ws 7 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: Fri, 20 Nov 2009 11:31:00 -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/20/t1258741909a8n2psawu1u5lke.htm/, Retrieved Fri, 20 Nov 2009 19:32:02 +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/20/t1258741909a8n2psawu1u5lke.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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2360 8.1 2214 7.4 2825 7.3 2355 7.7 2333 8 3016 8 2155 7.7 2172 6.9 2150 6.6 2533 6.9 2058 7.5 2160 7.9 2260 7.7 2498 6.5 2695 6.1 2799 6.4 2947 6.8 2930 7.1 2318 7.3 2540 7.2 2570 7 2669 7 2450 7 2842 7.3 3440 7.5 2678 7.2 2981 7.7 2260 8 2844 7.9 2546 8 2456 8 2295 7.9 2379 7.9 2479 8 2057 8.1 2280 8.1 2351 8.2 2276 8 2548 8.3 2311 8.5 2201 8.6 2725 8.7 2408 8.7 2139 8.5 1898 8.4 2537 8.5 2069 8.7 2063 8.7 2524 8.6 2437 7.9 2189 8.1 2793 8.2 2074 8.5 2622 8.6 2278 8.5 2144 8.3 2427 8.2 2139 8.7 1828 9.3 2072 9.3 1800 8.8 1758 7.4 2246 7.2 1987 7.5 1868 8.3 2514 8.8 2121 8.9

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] = + 4034.67414588099 -212.018661728933X[t] + 149.111280543151M1[t] -155.569382420216M2[t] + 125.531550666231M3[t] + 18.9031937939464M4[t] + 42.8421256459596M5[t] + 429.378880296264M6[t] -10.3214307325519M7[t] -131.409330864466M8[t] -134.291943506517M9[t] + 94.7117888392695M10[t] -220.682612642051M11[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) 4034.67414588099 453.024601 8.9061 0 0 X -212.018661728933 52.75716 -4.0188 0.000183 9.1e-05 M1 149.111280543151 167.757815 0.8888 0.378027 0.189013 M2 -155.569382420216 173.688078 -0.8957 0.374398 0.187199 M3 125.531550666231 173.017748 0.7255 0.471253 0.235626 M4 18.9031937939464 170.09019 0.1111 0.91192 0.45596 M5 42.8421256459596 168.148178 0.2548 0.799855 0.399927 M6 429.378880296264 167.687287 2.5606 0.013278 0.006639 M7 -10.3214307325519 167.70619 -0.0615 0.951153 0.475576 M8 -131.409330864466 177.088114 -0.7421 0.461269 0.230634 M9 -134.291943506517 178.337931 -0.753 0.454709 0.227354 M10 94.7117888392695 176.644335 0.5362 0.594041 0.297021 M11 -220.682612642051 175.268148 -1.2591 0.213405 0.106702 Multiple Linear Regression - Regression Statistics Multiple R 0.64418846056054 R-squared 0.414978772719358 Adjusted R-squared 0.284974055545882 F-TEST (value) 3.19202857974467 F-TEST (DF numerator) 12 F-TEST (DF denominator) 54 p-value 0.0016767257417023 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 276.877096315935 Sum Squared Residuals 4139690.02907454 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 2360 2466.43426641978 -106.434266419778 2 2214 2310.16666666667 -96.1666666666658 3 2825 2612.46946592601 212.530534073993 4 2355 2421.03364436215 -66.0336443621488 5 2333 2381.36697769548 -48.3669776954822 6 3016 2767.90373234579 248.096267654213 7 2155 2391.80901983565 -236.809019835651 8 2172 2440.33604908688 -268.336049086882 9 2150 2501.05903496351 -351.059034963512 10 2533 2666.45716879062 -133.457168790618 11 2058 2223.85157027194 -165.851570271939 12 2160 2359.72671822242 -199.726718222416 13 2260 2551.24173111135 -291.241731111353 14 2498 2500.98346222271 -2.98346222270652 15 2695 2866.89186000073 -171.891860000726 16 2799 2696.65790460976 102.342095390238 17 2947 2635.7893717702 311.210628229798 18 2930 2958.72052790183 -28.7205279018265 19 2318 2476.61648452722 -158.616484527224 20 2540 2376.73045056820 163.269549431797 21 2570 2416.25157027194 153.748429728062 22 2669 2645.25530261773 23.7446973822750 23 2450 2329.86090113641 120.139098863595 24 2842 2486.93791525978 355.062084740224 25 3440 2593.64546345714 846.35453654286 26 2678 2352.57039901245 325.429600987547 27 2981 2527.66200123443 453.337998765567 28 2260 2357.42804584347 -97.4280458434689 29 2844 2402.56884386838 441.431156131625 30 2546 2767.90373234579 -221.903732345787 31 2456 