*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 09:54:52 -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/t1258649774m7eevwb8g33ogp0.htm/, Retrieved Thu, 19 Nov 2009 17:56:26 +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/t1258649774m7eevwb8g33ogp0.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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344744 492865 338653 480961 327532 461935 326225 456608 318672 441977 317756 439148 337302 488180 349420 520564 336923 501492 330758 485025 321002 464196 320820 460170 327032 467037 324047 460070 316735 447988 315710 442867 313427 436087 310527 431328 330962 484015 339015 509673 341332 512927 339092 502831 323308 470984 325849 471067 330675 476049 332225 474605 331735 470439 328047 461251 326165 454724 327081 455626 346764 516847 344190 525192 343333 522975 345777 518585 344094 509239 348609 512238 354846 519164 356427 517009 353467 509933 355996 509127 352487 500857 355178 506971 374556 569323 375021 579714 375787 577992 372720 565464 364431 547344 370490 554788 376974 562325 377632 560854 378205 555332 370861 543599 369167 536662 371551 542722 382842 593530 381903 610763 384502 612613 392058 611324 384359 594167 388884 595454 386586 590865 387495 589379 385705 584428 378670 573100 377367 567456 376911 569028 389827 620735 387820 628884 3872 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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 107756.349835734 + 0.465346280212279X[t] + 4646.78857839405M1[t] + 5889.18188955366M2[t] + 6136.0129828292M3[t] + 6531.672854175M4[t] + 7278.30279838781M5[t] + 7017.24534200469M6[t] -1198.54933758642M7[t] -6602.51200200083M8[t] -6533.95173292422M9[t] -3172.51702113678M10[t] -2894.00700454304M11[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) 107756.349835734 5296.972888 20.343 0 0 X 0.465346280212279 0.009469 49.1424 0 0 M1 4646.78857839405 2326.470037 1.9974 0.050405 0.025202 M2 5889.18188955366 2329.062027 2.5286 0.014148 0.007074 M3 6136.0129828292 2336.641606 2.626 0.010988 0.005494 M4 6531.672854175 2345.091911 2.7853 0.00718 0.00359 M5 7278.30279838781 2356.913429 3.0881 0.003069 0.001535 M6 7017.24534200469 2355.050683 2.9797 0.004185 0.002093 M7 -1198.54933758642 2326.401335 -0.5152 0.608342 0.304171 M8 -6602.51200200083 2340.887441 -2.8205 0.006521 0.00326 M9 -6533.95173292422 2337.435952 -2.7954 0.006985 0.003492 M10 -3172.51702113678 2328.665265 -1.3624 0.178258 0.089129 M11 -2894.00700454304 2322.86763 -1.2459 0.217734 0.108867 Multiple Linear Regression - Regression Statistics Multiple R 0.988920632601208 R-squared 0.977964017584373 Adjusted R-squared 0.973482122855771 F-TEST (value) 218.203254829554 F-TEST (DF numerator) 12 F-TEST (DF denominator) 59 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4023.24052128466 Sum Squared Residuals 955001393.234303 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 344744 341756.032810954 2987.96718904641 2 338653 337458.944002466 1194.05599753383 3 327532 328852.096768423 -1320.09676842291 4 326225 326768.857005078 -543.857005077890 5 318672 320707.005523505 -2035.00552350486 6 317756 319129.483440401 -1373.48344040119 7 337302 333730.547572179 3571.45242782144 8 349420 343396.358846159 6023.64115384141 9 336923 334589.834859027 2333.16514097337 10 330758 330288.412374558 469.587625441537 11 321002 320874.224720611 127.775279389375 12 320820 321894.747601019 -1074.74760101903 13 327032 329737.069085631 -2705.06908563080 14 324047 327737.394862551 -3690.39486255146 15 316735 322361.912198302 -5626.91219830224 16 315710 320374.533768681 -4664.53376868096 17 313427 317966.115933055 -4539.11593305452 18 310527 315490.475529141 -4963.47552914117 19 330962 331792.380315094 -830.380315094416 20 339015 338328.272508367 686.727491633325 21 341332 339911.069573254 1420.93042674596 22 339092 338574.368240018 517.631759981688 23 323308 324032.995270692 -724.995270691583 24 325849 326965.626016492 -1116.62601649224 25 330675 333930.769762904 -3255.76976290386 26 332225 334501.203045437 -2276.20304543695 27 331735 332809.401535348 -1074.40153534812 28 328047 328929.459784103 -882.459784103503 29 326165 326638.774557371 -473.77455737077 30 327081 326797.459445739 283.54055426087 31 346764 347070.629387024 -306.629387023978 32 344190 345549.981430981 -1359.98143098104 33 343333 344586.868996827 -1253.86899682703 34 345777 345905.433538483 -128.433538482564 35 344094 341834.817220212 2259.18277978766 36 