earning merck

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R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Sun, 17 Apr 2011 22:56:49 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/Apr/18/t1303080843dzi683nqwrfvwnf.htm/, Retrieved Mon, 18 Apr 2011 00:54:13 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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0.79 4.372157 0.358171 0.768038 0.9 4.37581 0.402526 0.778505 0.83 4.378543 0.201355 0.756444 0.74 4.38421 0.210216 0.761823 0.88 4.390016 0.201257 0.761285 0.8 4.394889 0.194135 0.771903 0.856 4.4004 0.203109 0.789904 0.9 4.402502 0.215335 0.771369 0.8 4.406353 0.186933 0.771341 0.76 4.409155 0.212281 0.765422 0.82 4.415841 0.300082 0.756006 0.85 4.42116 0.316122 0.741814 0.5 4.427843 0.24835 0.751497 0.51 4.431814 0.24658 0.778627 0.73 4.437513 0.252709 0.799937 0.79 4.439901 0.286081 0.774228 0.64 4.441522 0.288254 0.771279 0.68 4.445791 0.326279 0.787727 0.62 4.449679 0.320449 0.762896 0.62 4.454067 0.27137 0.776688 0.72 4.461934 0.253831 0.770499 0.85 4.46565 0.288447 0.812129 0.81 4.47138 0.303094 0.796086 0.72 4.476353 0.327162 0.781913 0.67 4.482516 0.35257 0.811975 0.83 4.488015 0.275083 0.364749 0.83 4.491572 0.284799 0.368819 0.8 4.495281 0.26807 0.81384 0.81 4.499013 0.277758 0.820645 0.79 4.505014 0.288119 0.352631 0.77 4.512458 0.291262 0.344194 0.72 4.517143 0.298 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 9 seconds R Server 'Gwilym Jenkins' @ www.wessa.org Multiple Linear Regression - Estimated Regression Equation basiceps[t] = -23.9293930240113 + 5.70542661862854gdp[t] + 0.406023757176962`D/E`[t] -0.304011213321105GM[t] -0.0331158042092614t + 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) -23.9293930240113 13.45014 -1.7791 0.08118 0.04059 gdp 5.70542661862854 3.076833 1.8543 0.06948 0.03474 `D/E` 0.406023757176962 0.216751 1.8732 0.066773 0.033387 GM -0.304011213321105 0.110187 -2.759 0.008031 0.004015 t -0.0331158042092614 0.013768 -2.4053 0.019825 0.009912 Multiple Linear Regression - Regression Statistics Multiple R 0.830537538535335 R-squared 0.689792602916333 Adjusted R-squared 0.665462610988203 F-TEST (value) 28.3515343923639 F-TEST (DF numerator) 4 F-TEST (DF denominator) 51 p-value 2.02482475231136e-12 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.0848051288500866 Sum Squared Residuals 0.36678740384327 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 0.79 0.894445871277677 -0.104445871277677 2 0.9 0.896999088885986 0.00300091111401407 3 0.83 0.804502801747461 0.0254971982525388 4 0.74 0.805682150381863 -0.0656821503818628 5 0.88 0.802218044312576 0.0777819556874244 6 0.8 0.790785091754233 0.0092149082457671 7 0.856 0.787283044986148 0.0687169550138521 8 0.9 0.776758941823395 0.123241058176605 9 0.8 0.754091361085105 0.0459086389148948 10 0.76 0.74905349482981 0.0109465051701899 11 0.82 0.792596034481226 0.0274039655187736 12 0.85 0.800654542661022 0.0493454573389778 13 0.5 0.775207321894069 -0.275207321894069 14 0.51 0.755781280519776 -0.245781280519776 15 0.73 0.751190743261943 -0.0211907432619431 16 0.79 0.753065146925748 0.0369348530742524 17 0.64 0.730976657957713 -0.0909766579577131 18 0.68 0.732655996913325 -0.0526559969133246 19 0.62 0.726904675330925 -0.106904675330925 20 0.62 0.694704120491596 -0.0747041204915959 21 0.72 0.701233182213203 0.0187668177867968 22 0.85 0.690717674886645 0.159282325113355 23 0.81 0.701118247068805 0.108881752931195 24 0.72 0.710456460148117 0.00954353985188322 25 0.67 0.713680266716961 -0.0436802667169608 26 0.83 0.816438759499908 0.0135612405000921 27 0.83 0.806324758959622 0.0236752410403783 28 0.8 0.652286636481672 0.147713363518328 29 0.81 0.64232824626601 0.16767175373399 30 0.79 0.789939023334514 6.09766654858148e-05 31 0.77 0.803135490149919 -0.0331354901499185 32 0.72 0.785522315273001 -0.0655223152730008 33 0.82 0.759834991276226 