*Unverified author*

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 15:48:46 -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/t1227826144c6g36malfg7161o.htm/, Retrieved Thu, 27 Nov 2008 22:49:04 +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/t1227826144c6g36malfg7161o.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 «

2120.88 0 2174.56 0 2196.72 0 2350.44 0 2440.25 0 2408.64 0 2472.81 0 2407.6 0 2454.62 0 2448.05 0 2497.84 0 2645.64 0 2756.76 0 2849.27 0 2921.44 0 2981.85 0 3080.58 0 3106.22 0 3119.31 0 3061.26 0 3097.31 0 3161.69 0 3257.16 0 3277.01 0 3295.32 0 3363.99 0 3494.17 0 3667.03 0 3813.06 0 3917.96 0 3895.51 0 3801.06 0 3570.12 0 3701.61 0 3862.27 0 3970.1 0 4138.52 0 4199.75 0 4290.89 0 4443.91 0 4502.64 1 4356.98 1 4591.27 1 4696.96 1 4621.4 1 4562.84 1 4202.52 1 4296.49 1 4435.23 1 4105.18 1 4116.68 1 3844.49 1 3720.98 1 3674.4 1 3857.62 1 3801.06 1 3504.37 1 3032.6 1 3047.03 1 2962.34 1 2197.82 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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Bel20[t] = + 2428.57204344262 -356.705111904762dummy[t] + 36.0613393442623t + 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) 2428.57204344262 169.07626 14.3638 0 0 dummy -356.705111904762 261.800892 -1.3625 0.178306 0.089153 t 36.0613393442623 7.064803 5.1044 4e-06 2e-06 Multiple Linear Regression - Regression Statistics Multiple R 0.684147682972147 R-squared 0.468058052116158 Adjusted R-squared 0.44971522632706 F-TEST (value) 25.5172271436142 F-TEST (DF numerator) 2 F-TEST (DF denominator) 58 p-value 1.12218107028994e-08 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 551.778787430368 Sum Squared Residuals 17658670.1549714 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 2120.88 2464.63338278688 -343.753382786883 2 2174.56 2500.69472213115 -326.134722131148 3 2196.72 2536.75606147541 -340.03606147541 4 2350.44 2572.81740081967 -222.377400819672 5 2440.25 2608.87874016393 -168.628740163935 6 2408.64 2644.94007950820 -236.300079508197 7 2472.81 2681.00141885246 -208.191418852459 8 2407.6 2717.06275819672 -309.462758196722 9 2454.62 2753.12409754098 -298.504097540984 10 2448.05 2789.18543688525 -341.135436885246 11 2497.84 2825.24677622951 -327.406776229508 12 2645.64 2861.30811557377 -215.668115573771 13 2756.76 2897.36945491803 -140.609454918033 14 2849.27 2933.43079426230 -84.1607942622953 15 2921.44 2969.49213360656 -48.0521336065575 16 2981.85 3005.55347295082 -23.7034729508199 17 3080.58 3041.61481229508 38.9651877049178 18 3106.22 3077.67615163934 28.5438483606554 19 3119.31 3113.73749098361 5.57250901639325 20 3061.26 3149.79883032787 -88.5388303278687 21 3097.31 3185.86016967213 -88.5501696721313 22 3161.69 3221.92150901639 -60.2315090163935 23 3257.16 3257.98284836066 -0.822848360655949 24 3277.01 3294.04418770492 -17.0341877049179 25 3295.32 3330.10552704918 -34.7855270491802 26 3363.99 3366.16686639344 -2.17686639344292 27 3494.17 3402.22820573771 91.9417942622951 28 3667.03 3438.28954508197 228.740454918033 29 3813.06 3474.35088442623 338.709115573770 30 3917.96 3510.41222377049 407.547776229508 31 3895.51 3546.47356311475 349.036436885246 32 3801.06 3582.53490245902 218.525097540984 33 3570.12 3618.59624180328 -48.4762418032788 34 3701.61 3654.65758114754 46.9524188524591 35 3862.27 3690.7189204918 171.551079508197 36 3970.1 3726.78025983607 243.319740163934 37 4138.52 3762.84159918033 375.678400819673 38 4199.75 3798.90293852459 400.84706147541 39 4290.89 3834.96427786885 455.925722131148 40 4443.91 3871.02561721311 572.884382786885 41 4502.64 3550.38184465262 952.258155347385 42 4356.98 3586.44318399688 770.536816003122 43 4591.27 3622.50452334114 968.76547665886 44 4696.96 3658.5658626854 1038.39413731460 45 4621.4 3694.62720202966 926.772797970335 46 4562.84 3730.68854137393 832.151458626074 47 4202.52 3766.74988071819 435.770119281811 48 4296.49 3802.81122006245 493.678779937548 49 4435.23 3838.87255940671 596.357440593286 50 