Seatbeld law & tutorial 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: Thu, 20 Nov 2008 09:56:33 -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/20/t1227200360ycyosvl5miynyh9.htm/, Retrieved Thu, 20 Nov 2008 16:59:28 +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/20/t1227200360ycyosvl5miynyh9.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}, }

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Dataseries X:

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101,2 0 100,1 0 99 0 99,8 0 101 0 96,6 0 103,1 0 105,2 0 100 0 103,2 0 99,7 0 99,1 0 105,1 0 101,7 0 104,9 0 104,3 0 101,8 0 105,9 0 103,8 0 101,3 0 100,7 0 101,2 0 102,9 0 106,2 0 104,7 0 103,9 0 101,5 0 103,2 0 104,7 0 102,2 0 101,5 0 102,6 0 105,2 0 99,4 0 103,5 0 100,9 0 101,7 0 104,1 0 105,3 0 103,7 0 106,7 1 106,4 1 106 1 107 1 108,6 1 108,1 1 107,5 1 110 1 107,6 1 110 1 110 1 108,7 1 109,1 1 109,9 1 109,8 1 111,1 1 109,9 1 112,8 1 114,6 1 92,5 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 3 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation y[t] = + 97.4425 + 3.71250000000002x[t] + 3.92187500000005M1[t] + 3.74374999999999M2[t] + 3.845625M3[t] + 3.5675M4[t] + 3.46687499999998M5[t] + 2.92874999999999M6[t] + 3.49062499999999M7[t] + 4.01249999999999M8[t] + 3.37437500000000M9[t] + 3.35625000000000M10[t] + 3.978125M11[t] + 0.0781249999999991t + 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) 97.4425 1.749206 55.7067 0 0 x 3.71250000000002 1.514857 2.4507 0.018118 0.009059 M1 3.92187500000005 1.997383 1.9635 0.055649 0.027824 M2 3.74374999999999 1.99355 1.8779 0.066738 0.033369 M3 3.845625 1.990563 1.9319 0.059541 0.029771 M4 3.5675 1.988427 1.7941 0.079366 0.039683 M5 3.46687499999998 1.999935 1.7335 0.089707 0.044853 M6 2.92874999999999 1.994402 1.4685 0.148778 0.074389 M7 3.49062499999999 1.989709 1.7543 0.086032 0.043016 M8 4.01249999999999 1.985861 2.0205 0.049172 0.024586 M9 3.37437500000000 1.982863 1.7018 0.095549 0.047775 M10 3.35625000000000 1.980718 1.6945 0.096939 0.048469 M11 3.978125 1.979431 2.0097 0.050346 0.025173 t 0.0781249999999991 0.041229 1.8949 0.064402 0.032201 Multiple Linear Regression - Regression Statistics Multiple R 0.744507464650388 R-squared 0.554291364920149 Adjusted R-squared 0.428330228919322 F-TEST (value) 4.40049512507182 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 8.80495103134926e-05 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.12907560318296 Sum Squared Residuals 450.39125 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 101.2 101.442500000000 -0.24249999999978 2 100.1 101.3425 -1.24250000000002 3 99 101.5225 -2.52250000000001 4 99.8 101.3225 -1.52250000000001 5 101 101.3 -0.300000000000017 6 96.6 100.84 -4.24000000000002 7 103.1 101.48 1.61999999999999 8 105.2 102.08 3.12000000000000 9 100 101.52 -1.52000000000001 10 103.2 101.58 1.61999999999998 11 99.7 102.28 -2.58000000000001 12 99.1 98.38 0.719999999999979 13 105.1 102.38 2.71999999999993 14 101.7 102.28 -0.580000000000004 15 104.9 102.46 2.44000000000000 16 104.3 102.26 2.03999999999999 17 101.8 102.2375 -0.437500000000002 18 105.9 101.7775 4.1225 19 103.8 102.4175 1.38250000000000 20 101.3 103.0175 -1.71750000000000 21 100.7 102.4575 -1.7575 22 101.2 102.5175 -1.31750000000000 23 102.9 103.2175 -0.317499999999998 24 106.2 99.3175 6.8825 25 104.7 103.3175 1.38249999999995 26 103.9 103.2175 0.68250000000001 27 101.5 103.3975 -1.8975 28 103.2 103.1975 0.00250000000000451 29 104.7 103.175 1.52500000000002 30 102.2 102.715 -0.51499999999999 31 101.5 103.355 -1.85499999999999 32 102.6 103.955 -1.35499999999999 33 105.2 103.395 1.80500000000001 34 99.4 103.455 -4.05499999999998 35 103.5 104.155 -0.654999999999993 36 100.9 100.255 0.645000000000012 37 101.7 104.255 -2.55500000000004 38 104.1 104.155 -0.0549999999999903 39 105.3 104.335 0.965000000000009 40 103.7 104.135 -0.434999999999984 41 106.7 107.825 -1.12500000000000 42 106.4 107.365 -0.964999999999998 43 106 108.005 -2.005 44 107 108.605 -1.605 45 108.6 108.045 0.554999999999992 46 108.1 108.105 -0.00500000000000635 47 107.5 108.805 -1.30500000000000 48 110 104.905 5.095 49 107.6 108.905 -1.30500000000006 50 110 108.805 1.19500000000000 51 110 108.985 1.01500000000000 52 108.7 108.785 -0.084999999999995 53 109.1 108.7625 0.337500000000006 54 109.9 108.3025 1.59750000000001 55 109.8 108.9425 0.857500000000007 56 111.1 109.5425 1.55750000000000 57 109.9 108.9825 0.917500000000014 58 112.8 109.0425 3.75750000000001 59 114.6 109.7425 4.85750000000001 60 92.5 105.8425 -13.3425

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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