review ws8

*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: Sat, 04 Dec 2010 09:33:17 +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/04/t1291455087jobi48ul2jx8qtk.htm/, Retrieved Sat, 04 Dec 2010 10:31:27 +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/04/t1291455087jobi48ul2jx8qtk.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 «

9084 0 9700 9081 9743 0 9081 9084 8587 0 9084 9743 9731 0 9743 8587 9563 0 8587 9731 9998 0 9731 9563 9437 0 9563 9998 10038 0 9998 9437 9918 0 9437 10038 9252 0 10038 9918 9737 0 9918 9252 9035 0 9252 9737 9133 0 9737 9035 9487 0 9035 9133 8700 0 9133 9487 9627 0 9487 8700 8947 0 8700 9627 9283 0 9627 8947 8829 0 8947 9283 9947 0 9283 8829 9628 0 8829 9947 9318 0 9947 9628 9605 0 9628 9318 8640 0 9318 9605 9214 0 9605 8640 9567 0 8640 9214 8547 0 9214 9567 9185 0 9567 8547 9470 0 8547 9185 9123 0 9185 9470 9278 0 9470 9123 10170 0 9123 9278 9434 0 9278 10170 9655 0 10170 9434 9429 0 9434 9655 8739 0 9655 9429 9552 0 9429 8739 9687 0 8739 9552 9019 0 9552 9687 9672 0 9687 9019 9206 0 9019 9672 9069 0 9672 9206 9788 0 9206 9069 10312 0 9069 9788 10105 0 9788 10312 9863 0 10312 10105 9656 0 10105 9863 9295 0 9863 9656 9946 0 9656 9295 9701 0 9295 9946 9049 0 9946 9701 10190 0 9701 9049 9706 0 9049 10190 9765 0 10190 9706 9893 0 9706 9765 9994 0 9765 9893 1 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 5 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Births[t] = + 5632.42646760897 + 233.327295316956x[t] + 0.184925679115300`y-1`[t] + 0.141855719535449`y-2`[t] + 485.518122007314M1[t] + 884.077057591996M2[t] -117.371735721934M3[t] + 921.654299160091M4[t] + 567.78584832305M5[t] + 616.785989141178M6[t] + 611.199861323609M7[t] + 1154.83556367848M8[t] + 916.246498776956M9[t] + 598.938676886247M10[t] + 725.272206498409M11[t] + 4.70384799637204t + 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) 5632.42646760897 1521.695785 3.7014 0.000485 0.000242 x 233.327295316956 122.061409 1.9116 0.060965 0.030483 `y-1` 0.184925679115300 0.130178 1.4206 0.160892 0.080446 `y-2` 0.141855719535449 0.129205 1.0979 0.276861 0.13843 M1 485.518122007314 176.827297 2.7457 0.008064 0.004032 M2 884.077057591996 177.463322 4.9817 6e-06 3e-06 M3 -117.371735721934 157.726562 -0.7441 0.459844 0.229922 M4 921.654299160091 196.252407 4.6963 1.7e-05 9e-06 M5 567.78584832305 191.711759 2.9617 0.004455 0.002228 M6 616.785989141178 162.79502 3.7887 0.000367 0.000184 M7 611.199861323609 159.618277 3.8291 0.000322 0.000161 M8 1154.83556367848 157.843079 7.3164 0 0 M9 916.246498776956 162.994281 5.6213 1e-06 0 M10 598.938676886247 161.398589 3.7109 0.000471 0.000235 M11 725.272206498409 158.07279 4.5882 2.5e-05 1.3e-05 t 4.70384799637204 2.45333 1.9173 0.060212 0.030106 Multiple Linear Regression - Regression Statistics Multiple R 0.882356647284765 R-squared 0.77855325300761 Adjusted R-squared 0.720277793272771 F-TEST (value) 13.3598817847191 F-TEST (DF numerator) 15 F-TEST (DF denominator) 57 p-value 1.54876111935209e-13 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 267.664628275107 Sum Squared Residuals 4083728.13409011 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 9084 9204.61931413246 -120.619314132463 2 9743 9493.83866949976 249.161330500238 3 8587 8591.13142039341 -4.13142039341149 4 9731 9592.74211402581 138.257885974188 5 9563 9192.08636927641 370.91363072359 6 9998 9433.51357411686 564.486425883143 7 9437 9463.2710182022 -26.2710182022101 8 10038 10012.4721803092 25.5278196907818 9 9918 9760.0989448612 157.901055138809 10 9252 9541.6126177709 -289.612617770896 11 9737 9555.98300467498 181.016995325014 12 9035 8781.05416785685 253.945832143149 13 9133 9261.38237711757 -128.382377117572 14 9487 9548.72919447416 -61.7291944741601 15 8700 8620.32389042545 79.6761095745493 16 9627 9617.87701243627 9.12298756373444 17 8947 9254.67615214122 -307.676152141217 18 9283 9383.3443562115 -100.344356211494 19 8829 9304.3761363558 -475.376136355804 20 9947 9850.4482182207 96.5517817793093 21 9628 9691.20143743783 -63.2014374378281 22 9318 9540.09239826259 -222.092398262588 23 9605 9568.16321117735 36.8367888226475 24 8640 8830.98048365625 -190.980483656246 25 9214 9237.38535421432 -23.385354214315 26 9567 9543.62004046245 23.3799595375478 