4105.18 3874.93389875098 230.246101249024 51 4116.68 3910.99523809524 205.684761904762 52 3844.49 3947.0565774395 -102.566577439501 53 3720.98 3983.11791678376 -262.137916783763 54 3674.4 4019.17925612802 -344.779256128025 55 3857.62 4055.24059547229 -197.620595472287 56 3801.06 4091.30193481655 -290.241934816550 57 3504.37 4127.36327416081 -622.993274160812 58 3032.6 4163.42461350507 -1130.82461350507 59 3047.03 4199.48595284934 -1152.45595284934 60 2962.34 4235.5472921936 -1273.20729219360 61 2197.82 4271.60863153786 -2073.78863153786 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 6 0.0012330501597322 0.0024661003194644 0.998766949840268 7 0.000125332951525888 0.000250665903051775 0.999874667048474 8 8.15331396600582e-05 0.000163066279320116 0.99991846686034 9 1.65492720622308e-05 3.30985441244616e-05 0.999983450727938 10 4.41401464272651e-06 8.82802928545303e-06 0.999995585985357 11 7.40282257035088e-07 1.48056451407018e-06 0.999999259717743 12 1.40417003325124e-07 2.80834006650248e-07 0.999999859582997 13 5.56947619943806e-08 1.11389523988761e-07 0.999999944305238 14 2.80843676756801e-08 5.61687353513602e-08 0.999999971915632 15 1.18125593732797e-08 2.36251187465593e-08 0.99999998818744 16 3.8978740359724e-09 7.7957480719448e-09 0.999999996102126 17 1.71590256364918e-09 3.43180512729836e-09 0.999999998284097 18 4.33066365861056e-10 8.66132731722113e-10 0.999999999566934 19 8.83584220202666e-11 1.76716844040533e-10 0.999999999911642 20 3.86926459350303e-11 7.73852918700607e-11 0.999999999961307 21 1.97304112114701e-11 3.94608224229402e-11 0.99999999998027 22 8.67806485928243e-12 1.73561297185649e-11 0.999999999991322 23 3.09560668577837e-12 6.19121337155674e-12 0.999999999996904 24 1.5776227578459e-12 3.1552455156918e-12 0.999999999998422 25 1.38486941806839e-12 2.76973883613678e-12 0.999999999998615 26 1.29187477914848e-12 2.58374955829696e-12 0.999999999998708 27 1.24722715147477e-12 2.49445430294953e-12 0.999999999998753 28 4.43851527985131e-12 8.87703055970262e-12 0.999999999995561 29 4.64352925849488e-11 9.28705851698977e-11 0.999999999953565 30 3.55856654936341e-10 7.11713309872682e-10 0.999999999644143 31 4.15818643074891e-10 8.31637286149782e-10 0.999999999584181 32 3.42512833089105e-10 6.8502566617821e-10 0.999999999657487 33 3.7498040499142e-08 7.4996080998284e-08 0.99999996250196 34 4.17836420960822e-07 8.35672841921645e-07 0.99999958216358 35 1.09037549341319e-06 2.18075098682639e-06 0.999998909624507 36 1.83757417686924e-06 3.67514835373848e-06 0.999998162425823 37 1.96484304001420e-06 3.92968608002839e-06 0.99999803515696 38 1.6483350570102e-06 3.2966701140204e-06 0.999998351664943 39 1.24509599887680e-06 2.49019199775360e-06 0.999998754904001 40 1.43964371575192e-06 2.87928743150385e-06 0.999998560356284 41 2.62705444356474e-06 5.25410888712948e-06 0.999997372945556 42 4.17174897800175e-05 8.3434979560035e-05 0.99995828251022 43 5.8979329744877e-05 0.000117958659489754 0.999941020670255 44 3.73782631232077e-05 7.47565262464155e-05 0.999962621736877 45 1.96483749238310e-05 3.92967498476619e-05 0.999980351625076 46 1.32596565831383e-05 2.65193131662766e-05 0.999986740343417 47 0.00149409000424195 0.00298818000848389 0.998505909995758 48 0.00550129038968393 0.0110025807793679 0.994498709610316 49 0.004722443313809 0.009444886627618 0.995277556686191 50 0.0236802876805794 0.0473605753611587 0.97631971231942 51 0.0412564855876425 0.082512971175285 0.958743514412358 52 0.145517235257287 0.291034470514575 0.854482764742713 53 0.379099579726071 0.758199159452142 0.620900420273929 54 0.683475025735152 0.633049948529696 0.316524974264848 55 0.609789324695531 0.780421350608938 0.390210675304469 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 43 0.86 NOK 5% type I error level 45 0.9 NOK 10% type I error level 46 0.92 NOK

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) 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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