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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: Thu, 27 Nov 2008 15:25:06 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/27/t1227824734fvvhktejipdj72l.htm/, Retrieved Thu, 27 Nov 2008 22:25:43 +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/27/t1227824734fvvhktejipdj72l.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)

Feedback Forum:

2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc]  [reply]  test Post a new message

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

123,9 0 124,9 0 112,7 0 121,9 0 100,6 0 104,3 0 120,4 0 107,5 0 102,9 0 125,6 0 107,5 0 108,8 0 128,4 0 121,1 0 119,5 0 128,7 0 108,7 0 105,5 0 119,8 0 111,3 0 110,6 0 120,1 0 97,5 0 107,7 0 127,3 0 117,2 0 119,8 0 116,2 0 111 0 112,4 0 130,6 0 109,1 0 118,8 0 123,9 0 101,6 0 112,8 0 128 0 129,6 0 125,8 0 119,5 0 115,7 0 113,6 0 129,7 0 112 0 116,8 0 127 1 112,1 1 114,2 1 121,1 1 131,6 1 125 1 120,4 1 117,7 1 117,5 1 120,6 1 127,5 1 112,3 1 124,5 1 115,2 1 105,4 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 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Consumptieindex[t] = + 108.052592592593 + 4.31851851851852Dummy[t] + 16.8237037037037M1[t] + 15.9637037037037M2[t] + 11.6437037037037M3[t] + 12.4237037037037M4[t] + 1.82370370370369M5[t] + 1.7437037037037M6[t] + 15.3037037037037M7[t] + 4.5637037037037M8[t] + 3.36370370370369M9[t] + 14.44M10[t] -3.00000000000001M11[t] + 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) 108.052592592593 2.440387 44.2768 0 0 Dummy 4.31851851851852 1.602193 2.6954 0.009724 0.004862 M1 16.8237037037037 3.345477 5.0288 8e-06 4e-06 M2 15.9637037037037 3.345477 4.7717 1.8e-05 9e-06 M3 11.6437037037037 3.345477 3.4804 0.001091 0.000546 M4 12.4237037037037 3.345477 3.7136 0.000541 0.000271 M5 1.82370370370369 3.345477 0.5451 0.588245 0.294123 M6 1.7437037037037 3.345477 0.5212 0.604666 0.302333 M7 15.3037037037037 3.345477 4.5744 3.5e-05 1.7e-05 M8 4.5637037037037 3.345477 1.3641 0.17902 0.08951 M9 3.36370370370369 3.345477 1.0054 0.31983 0.159915 M10 14.44 3.330095 4.3362 7.6e-05 3.8e-05 M11 -3.00000000000001 3.330095 -0.9009 0.372248 0.186124 Multiple Linear Regression - Regression Statistics Multiple R 0.831779647608548 R-squared 0.6918573821758 Adjusted R-squared 0.613182671241963 F-TEST (value) 8.79389798785052 F-TEST (DF numerator) 12 F-TEST (DF denominator) 47 p-value 1.82025579054113e-08 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5.26534292248953 Sum Squared Residuals 1303.02029629630 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 123.9 124.876296296296 -0.97629629629647 2 124.9 124.016296296296 0.883703703703711 3 112.7 119.696296296296 -6.99629629629627 4 121.9 120.476296296296 1.42370370370371 5 100.6 109.876296296296 -9.27629629629632 6 104.3 109.796296296296 -5.4962962962963 7 120.4 123.356296296296 -2.95629629629628 8 107.5 112.616296296296 -5.11629629629629 9 102.9 111.416296296296 -8.5162962962963 10 125.6 122.492592592593 3.1074074074074 11 107.5 105.052592592593 2.44740740740741 12 108.8 108.052592592593 0.747407407407402 13 128.4 124.876296296296 3.52370370370375 14 121.1 124.016296296296 -2.91629629629630 15 119.5 119.696296296296 -0.196296296296296 16 128.7 120.476296296296 8.2237037037037 17 108.7 109.876296296296 -1.17629629629629 18 105.5 109.796296296296 -4.29629629629629 19 119.8 123.356296296296 -3.55629629629630 20 111.3 112.616296296296 -1.31629629629630 21 110.6 111.416296296296 -0.816296296296294 22 120.1 122.492592592593 -2.39259259259259 23 97.5 105.052592592593 -7.5525925925926 24 107.7 108.052592592593 -0.352592592592591 25 127.3 124.876296296296 2.42370370370374 26 117.2 124.016296296296 -6.81629629629629 27 119.8 119.696296296296 0.103703703703701 28 116.2 120.476296296296 -4.27629629629629 29 111 109.876296296296 1.12370370370371 30 112.4 109.796296296296 2.60370370370371 31 130.6 123.356296296296 7.2437037037037 32 109.1 112.616296296296 -3.5162962962963 33 118.8 111.416296296296 7.38370370370371 34 123.9 122.492592592593 1.40740740740742 35 101.6 105.052592592593 -3.4525925925926 36 112.8 108.052592592593 4.7474074074074 37 128 124.876296296296 3.12370370370375 38 129.6 124.016296296296 5.5837037037037 39 125.8 119.696296296296 6.1037037037037 40 119.5 120.476296296296 -0.976296296296296 41 115.7 109.876296296296 5.82370370370371 42 113.6 109.796296296296 3.8037037037037 43 129.7 123.356296296296 6.3437037037037 44 112 112.616296296296 -0.616296296296293 45 116.8 111.416296296296 5.38370370370371 46 127 126.811111111111 0.188888888888886 47 112.1 109.371111111111 2.72888888888888 48 114.2 112.371111111111 1.82888888888889 49 121.1 129.194814814815 -8.09481481481478 50 131.6 128.334814814815 3.26518518518518 51 125 124.014814814815 0.98518518518518 52 120.4 124.794814814815 -4.39481481481481 53 117.7 114.194814814815 3.50518518518519 54 117.5 114.114814814815 3.38518518518518 55 120.6 127.674814814815 -7.07481481481482 56 127.5 116.934814814815 10.5651851851852 57 112.3 115.734814814815 -3.43481481481481 58 124.5 126.811111111111 -2.31111111111111 59 115.2 109.371111111111 5.82888888888889 60 105.4 112.371111111111 -6.97111111111111 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.503340739056178 0.993318521887644 0.496659260943822 17 0.531300133388152 0.937399733223697 0.468699866611848 18 0.410686950487633 0.821373900975266 0.589313049512367 19 0.296162147077006 0.592324294154011 0.703837852922994 20 0.225713873316485 0.451427746632969 0.774286126683515 21 0.252994722262758 0.505989444525516 0.747005277737242 22 0.217278931907635 0.434557863815271 0.782721068092365 23 0.358187928041211 0.716375856082422 0.641812071958789 24 0.264616379968681 0.529232759937362 0.735383620031319 25 0.194810575265911 0.389621150531821 0.80518942473409 26 0.281082800442203 0.562165600884405 0.718917199557797 27 0.240978087643791 0.481956175287582 0.759021912356209 28 0.303239111095136 0.606478222190272 0.696760888904864 29 0.302253169495388 0.604506338990776 0.697746830504612 30 0.300799470813582 0.601598941627163 0.699200529186418 31 0.393775684821122 0.787551369642243 0.606224315178878 32 0.42911121631568 0.85822243263136 0.57088878368432 33 0.528269379776723 0.943461240446555 0.471730620223277 34 0.428751738633933 0.857503477267865 0.571248261366067 35 0.550962727269651 0.898074545460698 0.449037272730349 36 0.484502601838607 0.969005203677214 0.515497398161393 37 0.47080481354377 0.94160962708754 0.52919518645623 38 0.4312804054076 0.8625608108152 0.5687195945924 39 0.385838156446542 0.771676312893084 0.614161843553458 40 0.283454262268164 0.566908524536328 0.716545737731836 41 0.230945157629831 0.461890315259662 0.769054842370169 42 0.165655843518781 0.331311687037562 0.83434415648122 43 0.248553131372722 0.497106262745445 0.751446868627277 44 0.606187540553874 0.787624918892253 0.393812459446126 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 0 0 OK 10% type I error level 0 0 OK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