0.0601650087237738 34 0.85 0.751525207476593 0.098474792523407 35 0.79 0.766901965451555 0.0230980345484453 36 0.72 0.738528525403457 -0.0185285254034574 37 0.77 0.762388110320703 0.00761188967929737 38 0.8 0.735655924823306 0.0643440751766939 39 0.74 0.73305990681925 0.00694009318075026 40 0.65 0.675086269094241 -0.0250862690942414 41 0.68 0.67844097690595 0.00155902309404949 42 0.65 0.642360750469111 0.00763924953088872 43 0.63 0.61836910923182 0.0116308907681797 44 0.55 0.598040750657327 -0.0480407506573266 45 0.59 0.575199021835068 0.014800978164932 46 0.575 0.512138306567366 0.062861693432634 47 0.55 0.508369989659441 0.0416300103405593 48 0.487 0.471498381670089 0.015501618329911 49 0.52 0.473735649274818 0.0462643507251817 50 0.495 0.488802163752189 0.00619783624781115 51 0.48 0.471094489547945 0.00890551045205517 52 0.42 0.457963423695985 -0.0379634236959848 53 0.435 0.46890087291711 -0.0339008729171104 54 0.415 0.471606909183836 -0.0566069091838363 55 0.4 0.479498969591847 -0.0794989695918467 56 0.35 0.475261861854795 -0.125261861854795 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.368092839961436 0.736185679922871 0.631907160038564 9 0.382460138951777 0.764920277903555 0.617539861048223 10 0.34122660687997 0.68245321375994 0.65877339312003 11 0.226436220099159 0.452872440198319 0.77356377990084 12 0.148344618132942 0.296689236265884 0.851655381867058 13 0.872472920056497 0.255054159887006 0.127527079943503 14 0.985646474885092 0.0287070502298167 0.0143535251149084 15 0.982290703899982 0.0354185922000358 0.0177092961000179 16 0.977393861633798 0.045212276732404 0.022606138366202 17 0.986570544684846 0.0268589106303088 0.0134294553151544 18 0.984559126421533 0.030881747156935 0.0154408735784675 19 0.993069269878225 0.0138614602435507 0.00693073012177535 20 0.998437660302903 0.00312467939419361 0.0015623396970968 21 0.999525498708933 0.000949002582132943 0.000474501291066471 22 0.999711721297219 0.000576557405562896 0.000288278702781448 23 0.999676318108198 0.000647363783603804 0.000323681891801902 24 0.999680243184748 0.00063951363050319 0.000319756815251595 25 0.99998241795985 3.51640803016937e-05 1.75820401508468e-05 26 0.999993407271242 1.31854575155473e-05 6.59272875777363e-06 27 0.999988856358854 2.22872822919315e-05 1.11436411459658e-05 28 0.999986197975699 2.76040486024493e-05 1.38020243012246e-05 29 0.999981468888422 3.7062223156699e-05 1.85311115783495e-05 30 0.999968580265748 6.28394685033558e-05 3.14197342516779e-05 31 0.999976750472135 4.64990557308652e-05 2.32495278654326e-05 32 0.9999997101245 5.79750998889227e-07 2.89875499444614e-07 33 0.999999107596307 1.78480738657014e-06 8.92403693285068e-07 34 0.999998258064936 3.48387012872599e-06 1.74193506436299e-06 35 0.999995544123983 8.91175203309586e-06 4.45587601654793e-06 36 0.999999228873563 1.54225287434799e-06 7.71126437173993e-07 37 0.999998478897744 3.04220451248575e-06 1.52110225624287e-06 38 0.999999849508878 3.00982243772086e-07 1.50491121886043e-07 39 0.999999758444063 4.83111873014692e-07 2.41555936507346e-07 40 0.99999914811774 1.70376451948906e-06 8.51882259744531e-07 41 0.9999979581732 4.08365360130456e-06 2.04182680065228e-06 42 0.99999128619672 1.74276065597068e-05 8.7138032798534e-06 43 0.999954919957823 9.01600843548167e-05 4.50800421774084e-05 44 0.999925475210096 0.000149049579807533 7.45247899037667e-05 45 0.999602320318834 0.000795359362331551 0.000397679681165775 46 0.999197407416852 0.00160518516629618 0.00080259258314809 47 0.99558959491874 0.00882081016251913 0.00441040508125957 48 0.994105188375519 0.0117896232489629 0.00589481162448144 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 28 0.682926829268293 NOK 5% type I error level 35 0.853658536585366 NOK 10% type I error level 35 0.853658536585366 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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