851480366 37 83.5 83.5347654921634 -0.0347654921634399 38 90.1 90.8454963154327 -0.745496315432724 39 101.3 99.8975042349588 1.40249576504123 40 98.3 91.429863094446 6.87013690555391 41 106.7 84.9822540491347 21.7177459508653 42 109.9 85.7056486023754 24.1943513976246 43 111.1 103.783903793805 7.3160962061947 44 119 90.003576101003 28.996423898997 45 120.7 88.6777128256726 32.0222871743274 46 104.5 91.2196282182169 13.2803717817831 47 121.6 107.051450516601 14.5485494833988 48 129.6 103.355385070724 26.2446149292757 49 124.5 97.9590885209472 26.5409114790528 50 130.1 106.245191358240 23.8548086417596 51 142.3 110.186798287325 32.1132017126751 52 140 109.101385037771 30.8986149622290 53 143.3 100.909325072354 42.3906749276463 54 113.4 99.6303838786358 13.7696161213642 55 113.8 115.297647084876 -1.49764708487557 56 120.7 99.7925197841132 20.9074802158868 57 112.9 100.456870293814 12.4431297061856 58 115.5 105.853910892067 9.64608910793288 59 121.9 119.313732537439 2.58626746256124 60 119.3 110.698033349032 8.60196665096763 61 111 108.552071885271 2.44792811472914 62 114.2 114.306545608563 -0.106545608563337 63 113.5 121.330106095546 -7.83010609554628 64 94 118.190416885855 -24.190416885855 65 83.2 109.964335822971 -26.7643358229713 66 82.8 114.048844873956 -31.2488448739556 67 85.8 111.764167526672 -25.9641675266717 68 88.7 113.909097266710 -25.2090972667102 69 105.3 123.172419398981 -17.872419398981 70 113.1 127.79004226275 -14.6900422627501 71 113.8 110.730457792343 3.06954220765711 72 109.4 104.155249894476 5.24475010552434

Charts produced by software:

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Parameters (Session):

Parameters (R input):

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')

Copyright

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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