s 0650692 paper

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

Title produced by software: Multiple Regression

Date of computation: Sun, 06 Jan 2008 10:19:16 -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/06/t1199640052t1pf5fs5z6nddqe.htm/, Retrieved Sun, 06 Jan 2008 18:21:03 +0100

User-defined keywords:

dieselprijs te verklaren door inflatie

Dataseries X:

» Textbox « » Textfile « » CSV «

0,73 1,79 0,74 1,95 0,75 2,26 0,74 2,04 0,76 2,16 0,76 2,75 0,78 2,79 0,79 2,88 0,89 3,36 0,88 2,97 0,88 3,1 0,84 2,49 0,76 2,2 0,77 2,25 0,76 2,09 0,77 2,79 0,78 3,14 0,79 2,93 0,78 2,65 0,76 2,67 0,78 2,26 0,76 2,35 0,74 2,13 0,73 2,18 0,72 2,9 0,71 2,63 0,73 2,67 0,75 1,81 0,75 1,33 0,72 0,88 0,72 1,28 0,72 1,26 0,74 1,26 0,78 1,29 0,74 1,1 0,74 1,37 0,75 1,21 0,78 1,74 0,81 1,76 0,75 1,48 0,7 1,04 0,71 1,62 0,71 1,49 0,73 1,79 0,74 1,8 0,74 1,58 0,75 1,86 0,74 1,74 0,74 1,59 0,73 1,26 0,76 1,13 0,8 1,92 0,83 2,61 0,81 2,26 0,83 2,41 0,88 2,26 0,89 2,03 0,93 2,86 0,91 2,55 0,9 2,27 0,86 2,26 0,88 2,57 0,93 3,07 0,98 2,76 0,97 2,51 1,03 2,87 1,06 3,14 1,06 3,11 1,08 3,16 1,09 2,47 1,04 2,57 1 2,89

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 dsl[t] = + 0.490196229042141 + 0.0965244180906564`inf `[t] + 0.00301888250299787t + 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) 0.490196229042141 0.024886 19.6976 0 0 `inf ` 0.0965244180906564 0.009883 9.7671 0 0 t 0.00301888250299787 0.000301 10.0353 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.86202495733774 R-squared 0.743087027073131 Adjusted R-squared 0.735640274234671 F-TEST (value) 99.7867182102965 F-TEST (DF numerator) 2 F-TEST (DF denominator) 69 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.0530413350357076 Sum Squared Residuals 0.194123442343542 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 0.73 0.665993819927412 0.0640061800725882 2 0.74 0.684456609324917 0.055543390675083 3 0.75 0.717398061436018 0.032601938563982 4 0.74 0.699181571959072 0.0408184280409284 5 0.76 0.713783384632948 0.0462166153670518 6 0.76 0.773751673809433 -0.0137516738094333 7 0.78 0.780631533036057 -0.00063153303605741 8 0.79 0.792337613167214 -0.00233761316721433 9 0.89 0.841688216353727 0.0483117836462727 10 0.88 0.807062575801369 0.0729374241986308 11 0.88 0.822629632656152 0.0573703673438476 12 0.84 0.76676862012385 0.0732313798761501 13 0.76 0.741795421380557 0.0182045786194426 14 0.77 0.749640524788088 0.0203594752119119 15 0.76 0.737215500396581 0.0227844996034191 16 0.77 0.807801475563038 -0.0378014755630382 17 0.78 0.844603904397766 -0.0646039043977659 18 0.79 0.827352659101726 -0.0373526591017259 19 0.78 0.80334470453934 -0.0233447045393399 20 0.76 0.808294075404151 -0.0482940754041509 21 0.78 0.77173794648998 0.00826205351002031 22 0.76 0.783444026621137 -0.0234440266211367 23 0.74 0.76522753714419 -0.0252275371441901 24 0.73 0.773072640551721 -0.0430726405517209 25 0.72 0.845589104079991 -0.125589104079991 26 0.71 0.822546393698512 -0.112546393698512 27 0.73 0.829426252925136 -0.099426252925136 28 0.75 0.74943413587017 0.000565864129830549 29 0.75 0.706121297689652 0.0438787023103477 30 0.72 0.665704192051855 0.0542958079481452 31 0.72 0.707332841791115 0.0126671582088848 32 0.72 0.7084212359323 0.0115787640677000 33 0.74 0.711440118435298 0.0285598815647022 34 0.78 0.717354733481015 0.0626452665189847 35 0.74 0.702033976546789 0.0379660234532115 36 0.74 0.731114451934264 0.00888554806573639 37 0.75 0.718689427542756 0.0313105724572436 38 0.78 0.772866251633802 0.00713374836619783 39 0.81 0.777815622498613 0.0321843775013869 40 0.75 0.753807667936227 -0.00380766793622727 41 0.7 0.714355806479336 -0.0143558064793364 42 0.71 0.773358851474915 -0.0633588514749149 43 0.71 0.763829559626127 -0.0538295596261275 44 0.73 0.795805767556322 -0.0658057675563223 45 0.74 0.799789894240227 -0.0597898942402267 46 0.74 0.78157340476328 -0.0415734047632801 47 0.75 0.811619124331662 -0.0616191243316618 48 0.74 0.803055076663781 -0.0630550766637809 49 0.74 0.79159529645318 -0.0515952964531803 50 0.73 0.762761120986262 -0.0327611209862616 51 0.76 0.753231829137474 0.00676817086252592 52 0.8 0.83250500193209 -0.0325050019320905 53 0.83 0.902125732917641 -0.0721257329176413 54 0.81 0.87136106908891 -0.0613610690889093 55 0.83 0.888858614305506 -0.0588586143055058 56 0.88 0.877398834094905 0.00260116590509487 57 0.89 0.858217100437052 0.0317828995629480 58 0.93 0.941351249955295 -0.0113512499552947 59 0.91 0.91444756285019 -0.00444756285018907 60 0.9 0.890439608287803 0.00956039171219682 61 0.86 0.892493246609894 -0.0324932466098945 62 0.88 0.925434698720996 -0.0454346987209958 63 0.93 0.976715790269322 -0.0467157902693218 64 0.98 0.949812103164216 0.0301878968357837 65 0.97 0.92869988114455 0.0413001188554499 66 1.03 0.966467554160184 0.0635324458398158 67 1.06 0.99554802954766 0.0644519704523407 68 1.06 0.995671179507937 0.0643288204920626 69 1.08 1.00351628291547 0.0764837170845318 70 1.09 0.939933316935913 0.150066683064087 71 1.04 0.952604641247977 0.0873953587520234 72 1 0.986511337539985 0.0134886624600154

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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