2328.20342131697 127.796578683029 32 2295 2228.31738735795 66.6826126420505 33 2379 2225.4347747159 153.565225284101 34 2479 2433.23664088879 45.763359111208 35 2057 2096.64037323458 -39.6403732345787 36 2280 2317.32298587663 -37.3229858766295 37 2351 2445.23240024689 -94.232400246887 38 2276 2182.95546962931 93.044530370693 39 2548 2400.45080419707 147.549195802927 40 2311 2251.418714979 59.5812850209976 41 2201 2254.15578065812 -53.1557806581225 42 2725 2619.49066913553 105.509330864466 43 2408 2179.79035810672 228.209641893282 44 2139 2101.10619032059 37.8938096794103 45 1898 2119.42544385143 -221.425443851432 46 2537 2327.22731002433 209.772689975674 47 2069 1969.42917619722 99.570823802781 48 2063 2190.11178883927 -127.111788839270 49 2524 2360.42493555531 163.575064444686 50 2437 2204.1573358022 232.842664197800 51 2189 2442.85453654286 -253.85453654286 52 2793 2315.02431349768 477.975686502318 53 2074 2275.35764683102 -201.357646831016 54 2622 2640.69253530843 -18.6925353084269 55 2278 2222.19409045250 55.8059095474956 56 2144 2143.50992266638 0.490077333623784 57 2427 2161.82917619722 265.170823802781 58 2139 2284.82357767854 -145.823577678539 59 1828 1842.21797915986 -14.2179791598589 60 2072 2062.90059180191 9.09940819809035 61 1800 2318.02120320953 -518.021203209527 62 1758 2310.16666666667 -552.166666666667 63 2246 2633.6713320989 -387.6713320989 64 1987 2463.43737670794 -476.437376707936 65 1868 2317.76137917680 -449.761379176802 66 2514 2598.28880296264 -84.28880296264 67 2121 2137.38662576093 -16.3866257609312 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.243585764529288 0.487171529058576 0.756414235470712 17 0.255602054878227 0.511204109756455 0.744397945121773 18 0.206355725446027 0.412711450892054 0.793644274553973 19 0.127333817143743 0.254667634287485 0.872666182856257 20 0.155539102904025 0.311078205808051 0.844460897095975 21 0.200247470969106 0.400494941938213 0.799752529030894 22 0.137789324294898 0.275578648589796 0.862210675705102 23 0.113457450162302 0.226914900324604 0.886542549837698 24 0.165887385911855 0.331774771823710 0.834112614088145 25 0.775184527400033 0.449630945199935 0.224815472599967 26 0.792569819531496 0.414860360937009 0.207430180468504 27 0.867237380298591 0.265525239402817 0.132762619701409 28 0.816903462334444 0.366193075331113 0.183096537665556 29 0.91126352784083 0.17747294431834 0.08873647215917 30 0.890423120252179 0.219153759495642 0.109576879747821 31 0.869468948953047 0.261062102093907 0.130531051046953 32 0.82391896602947 0.35216206794106 0.17608103397053 33 0.786289245297884 0.427421509404232 0.213710754702116 34 0.724228411633905 0.551543176732189 0.275771588366095 35 0.653883002726569 0.692233994546863 0.346116997273431 36 0.611479766146738 0.777040467706524 0.388520233853262 37 0.57763523212851 0.84472953574298 0.42236476787149 38 0.493046044798612 0.986092089597225 0.506953955201388 39 0.430461746397717 0.860923492795433 0.569538253602283 40 0.353046587211779 0.706093174423557 0.646953412788221 41 0.313072664583677 0.626145329167354 0.686927335416323 42 0.244745341111718 0.489490682223437 0.755254658888282 43 0.207372876098845 0.414745752197689 0.792627123901155 44 0.143058175088548 0.286116350177095 0.856941824911452 45 0.166110710453573 0.332221420907146 0.833889289546427 46 0.158851377101226 0.317702754202452 0.841148622898774 47 0.137795902344098 0.275591804688196 0.862204097655902 48 0.0940173949073892 0.188034789814778 0.905982605092611 49 0.257436976606669 0.514873953213338 0.74256302339333 50 0.308264046101571 0.616528092203142 0.691735953898429 51 0.417755435977154 0.835510871954307 0.582244564022846 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 = 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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