R code (references can be found in the software module):

library(lattice) library(lmtest) n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test 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)) if (n > n25) { kp3 <- k + 3 nmkm3 <- n - k - 3 gqarr <- array(NA, dim=c(nmkm3-kp3+1,3)) numgqtests <- 0 numsignificant1 <- 0 numsignificant5 <- 0 numsignificant10 <- 0 for (mypoint in kp3:nmkm3) { j <- 0 numgqtests <- numgqtests + 1 for (myalt in c('greater', 'two.sided', 'less')) { j <- j + 1 gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value } if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1 if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1 if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1 } gqarr } bitmap(file='test0.png') plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index') points(x[,1]-mysum$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') qqline(mysum$resid) grid() dev.off() (myerror <- as.ts(mysum$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() if (n > n25) { bitmap(file='test9.png') plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint') grid() 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') if (n > n25) { a<-table.start() a<-table.row.start(a) a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'p-values',header=TRUE) a<-table.element(a,'Alternative Hypothesis',3,header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'breakpoint index',header=TRUE) a<-table.element(a,'greater',header=TRUE) a<-table.element(a,'2-sided',header=TRUE) a<-table.element(a,'less',header=TRUE) a<-table.row.end(a) for (mypoint in kp3:nmkm3) { a<-table.row.start(a) a<-table.element(a,mypoint,header=TRUE) a<-table.element(a,gqarr[mypoint-kp3+1,1]) a<-table.element(a,gqarr[mypoint-kp3+1,2]) a<-table.element(a,gqarr[mypoint-kp3+1,3]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable5.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Description',header=TRUE) a<-table.element(a,'# significant tests',header=TRUE) a<-table.element(a,'% significant tests',header=TRUE) a<-table.element(a,'OK/NOK',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'1% type I error level',header=TRUE) a<-table.element(a,numsignificant1) a<-table.element(a,numsignificant1/numgqtests) if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'5% type I error level',header=TRUE) a<-table.element(a,numsignificant5) a<-table.element(a,numsignificant5/numgqtests) if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'10% type I error level',header=TRUE) a<-table.element(a,numsignificant10) a<-table.element(a,numsignificant10/numgqtests) if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable6.tab') }

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