Seatbelt Q3

*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: Sat, 22 Nov 2008 07:38:00 -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/Nov/22/t1227365307ot8ap441cr0r4cj.htm/, Retrieved Sat, 22 Nov 2008 14:48:27 +0000

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/2008/Nov/22/t1227365307ot8ap441cr0r4cj.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

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 0 103.6 0 94.1 0 98.7 0 119.5 0 112.7 0 104.4 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

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 6 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation y[t] = + 99.042467948718 -0.268269230769214x[t] -6.53221153846149M1[t] -4.30304487179487M2[t] + 8.55945512820513M3[t] + 3.12195512820513M4[t] + 1.04583333333333M5[t] + 14.4583333333333M6[t] -20.5458333333333M7[t] -9.93333333333334M8[t] + 9.92916666666667M9[t] + 12.8583333333333M10[t] + 5.75416666666667M11[t] + 0.204166666666666t + 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) 99.042467948718 2.816468 35.1655 0 0 x -0.268269230769214 2.640991 -0.1016 0.919441 0.459721 M1 -6.53221153846149 3.24228 -2.0147 0.048581 0.02429 M2 -4.30304487179487 3.236726 -1.3294 0.188907 0.094454 M3 8.55945512820513 3.2324 2.648 0.010411 0.005205 M4 3.12195512820513 3.229307 0.9668 0.337679 0.16884 M5 1.04583333333333 3.249386 0.3219 0.748719 0.37436 M6 14.4583333333333 3.241379 4.4606 3.8e-05 1.9e-05 M7 -20.5458333333333 3.234588 -6.3519 0 0 M8 -9.93333333333334 3.229021 -3.0763 0.003196 0.001598 M9 9.92916666666667 3.224685 3.0791 0.00317 0.001585 M10 12.8583333333333 3.221584 3.9913 0.000187 9.4e-05 M11 5.75416666666667 3.219722 1.7872 0.079137 0.039568 t 0.204166666666666 0.063229 3.229 0.002047 0.001023 Multiple Linear Regression - Regression Statistics Multiple R 0.906855705245502 R-squared 0.822387270136318 Adjusted R-squared 0.782577520339285 F-TEST (value) 20.6579361671252 F-TEST (DF numerator) 13 F-TEST (DF denominator) 58 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5.5756462664594 Sum Squared Residuals 1803.09421474359 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 97.3 92.7144230769229 4.58557692307713 2 101 95.1477564102564 5.85224358974357 3 113.2 108.214423076923 4.98557692307691 4 101 102.981089743590 -1.98108974358975 5 105.7 101.109134615385 4.59086538461537 6 113.9 114.725801282051 -0.825801282051288 7 86.4 79.9258012820513 6.47419871794872 8 96.5 90.742467948718 5.75753205128204 9 103.3 110.809134615385 -7.50913461538463 10 114.9 113.942467948718 0.957532051282047 11 105.8 107.042467948718 -1.24246794871797 12 94.2 101.492467948718 -7.29246794871796 13 98.4 95.1644230769231 3.23557692307688 14 99.4 97.5977564102564 1.80224358974359 15 108.8 110.664423076923 -1.86442307692309 16 112.6 105.431089743590 7.16891025641024 17 104.4 103.559134615385 0.840865384615384 18 112.2 117.175801282051 -4.97580128205128 19 81.1 82.3758012820513 -1.27580128205129 20 97.1 93.192467948718 3.90753205128205 21 112.6 113.259134615385 -0.659134615384621 22 113.8 116.392467948718 -2.59246794871795 23 107.8 109.492467948718 -1.69246794871795 24 103.2 103.942467948718 -0.742467948717947 25 103.3 97.6144230769231 5.68557692307688 26 101.2 100.047756410256 1.15224358974359 27 107.7 113.114423076923 -5.41442307692307 28 110.4 107.881089743590 2.51891025641027 29 101.9 106.009134615385 -4.10913461538461 30 115.9 119.625801282051 -3.72580128205127 31 89.9 84.8258012820513 5.07419871794872 32 88.6 95.642467948718 -7.04246794871795 33 117.2 115.709134615385 1.49086538461539 34 123.9 118.842467948718 5.05753205128207 35 100 111.942467948718 -11.9424679487179 36 103.6 106.392467948718 -2.79246794871795 37 94.1 100.064423076923 -5.96442307692312 38 98.7 102.497756410256 -3.7977564102564 39 119.5 115.564423076923 3.93557692307693 40 112.7 110.331089743590 2.36891025641027 41 104.4 108.190865384615 -3.79086538461539 42 124.7 121.807532051282 2.89246794871795 43 89.1 87.007532051282 2.09246794871794 44 97 97.8241987179487 -0.82419871794872 45 121.6 117.890865384615 3.70913461538461 46 118.8 121.024198717949 -2.22419871794873 47 114 114.124198717949 -0.124198717948722 48 111.5 108.574198717949 2.92580128205128 49 97.2 102.246153846154 -5.04615384615389 50 102.5 104.679487179487 -2.17948717948718 51 113.4 117.746153846154 -4.34615384615384 52 109.8 112.512820512821 -2.71282051282051 53 104.9 110.640865384615 -5.74086538461538 54 126.1 124.257532051282 1.84246794871794 55 80 89.457532051282 -9.45753205128205 56 96.8 100.274198717949 -3.47419871794871 57 117.2 120.340865384615 -3.14086538461538 58 112.3 123.474198717949 -11.1741987179487 59 117.3 116.574198717949 0.725801282051282 60 111.1 111.024198717949 0.0758012820512806 61 102.2 104.696153846154 -2.49615384615388 62 104.3 107.129487179487 -2.82948717948718 63 122.9 120.196153846154 2.70384615384617 64 107.6 114.962820512820 -7.36282051282051 65 121.3 113.090865384615 8.20913461538462 66 131.5 126.707532051282 4.79246794871795 67 89 91.907532051282 -2.90753205128204 68 104.4 102.724198717949 1.67580128205130 69 128.9 122.790865384615 6.10913461538463 70 135.9 125.924198717949 9.9758012820513 71 133.3 119.024198717949 14.2758012820513 72 121.3 113.474198717949 7.82580128205129

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) 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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