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broodprijs trend met twee dummies

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

Title produced by software: Multiple Regression

Date of computation: Mon, 17 Dec 2007 09:21:19 -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/17/t119790750680y3mio5vx4ubgk.htm/, Retrieved Mon, 17 Dec 2007 17:05:07 +0100

User-defined keywords:

Dataseries X:

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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 5 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation y[t] = + 1.42075612518015 + 0.0466855397707776x[t] + 0.0575424644842497z[t] + 0.00161879761169445t + 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) 1.42075612518015 0.004615 307.8359 0 0 x 0.0466855397707776 0.007817 5.972 0 0 z 0.0575424644842497 0.008227 6.9943 0 0 t 0.00161879761169445 0.000163 9.9368 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.979240886159292 R-squared 0.958912713126035 Adjusted R-squared 0.957100038705124 F-TEST (value) 529.004382731076 F-TEST (DF numerator) 3 F-TEST (DF denominator) 68 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.0160562058128972 Sum Squared Residuals 0.0175305186672157 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1.43 1.42237492279184 0.0076250772081565 2 1.43 1.42399372040354 0.00600627959645836 3 1.43 1.42561251801524 0.00438748198476401 4 1.43 1.42723131562693 0.00276868437306952 5 1.43 1.42885011323862 0.00114988676137508 6 1.43 1.43046891085032 -0.000468910850319373 7 1.43 1.43208770846201 -0.00208770846201383 8 1.43 1.43370650607371 -0.00370650607370828 9 1.43 1.43532530368540 -0.00532530368540274 10 1.43 1.43694410129710 -0.00694410129709719 11 1.43 1.43856289890879 -0.00856289890879165 12 1.43 1.44018169652049 -0.0101816965204861 13 1.43 1.44180049413218 -0.0118004941321806 14 1.43 1.44341929174387 -0.013419291743875 15 1.43 1.44503808935557 -0.0150380893555695 16 1.43 1.44665688696726 -0.0166568869672639 17 1.43 1.44827568457896 -0.0182756845789584 18 1.43 1.44989448219065 -0.0198944821906528 19 1.44 1.45151327980235 -0.0115132798023473 20 1.48 1.45313207741404 0.0268679225859583 21 1.48 1.45475087502574 0.0252491249742639 22 1.48 1.45636967263743 0.0236303273625694 23 1.48 1.45798847024913 0.0220115297508750 24 1.48 1.45960726786082 0.0203927321391805 25 1.48 1.46122606547251 0.0187739345274861 26 1.48 1.46284486308421 0.0171551369157916 27 1.48 1.46446366069590 0.0155363393040971 28 1.48 1.46608245830760 0.0139175416924027 29 1.48 1.46770125591929 0.0122987440807082 30 1.48 1.46932005353099 0.0106799464690138 31 1.48 1.47093885114268 0.00906114885731933 32 1.48 1.47255764875438 0.00744235124562488 33 1.48 1.47417644636607 0.00582355363393042 34 1.48 1.47579524397776 0.00420475602223597 35 1.48 1.47741404158946 0.00258595841054151 36 1.48 1.47903283920115 0.00096716079884706 37 1.48 1.48065163681285 -0.000651636812847394 38 1.48 1.48227043442454 -0.00227043442454185 39 1.48 1.48388923203624 -0.0038892320362363 40 1.48 1.48550802964793 -0.00550802964793076 41 1.48 1.48712682725963 -0.00712682725962521 42 1.48 1.48874562487132 -0.00874562487131966 43 1.48 1.49036442248301 -0.0103644224830141 44 1.48 1.49198322009471 -0.0119832200947086 45 1.48 1.49360201770640 -0.0136020177064030 46 1.48 1.49522081531810 -0.0152208153180975 47 1.48 1.49683961292979 -0.0168396129297919 48 1.48 1.49845841054149 -0.0184584105414864 49 1.48 1.55761967263743 -0.0776196726374306 50 1.57 1.55923847024913 0.0107615297508750 51 1.58 1.56085726786082 0.0191427321391806 52 1.58 1.56247606547251 0.0175239345274861 53 1.58 1.56409486308421 0.0159051369157917 54 1.58 1.56571366069590 0.0142863393040972 55 1.59 1.61401799807837 -0.0240179980783748 56 1.6 1.61563679569007 -0.0156367956900693 57 1.6 1.61725559330176 -0.0172555933017637 58 1.61 1.61887439091346 -0.00887439091345817 59 1.61 1.62049318852515 -0.0104931885251526 60 1.61 1.62211198613685 -0.0121119861368471 61 1.62 1.62373078374854 -0.00373078374854152 62 1.63 1.62534958136024 0.00465041863976382 63 1.63 1.62696837897193 0.00303162102806937 64 1.64 1.62858717658363 0.0114128234163749 65 1.64 1.63020597419532 0.00979402580468047 66 1.64 1.63182477180701 0.00817522819298602 67 1.64 1.63344356941871 0.00655643058129156 68 1.64 1.63506236703040 0.00493763296959711 69 1.65 1.63668116464210 0.0133188353579027 70 1.65 1.63829996225379 0.0117000377462082 71 1.65 1.63991875986549 0.0100812401345138 72 1.65 1.64153755747718 0.0084624425228193

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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