348609 346124.397719112 2484.602280888 37 354846 353994.174634256 851.825365743703 38 356427 354233.746711558 2193.25328844155 39 353467 351187.787526052 2279.21247394811 40 355996 351208.378295547 4787.6217044534 41 352487 348106.594502404 4380.40549759614 42 355178 350690.664203239 4487.33579676138 43 374556 371490.140787444 3065.85921255644 44 375021 370921.591320715 4099.40867928505 45 375787 370188.825295266 5598.17470473399 46 372720 367720.401808554 4999.59819144598 47 364431 359566.837227701 4864.16277229875 48 370490 365924.881942144 4565.11805785551 49 376974 374078.985434499 2895.01456550151 50 377632 374636.854367466 2995.14563253415 51 378205 372314.043301409 5890.95669859082 52 370861 367249.795267024 3611.20473297570 53 369167 364768.318065405 4398.68193459547 54 371551 367327.259067108 4223.74093289217 55 382842 382754.778192542 87.2218074577937 56 381903 385370.127975026 -3467.12797502602 57 384502 386299.578862495 -1797.57886249534 58 392058 389061.182219089 2996.81778091084 59 384359 381355.746106081 3003.25389391919 60 388884 384848.653773257 4035.34622674295 61 386586 387359.968271757 -773.96827175695 62 387495 387910.857010521 -415.857010521121 63 385705 385853.758670466 -148.75867046566 64 378670 380977.975879567 -2307.97587956675 65 377367 379098.191418261 -1731.19141826147 66 376911 379568.658314372 -2657.65831437206 67 389827 395414.523745717 -5587.52374571728 68 387820 393802.667918753 -5982.66791875273 69 387267 393567.822413131 -6300.82241313094 70 380575 389430.201819298 -8855.20181929749 71 372402 381931.379454703 -9529.3794547034 72 376740 385633.692947975 -8893.69294797517 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.00304819391745426 0.00609638783490853 0.996951806082546 17 0.00088281379700344 0.00176562759400688 0.999117186202997 18 0.00058986871609564 0.00117973743219128 0.999410131283904 19 0.00217219252978077 0.00434438505956154 0.99782780747022 20 0.00137770432856784 0.00275540865713568 0.998622295671432 21 0.00264268213814901 0.00528536427629802 0.99735731786185 22 0.00373631210848664 0.00747262421697328 0.996263687891513 23 0.00206786847422759 0.00413573694845518 0.997932131525772 24 0.00116703587295805 0.00233407174591610 0.998832964127042 25 0.000976561032553229 0.00195312206510646 0.999023438967447 26 0.00062734241856427 0.00125468483712854 0.999372657581436 27 0.000322325048177439 0.000644650096354878 0.999677674951823 28 0.000159920423282380 0.000319840846564759 0.999840079576718 29 8.21240665046418e-05 0.000164248133009284 0.999917875933495 30 4.21951197615399e-05 8.43902395230798e-05 0.999957804880238 31 0.000685316619325973 0.00137063323865195 0.999314683380674 32 0.00255843782114721 0.00511687564229443 0.997441562178853 33 0.00491040374545432 0.00982080749090863 0.995089596254546 34 0.00515098341891328 0.0103019668378266 0.994849016581087 35 0.00314921620258725 0.0062984324051745 0.996850783797413 36 0.00204495387539322 0.00408990775078644 0.997955046124607 37 0.00183487642336095 0.00366975284672191 0.998165123576639 38 0.00158243047203305 0.0031648609440661 0.998417569527967 39 0.00298661334725444 0.00597322669450889 0.997013386652746 40 0.00241349133481990 0.00482698266963981 0.99758650866518 41 0.00243982749497725 0.00487965498995449 0.997560172505023 42 0.00212938581193953 0.00425877162387906 0.99787061418806 43 0.00229487562186315 0.0045897512437263 0.997705124378137 44 0.00153562632701370 0.00307125265402739 0.998464373672986 45 0.000797286310377515 0.00159457262075503 0.999202713689622 46 0.000368893060013302 0.000737786120026603 0.999631106939987 47 0.000166064279037451 0.000332128558074902 0.999833935720963 48 7.37272943460321e-05 0.000147454588692064 0.999926272705654 49 3.80917532514781e-05 7.61835065029563e-05 0.999961908246749 50 1.95832797848147e-05 3.91665595696293e-05 0.999980416720215 51 7.89805379748756e-06 1.57961075949751e-05 0.999992101946203 52 2.87932402917856e-06 5.75864805835713e-06 0.99999712067597 53 8.8582979110376e-07 1.77165958220752e-06 0.999999114170209 54 2.54582050721663e-07 5.09164101443326e-07 0.99999974541795 55 6.2274978379137e-07 1.24549956758274e-06 0.999999377250216 56 1.05832552454630e-05 2.11665104909261e-05 0.999989416744755 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 40 0.97560975609756 NOK 5% type I error level 41 1 NOK 10% type I error level 41 1 NOK

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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