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

Title produced by software: Multiple Regression

Date of computation: Tue, 15 Jan 2008 08:50:26 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Jan/15/t1200411981qo8t8r5al9onuhw.htm/, Retrieved Tue, 15 Jan 2008 16:46:32 +0100

User-defined keywords:

Dataseries X:

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589 122302.01 100.01 606 109264.65 100.73 566 103674.75 100.46 487 103890.3 100.99 442 75512.66 100.8 463 83121.3 101.24 547 125096.81 101.05 432 74206.73 101.11 513 88481.63 100.86 602 111598.17 100.92 637 146919.48 101.43 913 150790.85 101.55 576 113780.5 101.49 634 110870.76 101.11 563 118785.32 100.43 513 112820.5 99.79 483 102188.92 99.09 477 97092.73 99.69 524 114067.82 100.08 470 89690.15 99.53 427 89267.9 99.58 537 96198.64 99.41 662 129599.75 99.5 1079 169424.7 100.42 816 152510.91 99.9 705 121850.2 100.02 653 144737.64 99.92 584 121381.88 99.55 508 106894.86 99.74 446 94305.06 99.76 604 116800.42 99.86 446 77584.28 99.75 512 100680.88 99.92 533 106634.05 99.86 791 168390.77 99.66 1206 211971.89 99.5 783 136163.28 99.28 567 168950.25 99.6 473 89816.88 100.15 412 85406.93 100.28 314 66055.52 100.44 323 73311.68 100.3 438 85674.51 100.87 429 82822.59 100.45 468 94277.63 100.64 518 100991.65 100.13 555 149245.88 99.9 816 208517.17 100.11 673 40733.51 99.14 593 121352.23 99.79 569 104020.11 100.31 505 99566.82 100.43 447 101352.17 100.92 433 106628.41 101.48 549 109696.95 101.64 553 248696.37 102.41 505 105628.33 102.74 601 120449.17 102.77 706 136547.7 102.37 852 140896.42 102 643 131509.91 102.45 448 95450.31 102.51 551 133592.64 102.34 476 110332.9 102.55 416 88110.54 102.25 331 64931.25 102.56 435 98446.22 102.8 395 84212.38 103.09 405 77519.55 102.65 619 124806.02 103.29 596 102185.94 104 889 151348.79 104.01 668 124378.28 103.59 555 101433.13 103.59 620 126724.22 103.84 472 87461.88 103.61 460 95288.27 103.76 417 129055.33 104.12 582 107753.06 103.95 525 96364.03 104.03 507 71662.75 104.52 750 125666.24 104.79 899 456841.51 104.91 1075 167642.32 105.1 993 167154.73 105.22 777 139685.18 105.64 675 119275.2 105.2 655 122746.05 105.19 535 107337.43 105.23 491 112584.89 105.22 686 133183.08 105.65 637 121152.57 105.93 652 119815.6 105.65 794 122858.44 106.55 859 152077.17 107.44 1049 157221.96 107.74 1022 140435.08 107.44 762 101455.09 108.2 762 104791.29 108.86 563 77226.59 108.82 573 84477.43 108.37 473 66227.74 108.35 527 89076.23 107.61 710 108924.43 107.98 630 83926.11 107.8 706 91764.8 107.44 870 120892.76 107.46 1069 129952.42 107.18 1021 135865.14 107.75 799 105512.77 108.28 694 96486.62 108.64 521 78064.88 108.52 622 92370.22 108.58 614 98454.46 108.09 661 96703.93 108.68 630 83170.95 109.18

Text written by user:

