Experiment 2

*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: Mon, 20 Dec 2010 18:51:12 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/20/t1292870958hhfarkq8vrseto4.htm/, Retrieved Mon, 20 Dec 2010 19:49:18 +0100

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/2010/Dec/20/t1292870958hhfarkq8vrseto4.htm/}, year = {2010}, } @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 = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

-999,0 -999,0 38,6 6654,000 5712,000 645,0 3 5 3 6,3 2,0 4,5 1,000 6,600 42,0 3 1 3 -999,0 -999,0 14,0 3,385 44,500 60,0 1 1 1 -999,0 -999,0 -999,0 0,920 5,700 25,0 5 2 3 2,1 1,8 69,0 2547,000 4603,000 624,0 3 5 4 9,1 0,7 27,0 10,550 179,500 180,0 4 4 4 15,8 3,9 19,0 0,023 0,300 35,0 1 1 1 5,2 1.0 30,4 160,000 169,000 392,0 4 5 4 10,9 36,0 28,0 3,300 25,600 63,0 1 2 1 8,3 1,4 50,0 52,160 440,000 230,0 1 1 1 11,0 1,5 7,0 0,425 6,400 112,0 5 4 4 3,2 0,7 30,0 465,000 423,000 281,0 5 5 5 7,6 2,7 -999,0 0,550 2,400 -999,0 2 1 2 -999,0 -999,0 40,0 187,100 419,000 365,0 5 5 5 6,3 2,1 3,5 0,075 1,200 42,0 1 1 1 8,6 0,0 50,0 3,000 25,000 28,0 2 2 2 6,6 4,1 6,0 0,785 3,500 42,0 2 2 2 9,5 1,2 10,4 0,200 5,000 120,0 2 2 2 4,8 1,3 34,0 1,410 17,500 -999,0 1 2 1 12,0 6,1 7,0 60,000 81,000 -999,0 1 1 1 -999,0 0,3 28,0 529,000 680,000 400,0 5 5 5 3,3 0,5 20,0 27,660 115,000 148,0 5 5 5 11,0 3,4 3,9 0,120 1,000 16,0 3 1 2 -999,0 -999,0 39,3 207,000 406,000 252,0 1 4 1 4,7 1,5 41,0 85,000 325,000 310,0 etc...

