*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: Thu, 19 Nov 2009 12:25:15 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/19/t1258658768dvfi8u0uvij335v.htm/, Retrieved Thu, 19 Nov 2009 20:26:20 +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/2009/Nov/19/t1258658768dvfi8u0uvij335v.htm/}, year = {2009}, } @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 = {2009}, 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:

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595 0 594 611 591 0 595 594 589 0 591 595 584 0 589 591 573 0 584 589 567 0 573 584 569 0 567 573 621 0 569 567 629 0 621 569 628 0 629 621 612 0 628 629 595 0 612 628 597 0 595 612 593 0 597 595 590 0 593 597 580 0 590 593 574 0 580 590 573 0 574 580 573 0 573 574 620 0 573 573 626 0 620 573 620 0 626 620 588 0 620 626 566 0 588 620 557 0 566 588 561 0 557 566 549 0 561 557 532 0 549 561 526 0 532 549 511 0 526 532 499 0 511 526 555 0 499 511 565 0 555 499 542 0 565 555 527 0 542 565 510 0 527 542 514 0 510 527 517 0 514 510 508 0 517 514 493 0 508 517 490 0 493 508 469 0 490 493 478 0 469 490 528 0 478 469 534 0 528 478 518 1 534 528 506 1 518 534 502 1 506 518 516 1 502 506 528 1 516 502 533 1 528 516 536 1 533 528 537 1 536 533 524 1 537 536 536 1 524 537 587 1 536 524 597 1 587 536 581 1 597 587

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 Y[t] = + 32.0112178808194 + 12.8517679356726X[t] + 0.912623590451367Y1[t] + 0.0121064299814901Y2[t] + 16.312803980732M1[t] + 16.7900026964816M2[t] + 10.8342316766507M3[t] + 6.12167292170496M4[t] + 9.48466383471706M5[t] + 3.23537468192878M6[t] + 15.9983473560093M7[t] + 65.6072237839268M8[t] + 27.1353181179752M9[t] + 4.52518290329523M10[t] -2.53197257686806M11[t] -0.281056311117769t + 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) 32.0112178808194 26.746814 1.1968 0.238087 0.119044 X 12.8517679356726 3.576842 3.593 0.000851 0.000425 Y1 0.912623590451367 0.150369 6.0692 0 0 Y2 0.0121064299814901 0.15013 0.0806 0.936111 0.468056 M1 16.312803980732 4.325219 3.7716 0.000502 0.000251 M2 16.7900026964816 5.357977 3.1336 0.003144 0.001572 M3 10.8342316766507 5.316689 2.0378 0.047903 0.023952 M4 6.12167292170496 4.810217 1.2726 0.210146 0.105073 M5 9.48466383471706 4.566352 2.0771 0.043948 0.021974 M6 3.23537468192878 4.825293 0.6705 0.506207 0.253104 M7 15.9983473560093 4.560623 3.5079 0.00109 0.000545 M8 65.6072237839268 5.464229 12.0067 0 0 M9 27.1353181179752 11.333842 2.3942 0.021199 0.010599 M10 4.52518290329523 5.787825 0.7818 0.438691 0.219346 M11 -2.53197257686806 4.613779 -0.5488 0.586059 0.293029 t -0.281056311117769 0.12654 -2.2211 0.031792 0.015896 Multiple Linear Regression - Regression Statistics Multiple R 0.99150564049245 R-squared 0.983083435128344 Adjusted R-squared 0.977041804817038 F-TEST (value) 162.718237375218 F-TEST (DF numerator) 15 F-TEST (DF denominator) 42 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 6.3018287623476 Sum Squared Residuals 1667.94792149796 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 595 597.538406997237 -2.53840699723690 2 591 598.441363682634 -7.44136368263409 3 589 588.566148419862 0.433851580138386 4 584 581.698860452969 2.30113954703075 5 573 580.193464242644 -7.19346424264373 6 567 563.563727133865 3.43627286613481 7 569 570.436731224323 -1.43673122432336 8 621 621.517159942137 -0.517159942136772 9 629 630.244837528502 -1.24483752850162 10 628 615.284169085352 12.7158309146477 11 612 607.130185143472 4.8698148565282 12 