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 compuational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation omzet[t] = + 351434.690358891 + 157.708811974345aantal[t] -3229.20992140079koers[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) 351434.690358891 115174.921702 3.0513 0.00284 0.00142 aantal 157.708811974345 20.050545 7.8656 0 0 koers -3229.20992140079 1152.682171 -2.8015 0.005986 0.002993 Multiple Linear Regression - Regression Statistics Multiple R 0.594886203238485 R-squared 0.3538895948035 Adjusted R-squared 0.342454012410642 F-TEST (value) 30.946355213575 F-TEST (DF numerator) 2 F-TEST (DF denominator) 113 p-value 1.9157120334512e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 36132.9729289891 Sum Squared Residuals 147531865793.637 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 122302.01 121371.896372487 930.113627513356 2 109264.65 121727.915032643 -12463.2650326426 3 103674.75 116291.449232447 -12616.6992324468 4 103890.3 102120.971828131 1769.32817186889 5 75512.66 95637.6251743517 -20124.9651743517 6 83121.3 97528.6578603966 -14407.3578603966 7 125096.81 111389.747951308 13707.0620486923 8 74206.73 93059.481978974 -18852.7519789741 9 88481.63 106641.198229246 -18159.5682292462 10 111598.17 120483.529899679 -8885.35989967878 11 146919.48 124356.441258866 22563.0387411336 12 150790.85 167496.568173217 -16705.7181732175 13 113780.5 114542.451133147 -761.95113314739 14 110870.76 124916.661997792 -14045.9019977917 15 118785.32 115915.199094166 2870.12090583429 16 112820.5 110096.452845145 2724.04715485501 17 102188.92 107625.635430895 -5436.71543089522 18 97092.73 104741.856606209 -7649.1266062087 19 114067.82 110894.778899657 3173.04110034343 20 89690.15 104154.568509812 -14464.4185098124 21 89267.9 97211.6290988455 -7943.72909884555 22 96198.64 115108.564102662 -18909.9241026616 23 129599.75 134531.536706529 -4931.78670652859 24 169424.7 197325.238172142 -27900.5381721416 25 152510.91 157527.009782017 -5016.09978201734 26 121850.2 139633.826462297 -17783.6264622970 27 144737.64 131755.889231771 12981.7507682289 28 121381.88 122068.788876460 -686.908876459676 29 106894.86 109469.369281343 -2574.50928134334 30 94305.06 99626.838740506 -5321.77874050593 31 116800.42 124221.910040312 -7421.49004031232 32 77584.28 99659.13083972 -22074.8508397199 33 100680.88 109518.946743389 -8838.06674338855 34 106634.05 113024.584390134 -6390.53439013385 35 168390.77 154359.299863795 14031.4701362050 36 211971.89 220325.130420572 -8353.24042057208 37 136163.28 154324.729138132 -18161.4491381325 38 168950.25 119226.278576826 49723.9714231742 39 89816.88 102625.584794467 -12808.7047944669 40 85406.93 92585.5499742498 -7178.61997424981 41 66055.52 76613.4128133399 -10557.8928133399 42 73311.68 78484.8815101051 -5173.20151010514 43 85674.51 94780.7452319563 -9106.23523195629 44 82822.59 94717.6340911755 -11895.0440911755 45 94277.63 100254.727873109 -5977.09787310882 46 100991.65 109787.065531740 -8795.41553174049 47 149245.88 116365.009856713 32880.8701432866 48 208517.17 156848.875698523 51668.2943014768 49 40733.51 137428.849209951 -96695.3392099507 50 121352.23 122713.157803093 -1360.92780309257 51 104020.11 117248.95715658 -13228.8471565799 52 99566.82 106768.087999654 -7201.26799965372 53 101352.17 96038.6640436554 5313.50595634464 54 106628.41 92022.38312003 14606.0268799699 55 109696.95 109799.93172163 -102.981721629949 56 248696.37 107944.275330049 140752.094669951 57 105628.33 99308.613081218 6319.71691878208 58 120449.17 114351.782733113 6097.38726688701 59 136547.7 132202.891958979 4344.80804102054 60 140896.42 156423.186178152 -15526.7661781521 61 131509.91 122008.900010884 9501.00998911631 62 95450.31 91061.9290806024 4388.38091939757 63 133592.64 107854.902400598 25737.7375994019 64 110332.9 95348.607419028 14984.2925809719 65 88110.54 86854.8416769876 1255.69832301237 66 64931.25 72448.5375835341 -7517.28758353408 67 98446.22 88075.2436477297 10370.9763522703 68 84212.38 80830.4202915497 3381.95970845029 69 77519.55 83828.3607767095 -6308.8107767095 70 124806.02 115511.352189523 9294.66781047726 71 102185.94 109591.310469918 -7405.37046991827 72 151348.79 155767.700279187 -4418.91027918722 73 124378.28 122270.320999845 2107.95900015459 74 101433.13 104449.225246744 -3016.09524674445 75 126724.22 113892.995544727 12831.2244552733 76 87461.88 91294.8096544459 -3832.92965444584 77 95288.27 88917.9224225436 6370.34757745643 78 129055.33 80973.9279359425 48081.4020640575 79 107753.06 107544.847598347 208.212401652519 80 96364.03 98297.1085220978 -1933.07852209777 81 71662.75 93876.0370450732 -22213.2870450732 82 125666.24 131327.391676061 -5661.1516760607 83 456841.51 154438.49946967 302403.01053033 84 167642.32 181581.700492089 -13939.3804920885 85 167154.73 168262.072719624 -1107.34271962412 86 139685.18 132840.701166177 6844.47883382264 87 119275.2 118175.254710211 1099.94528978946 88 122746.05 115053.370569938 7692.67943006233 89 107337.43 95999.1447361603 11338.2852638397 90 112584.89 89092.2491085031 23492.6408914969 91 133183.08 118456.907177298 14726.1728227020 92 121152.57 109824.996612563 11327.5733874372 93 119815.6 113094.807570170 6720.79242982976 94 122858.44 132583.169941267 -9724.7299412665 95 152077.17 139960.245889552 12116.9241104478 96 157221.96 168956.157188257 -11734.1971882575 97 140435.08 165666.782241370 -25231.7022413704 98 101455.09 122208.291587776 -20753.2015877761 99 104791.29 120077.013039652 -15285.7230396516 100 77226.59 88822.127853613 -11595.5378536131 101 84477.43 91852.3604379869 -7374.93043798687 102 66227.74 76146.0634389804 -9918.32343898044 103 89076.23 87051.9546274316 2024.27537256837 104 108924.43 114717.859547818 -5793.4295478184 105 83926.11 102682.412375723 -18756.3023757230 106 91764.8 115830.797657477 -24065.9976574775 107 120892.76 141630.458622842 -20737.698622842 108 129952.42 173918.690983729 -43966.2709837287 109 135865.14 164508.018353762 -28642.8783537618 110 105512.77 127785.180837115 -22272.4108371148 111 96486.62 110063.240008104 -13576.6200081044 112 78064.88 83167.1207271108 -5102.24072711084 113 92370.22 98901.9581412356 -6531.7381412356 114 98454.46 99222.6005069272 -768.140506927211 115 96703.93 104729.680816095 -8025.75081609495 116 83170.95 98226.1026841899 -15055.1526841899

Charts produced by software:

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Parameters (Session):

par1 = 2 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ; par4 = FALSE ;

Parameters (R input):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ; par4 = FALSE ;

R code (references can be found in the software module):

library(lattice) 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)) 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$resid, main='Residual Normal Q-Q Plot') grid() dev.off() (myerror <- as.ts(mysum$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() 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')

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

Privacy Policy

We may request personal information to be submitted to our servers in order to be able to:

• personalize online software applications according to your needs
• enforce strict security rules with respect to the data that you upload (e.g. statistical data)
• manage user sessions of online applications
• alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

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