27 8547 8703.09750395309 -156.09750395309 28 9185 9667.41331763303 -482.413317633031 29 9470 9220.12847115837 249.871528841628 30 9123 9432.24392331603 -309.243923316035 31 9278 9434.8415273639 -156.841527363899 32 10170 9940.99950359012 229.000496409876 33 9434 9862.31306877347 -428.313068773467 34 9655 9610.25699107189 44.7430089281129 35 9429 9636.5391828689 -207.539182868895 36 8739 8924.78000683633 -185.780006836327 37 9552 9275.3283268805 276.671673119504 38 9687 9666.32109185431 20.6789081456868 39 9019 8839.07124579478 179.92875420522 40 9672 9813.00647470406 -141.006474704063 41 9206 9432.94330307102 -226.943303071022 42 9069 9541.2989950443 -472.298995044292 43 9788 9434.80711517901 353.192884820990 44 10312 10059.8061098374 252.193890162559 45 10105 10033.2148532528 71.7851467472319 46 9863 9788.14780127101 74.8521987289898 47 9656 9846.5764791751 -190.576479175099 48 9295 9051.89197238332 243.108027616679 49 9946 9452.62441205784 493.375587942157 50 9701 9881.47709889585 -180.477098895851 51 9049 8970.36411939617 78.6358806038313 52 10190 9876.2972817542 313.702718245795 53 9706 9568.4185121203 137.581487879692 54 9765 9764.4645325502 0.535467449793721 55 9893 9682.4477114898 210.552288510204 56 9994 10259.8554090094 -265.855409009376 57 10433 10297.2954020210 135.704597978978 58 10073 10065.6435825934 7.35641740660755 59 10112 10226.7952743008 -114.795274300782 60 9266 9445.18604437912 -179.186044379119 61 9820 9822.61017714131 -2.61017714131218 62 10097 10148.0139048135 -51.0139048134611 63 9115 9293.0118200371 -178.011820037099 64 10411 10248.6637994466 162.336200553376 65 9678 9901.74719223267 -223.747192232672 66 10408 10091.1346187611 316.865381238885 67 10153 10058.2564914093 94.7435085907183 68 10368 10705.4185790332 -337.418579033151 69 10581 10454.8762936537 126.123706346277 70 10597 10212.2466090302 384.753390969774 71 10680 10384.9428478029 295.057152197114 72 9738 9679.10732488813 58.8926751118645 73 9556 10051.050038456 -495.050038455999 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 19 0.722416958132689 0.555166083734622 0.277583041867311 20 0.694757275701564 0.610485448596872 0.305242724298436 21 0.597392911243731 0.805214177512537 0.402607088756269 22 0.583922238097266 0.832155523805467 0.416077761902734 23 0.476526460963469 0.953052921926939 0.523473539036531 24 0.383682946082648 0.767365892165295 0.616317053917352 25 0.509918947750997 0.980162104498006 0.490081052249003 26 0.431390823401617 0.862781646803233 0.568609176598383 27 0.336067772354845 0.672135544709689 0.663932227645155 28 0.344518556101432 0.689037112202865 0.655481443898568 29 0.497821783578187 0.995643567156373 0.502178216421813 30 0.462961157724357 0.925922315448714 0.537038842275643 31 0.407167522464835 0.81433504492967 0.592832477535165 32 0.532559660479788 0.934880679040424 0.467440339520212 33 0.53161246076555 0.9367750784689 0.46838753923445 34 0.564035048406048 0.871929903187904 0.435964951593952 35 0.532193176938636 0.935613646122728 0.467806823061364 36 0.465282394551828 0.930564789103656 0.534717605448172 37 0.574605858158626 0.850788283682748 0.425394141841374 38 0.513267448129986 0.973465103740027 0.486732551870014 39 0.552088545837763 0.895822908324474 0.447911454162237 40 0.468435732481262 0.936871464962524 0.531564267518738 41 0.406984218252647 0.813968436505293 0.593015781747353 42 0.69446502839964 0.611069943200721 0.305534971600361 43 0.744496965357579 0.511006069284842 0.255503034642421 44 0.728528443001407 0.542943113997186 0.271471556998593 45 0.66122487451998 0.677550250960039 0.338775125480020 46 0.591943590782632 0.816112818434737 0.408056409217368 47 0.634965879046198 0.730068241907604 0.365034120953802 48 0.550837340144558 0.898325319710884 0.449162659855442 49 0.78590511568797 0.428189768624061 0.214094884312031 50 0.695163037145905 0.60967392570819 0.304836962854095 51 0.60515170020158 0.78969659959684 0.39484829979842 52 0.515026900603477 0.969946198793046 0.484973099396523 53 0.582099673288738 0.835800653422524 0.417900326711262 54 0.408364486409824 0.816728972819649 0.591635513590176 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 = 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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