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 R Framework error message The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'. Multiple Linear Regression - Estimated Regression Equation PS[t] = -90.7471201795934 + 0.747139236735807SWS[t] + 0.0480756077894083L[t] -0.0585083359047774wb[t] + 0.0501497584438397wbr[t] + 0.00720177972023492tg[t] -56.5039953128544P[t] -57.1689370103844S[t] + 138.812334264370`D `[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) -90.7471201795934 72.068777 -1.2592 0.213485 0.106743 SWS 0.747139236735807 0.077462 9.6453 0 0 L 0.0480756077894083 0.129588 0.371 0.712125 0.356063 wb -0.0585083359047774 0.099518 -0.5879 0.559084 0.279542 wbr 0.0501497584438397 0.099368 0.5047 0.615869 0.307935 tg 0.00720177972023492 0.118331 0.0609 0.951699 0.475849 P -56.5039953128544 59.041082 -0.957 0.342898 0.171449 S -57.1689370103844 37.237168 -1.5353 0.130667 0.065334 `D ` 138.812334264370 75.848946 1.8301 0.072859 0.036429 Multiple Linear Regression - Regression Statistics Multiple R 0.833238085909915 R-squared 0.694285707810819 Adjusted R-squared 0.64814015427283 F-TEST (value) 15.0455602886905 F-TEST (DF numerator) 8 F-TEST (DF denominator) 53 p-value 3.10692582772276e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 236.662993065487 Sum Squared Residuals 2968496.73119589 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 -999 -972.417066374995 -26.5829336250051 2 2 104.507231909130 -102.507231909130 3 -999 -808.861036911555 -190.138963088445 4 -999 -865.175527205112 -133.824472794888 5 1.8 100.344272334967 -98.5442723349672 6 0.7 27.5884350960561 -26.8884350960561 7 3.9 -52.6237202240226 56.5237202240226 8 1 -40.0747538350533 41.0747538350533 9 36 -111.742252120272 147.742252120272 10 1.4 -36.3321739339346 37.7321739339346 11 1.5 -37.0357551293571 38.5357551293571 12 0.7 34.8136750447066 -34.1136750447066 13 2.7 -32.7550513743712 35.4550513743712 14 -999 -696.824694923363 -302.175305076637 15 2.1 -60.3742100865744 62.4742100865744 16 0 -30.3592696863851 30.3592696863851 17 4.1 -34.8166738290208 38.9166738290208 18 1.2 -31.7672465358652 32.9672465358652 19 1.3 -123.955270169048 125.255270169048 20 6.1 -62.9484658039572 69.0484658039572 21 0.3 -704.06445301863 704.36445301863 22 0.5 43.5917062115877 -43.0917062115877 23 3.4 -31.2389908916701 34.6389908916701 24 -999 -971.552830497154 -27.4471695028457 25 1.5 -160.904923271592 162.404923271592 26 -999 -806.899990478353 -192.100009521647 27 3.4 -5.39976290496808 8.79976290496808 28 0.8 17.0743302765808 -16.2743302765808 29 0.8 43.5154066418439 -42.7154066418439 30 -999 -808.180065665823 -190.819934334177 31 -999 -735.464665757749 -263.535334242251 32 1.4 73.6839016844503 -72.2839016844503 33 2 -50.7080699716821 52.7080699716821 34 1.9 8.25043138964159 -6.35043138964159 35 2.4 -163.653339341744 166.053339341744 36 2.8 57.908703948864 -55.108703948864 37 1.3 51.705311240132 -50.405311240132 38 2 50.9000137358092 -48.9000137358092 39 5.6 -111.257913381615 116.857913381615 40 3.1 -109.914079233409 113.014079233409 41 1 -697.19254289099 698.19254289099 42 1.8 -26.7774061899964 28.5774061899964 43 0.9 24.659448644068 -23.759448644068 44 1.8 26.8159145288091 -25.0159145288091 45 1.9 14.5864947280278 -12.6864947280278 46 0.9 42.1025911505248 -41.2025911505248 47 -999 -784.033079060675 -214.966920939325 48 2.6 107.384730511693 -104.784730511693 49 2.4 -56.9534893618164 59.3534893618164 50 1.2 -80.207049141829 81.407049141829 51 0.9 -33.6797321794282 34.5797321794282 52 0.5 48.2523739160418 -47.7523739160418 53 -999 -705.487628024838 -293.512371975162 54 0.6 44.9187110621161 -44.3187110621161 55 -999 -785.056733092375 -213.943266907625 56 2.2 -179.543555101573 181.743555101573 57 2.3 25.4868920512075 -23.1868920512075 58 0.5 -644.8466856103 645.3466856103 59 -999 -86.5489283910512 -912.451071608949 60 0.6 79.0357590634919 -78.4357590634919 61 6.6 -112.312474699383 118.912474699383 62 2.6 -34.1847788682181 36.7847788682181 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 12 0.000246978458117911 0.000493956916235823 0.999753021541882 13 1.99337427561908e-05 3.98674855123816e-05 0.999980066257244 14 1.08838234503863e-06 2.17676469007725e-06 0.999998911617655 15 5.02492959669024e-08 1.00498591933805e-07 0.999999949750704 16 2.35559126978631e-09 4.71118253957262e-09 0.999999997644409 17 9.1580238955034e-11 1.83160477910068e-10 0.99999999990842 18 3.95044996609602e-12 7.90089993219204e-12 0.99999999999605 19 1.47601259810091e-13 2.95202519620182e-13 0.999999999999852 20 5.06193861256486e-15 1.01238772251297e-14 0.999999999999995 21 0.363090168096487 0.726180336192974 0.636909831903513 22 0.290096601400035 0.58019320280007 0.709903398599965 23 0.221553351245751 0.443106702491502 0.778446648754249 24 0.167660270357316 0.335320540714633 0.832339729642684 25 0.134072969854929 0.268145939709857 0.865927030145071 26 0.112699852941344 0.225399705882687 0.887300147058656 27 0.0763234693853996 0.152646938770799 0.9236765306146 28 0.049457993371618 0.098915986743236 0.950542006628382 29 0.0515021794804365 0.103004358960873 0.948497820519563 30 0.0590941017851865 0.118188203570373 0.940905898214814 31 0.0574179358711955 0.114835871742391 0.942582064128805 32 0.0370605577419927 0.0741211154839855 0.962939442258007 33 0.0230106907760334 0.0460213815520667 0.976989309223967 34 0.0343220837172896 0.0686441674345792 0.96567791628271 35 0.0310223190524516 0.0620446381049032 0.968977680947548 36 0.0198475034714068 0.0396950069428136 0.980152496528593 37 0.0120769111502844 0.0241538223005688 0.987923088849716 38 0.00739785752522244 0.0147957150504449 0.992602142474778 39 0.00521820701390976 0.0104364140278195 0.99478179298609 40 0.00467567757710391 0.00935135515420782 0.995324322422896 41 0.0571047654470387 0.114209530894077 0.942895234552961 42 0.0392076570128015 0.078415314025603 0.960792342987199 43 0.0235735197561388 0.0471470395122776 0.976426480243861 44 0.0159017397229546 0.0318034794459093 0.984098260277045 45 0.00876705562416511 0.0175341112483302 0.991232944375835 46 0.0183179143743212 0.0366358287486424 0.981682085625679 47 0.0179989788308315 0.035997957661663 0.982001021169169 48 0.0262310505957606 0.0524621011915212 0.97376894940424 49 0.0155361264021624 0.0310722528043247 0.984463873597838 50 0.0584109672903242 0.116821934580648 0.941589032709676 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 10 0.256410256410256 NOK 5% type I error level 21 0.538461538461538 NOK 10% type I error level 27 0.692307692307692 NOK

Charts produced by software:

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Parameters (Session):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = First Differences ;

Parameters (R input):

par1 = 2 ; par2 = Do not include Seasonal 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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