595 594.767017532019 0.232982467981304 13 597 595.090461284256 1.90953871574416 14 593 596.906041560105 -3.90604156010503 15 590 587.042932727314 2.95706727268607 16 580 579.26302116997 0.73697883002963 17 574 573.182400577406 0.817599422593482 18 573 561.055249270977 11.9447507290226 19 573 572.5519034636 0.448096536400176 20 620 621.867617150418 -1.86761715041804 21 626 626.007963924563 -0.00796392456298972 22 620 609.161516150603 10.8384838493965 23 588 596.420201396503 -8.42020139650315 24 566 569.394524187921 -3.39452418792072 25 557 564.961147108197 -7.96114710819718 26 561 556.677335739174 4.32266426082613 27 549 553.982044900197 -4.98204490019733 28 532 538.085372468643 -6.08537246864337 29 526 525.507428873086 0.492571126913469 30 511 513.295532556787 -2.29553255678695 31 499 512.01545648309 -13.0154564830903 32 555 550.210197064751 4.78980293524882 33 565 562.41887899318 2.58112100681942 34 542 549.33188345086 -7.33188345085994 35 527 521.124393379012 5.87560662098768 36 510 509.407507898418 0.592492101582176 37 514 509.743058080636 4.25694191936355 38 517 513.383885537388 3.61611446261162 39 508 509.93335469772 -1.93335469771984 40 493 496.762446607538 -3.76244660753850 41 490 486.046069482829 3.95393051717114 42 469 476.596256797846 -7.59625679784636 43 478 469.876758471386 8.12324152861406 44 528 527.163955872637 0.836044127363355 45 534 534.151131287969 -0.151131287969133 46 518 530.192770739627 -12.1927707396267 47 506 508.325220081013 -2.32522008101273 48 502 499.430950381643 2.56904961835724 49 516 511.666926529674 4.33307347032636 50 528 524.591373480699 3.40862651930139 51 533 529.475519254907 3.52448074509272 52 536 529.190299300879 6.80970069912149 53 537 535.070636824034 1.92936317596564 54 524 529.489234240524 -5.48923424052415 55 536 530.1191503576 5.88084964239938 56 587 590.241069970057 -3.24106997005736 57 597 598.177188265786 -1.17718826578568 58 581 585.029660573558 -4.02966057355759 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 19 0.0344739787319636 0.0689479574639272 0.965526021268036 20 0.00977607750869783 0.0195521550173957 0.990223922491302 21 0.00227413954927335 0.0045482790985467 0.997725860450727 22 0.0614957262071957 0.122991452414391 0.938504273792804 23 0.337832471478015 0.67566494295603 0.662167528521985 24 0.277662237525046 0.555324475050092 0.722337762474954 25 0.242578416835861 0.485156833671722 0.757421583164139 26 0.496626159021584 0.993252318043168 0.503373840978416 27 0.467616680123755 0.93523336024751 0.532383319876245 28 0.41834712709958 0.83669425419916 0.58165287290042 29 0.376302401268379 0.752604802536757 0.623697598731621 30 0.360064808239721 0.720129616479441 0.639935191760279 31 0.831674726267036 0.336650547465929 0.168325273732964 32 0.929782112968226 0.140435774063548 0.0702178870317741 33 0.922170572486452 0.155658855027097 0.0778294275135484 34 0.922823112968372 0.154353774063255 0.0771768870316277 35 0.966156467488886 0.0676870650222279 0.0338435325111139 36 0.937003067278525 0.125993865442951 0.0629969327214755 37 0.922381686622909 0.155236626754183 0.0776183133770914 38 0.953076963997935 0.0938460720041303 0.0469230360020651 39 0.994762307880292 0.0104753842394159 0.00523769211970797 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 1 0.0476190476190476 NOK 5% type I error level 3 0.142857142857143 NOK 10% type I error level 6 0.285714285714286 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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