ws7

*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: Tue, 23 Nov 2010 12:18:38 +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/Nov/23/t1290514753t85vzlmsxvyt21s.htm/, Retrieved Tue, 23 Nov 2010 13:19:39 +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/Nov/23/t1290514753t85vzlmsxvyt21s.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:

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184 40 74 11 31 20 213 32 72 11 43 18 347 57 70 18 16 16 565 31 71 11 25 19 327 67 72 9 29 24 260 25 68 8 32 15 325 34 68 12 24 14 102 33 62 13 28 11 38 36 69 7 25 12 226 31 66 9 58 15 137 35 60 13 21 9 369 30 81 4 77 36 109 44 66 9 37 12 809 32 67 11 37 16 29 30 65 12 35 11 245 16 64 10 42 14 118 29 64 12 21 10 148 36 62 7 81 27 387 30 59 15 31 16 98 23 56 15 50 15 608 33 46 22 24 8 218 35 54 14 27 13 254 38 54 20 22 11 697 44 45 26 18 8 827 28 57 12 23 11 693 35 57 9 60 18 448 31 61 19 14 12 942 39 52 17 31 10 1017 27 44 21 24 9 216 36 43 18 23 8 673 38 48 19 22 10 989 46 57 14 25 12 630 29 47 19 25 9 404 32 50 19 21 9 692 39 48 16 32 11 1517 44 49 13 31 14 879 33 72 13 13 22 631 43 59 14 21 13 1375 22 49 9 46 13 1139 30 54 13 27 12 3545 86 62 22 18 15 706 30 47 17 39 11 451 32 45 34 15 10 433 43 48 26 23 12 601 20 69 23 7 12 1024 55 42 23 23 11 457 44 49 18 30 12 1441 37 57 15 35 13 1022 82 72 22 15 16 1244 66 67 26 18 16

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' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Crimerate[t] = + 1171.26771409283 + 21.0103219132378Funding[t] -23.9108325876178`25+HSgraduate`[t] -7.09689304546211`Dropouts16-19`[t] -6.5648075481889`CollegeStudents18-24`[t] + 26.2734721567441`25+CollegeGrads`[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) 1171.26771409283 920.597682 1.2723 0.209953 0.104976 Funding 21.0103219132378 5.998317 3.5027 0.00107 0.000535 `25+HSgraduate` -23.9108325876178 12.75304 -1.8749 0.067452 0.033726 `Dropouts16-19` -7.09689304546211 19.593344 -0.3622 0.71893 0.359465 `CollegeStudents18-24` -6.5648075481889 8.609098 -0.7625 0.449805 0.224902 `25+CollegeGrads` 26.2734721567441 26.805098 0.9802 0.332363 0.166181 Multiple Linear Regression - Regression Statistics Multiple R 0.579348289671035 R-squared 0.335644440744753 Adjusted R-squared 0.260149490829384 F-TEST (value) 4.44591911274881 F-TEST (DF numerator) 5 F-TEST (DF denominator) 44 p-value 0.00230284525919422 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 493.499245200084 Sum Squared Residuals 10715826.2205743 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 184 486.173564779561 -302.173564779561 2 213 234.588019757143 -21.5880197571431 3 347 882.692340932702 -535.692340932702 4 565 381.928538455668 183.071461544332 5 327 1233.6912114265 -906.6912114265 6 260 197.842242411182 62.1577575888176 7 325 384.792555677241 -59.7925556772414 8 102 395.070689581261 -293.070689581261 9 38 379.275080281733 -341.275080281733 10 226 193.943949767472 32.0560502325284 11 137 478.319707106806 -341.319707106806 12 369 276.767176143313 92.2328238566865 13 109 526.118676681298 -417.118676681298 14 809 340.984083670878 468.015916329122 15 29 221.450466286834 -192.450466286834 16 245 -1.72265818704375 246.722658187044 17 118 289.984810479114 -171.984810479114 18 148 573.123768047641 -425.123768047641 19 387 501.25137365263 -114.251373652630 20 98 274.906802450486 -176.906802450486 21 608 661.21078729651 -53.2107872965103 22 218 680.392852924894 -462.392852924894 23 254 681.119553819291 -427.119553819291 24 697 927.236434037029 -230.236434037029 25 827 449.494173739568 377.505826260432 26 693 558.873532082838 134.126467917162 27 448 452.560297901019 -4.56029790101876 28 942 685.885479953707 256.114520046293 29 1017 616.340886194525 400.659113805475 30 216 830.926630529115 -614.926630529115 31 673 805.407970233716 -132.407970233716 32 989 826.63003914729 162.369960852710 33 630 594.258010800883 35.7419891991172 34 404 611.815708970498 -207.815708970498 35 692 808.334367958195 -116.334367958195 36 1517 996.151048091574 520.848951908426 37 879 543.4426706521 335.557329347899 38 631 768.310110581841 -137.310110581841 39 1375 437.565952802613 937.434047197387 40 1139 556.164664247423 582.835335752577 41 3545 1615.48767768257 1929.51232231743 42 706 590.101757443888 115.898242556112 43 451 690.578793672533 -239.578793672533 44 433 906.76346524697 -473.76346524697 45 601 47.7261768099338 553.273823190066 46 1024 1297.36953071117 -273.369530711173 47 457 914.684446098964 -457.684446098964 48 1441 591.065645557543 849.934354442457 49 1022 1338.30595895475 -316.305958954752 50 1244 1073.61297645462 170.387023545379 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.0148708488024318 0.0297416976048637 0.985129151197568 10 0.0103049347191107 0.0206098694382213 0.98969506528089 11 0.00263411226467303 0.00526822452934606 0.997365887735327 12 0.00120938099638855 0.00241876199277709 0.998790619003611 13 0.000360336764615707 0.000720673529231414 0.999639663235384 14 0.00776592716627426 0.0155318543325485 0.992234072833726 15 0.00429833189186616 0.00859666378373231 0.995701668108134 16 0.00172336613530696 0.00344673227061393 0.998276633864693 17 0.000861641086505882 0.00172328217301176 0.999138358913494 18 0.000495780867374771 0.000991561734749542 0.999504219132625 19 0.000179094345671992 0.000358188691343984 0.999820905654328 20 9.36609231010158e-05 0.000187321846202032 0.999906339076899 21 6.8632824701065e-05 0.00013726564940213 0.9999313671753 22 4.05731542604472e-05 8.11463085208944e-05 0.99995942684574 23 2.26132406784822e-05 4.52264813569645e-05 0.999977386759322 24 1.28592512865821e-05 2.57185025731641e-05 0.999987140748713 25 5.41325695651078e-05 0.000108265139130216 0.999945867430435 26 0.000143836801387097 0.000287673602774194 0.999856163198613 27 5.50283007853729e-05 0.000110056601570746 0.999944971699215 28 0.000127948348802981 0.000255896697605962 0.999872051651197 29 0.000150364213064534 0.000300728426129068 0.999849635786936 30 0.000202462996224516 0.000404925992449033 0.999797537003775 31 8.36988531055383e-05 0.000167397706211077 0.999916301146894 32 0.000148311466881279 0.000296622933762557 0.999851688533119 33 5.72101955597952e-05 0.000114420391119590 0.99994278980444 34 2.52450014706135e-05 5.04900029412271e-05 0.99997475499853 35 1.21530895831621e-05 2.43061791663242e-05 0.999987846910417 36 4.12944674743667e-05 8.25889349487334e-05 0.999958705532526 37 1.72170431611879e-05 3.44340863223757e-05 0.999982782956839 38 1.42908300143164e-05 2.85816600286328e-05 0.999985709169986 39 2.47357962928637e-05 4.94715925857275e-05 0.999975264203707 40 1.31996869004974e-05 2.63993738009949e-05 0.9999868003131 41 0.495822757989960 0.991645515979921 0.504177242010040 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 29 0.878787878787879 NOK 5% type I error level 32 0.96969696969697 NOK 10% type I error level 32 0.96969696969697 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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Software written by Ed van Stee & Patrick Wessa

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