Home » date » 2007 » Nov » 22 » attachments

WS_03: Q3

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

Title produced by software: Multiple Regression

Date of computation: Thu, 22 Nov 2007 06:36:57 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2007/Nov/22/t1195738658pr04x52dhbikwj5.htm/, Retrieved Thu, 22 Nov 2007 14:37:39 +0100

User-defined keywords:

Christel Stuer, Steven Coomans

Dataseries X:

» Textbox « » Textfile « » CSV «

527 0 516 0 503 0 489 0 479 0 475 0 524 0 552 0 532 0 511 0 492 0 492 0 493 0 481 0 462 0 457 0 442 0 439 0 488 0 521 0 501 0 485 0 464 0 460 0 467 0 460 0 448 0 443 0 436 0 431 0 484 0 510 0 513 0 503 0 471 0 471 1 476 1 475 1 470 1 461 1 455 1 456 1 517 1 525 1 523 1 519 1 509 1 512 1 519 1 517 1 510 1 509 1 501 1 507 1 569 1 580 1 578 1 565 1 547 1 555 1 562 1 561 1 555 1 544 1 537 1 543 1 594 1 611 1 613 1 611 1 594 1 595 1 591 1 589 1 584 1 573 1 567 1 569 1 621 1 629 1 628 1 612 1 595 1 597 1 593 1 590 1 580 1 574 1 573 1 573 1 620 1 626 1

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 6 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation y[t] = + 448.89250965251 -7.84630630630631x[t] + 10.4152697340197M1[t] + 3.81710317460317M2[t] -7.53106338481338M3[t] -17.0042299442299M4[t] -26.2273965036465M5[t] -27.5755630630631M6[t] + 23.7012703775204M7[t] + 39.1031038181038M8[t] + 33.4771702059202M9[t] + 20.0397179322179M10[t] -0.826305770055772M11[t] + 1.72316655941656t + 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) 448.89250965251 11.848193 37.887 0 0 x -7.84630630630631 11.26193 -0.6967 0.488055 0.244028 M1 10.4152697340197 14.517438 0.7174 0.475251 0.237625 M2 3.81710317460317 14.516335 0.263 0.793281 0.39664 M3 -7.53106338481338 14.518154 -0.5187 0.605415 0.302707 M4 -17.0042299442299 14.522893 -1.1709 0.245221 0.12261 M5 -26.2273965036465 14.530549 -1.805 0.074936 0.037468 M6 -27.5755630630631 14.541118 -1.8964 0.061612 0.030806 M7 23.7012703775204 14.554593 1.6284 0.107465 0.053732 M8 39.1031038181038 14.570967 2.6836 0.00889 0.004445 M9 33.4771702059202 15.025097 2.2281 0.028756 0.014378 M10 20.0397179322179 15.036654 1.3327 0.186502 0.093251 M11 -0.826305770055772 15.05102 -0.0549 0.956358 0.478179 t 1.72316655941656 0.205936 8.3675 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.880000929800104 R-squared 0.774401636449048 Adjusted R-squared 0.736801909190556 F-TEST (value) 20.5959376014928 F-TEST (DF numerator) 13 F-TEST (DF denominator) 78 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 28.0288528529369 Sum Squared Residuals 61278.0941956242 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 527 461.030945945946 65.9690540540539 2 516 456.155945945946 59.844054054054 3 503 446.530945945946 56.469054054054 4 489 438.780945945946 50.2190540540541 5 479 431.280945945946 47.7190540540541 6 475 431.655945945946 43.344054054054 7 524 484.655945945946 39.3440540540541 8 552 501.780945945946 50.219054054054 9 532 497.878178893179 34.1218211068211 10 511 486.163893178893 24.8361068211068 11 492 467.021036036036 24.978963963964 12 492 469.570508365508 22.4294916344916 13 493 481.708944658945 11.2910553410554 14 481 476.833944658945 4.16605534105536 15 462 467.208944658945 -5.20894465894465 16 457 459.458944658945 -2.45894465894465 17 442 451.958944658945 -9.95894465894465 18 439 452.333944658945 -13.3339446589447 19 488 505.333944658945 -17.3339446589447 20 521 522.458944658945 -1.45894465894465 21 501 518.556177606178 -17.5561776061776 22 485 506.841891891892 -21.8418918918919 23 464 487.699034749035 -23.6990347490347 24 460 490.248507078507 -30.2485070785071 25 467 502.386943371943 -35.3869433719434 26 460 497.511943371943 -37.5119433719434 27 448 487.886943371943 -39.8869433719434 28 443 480.136943371943 -37.1369433719434 29 436 472.636943371943 -36.6369433719434 30 431 473.011943371943 -42.0119433719434 31 484 526.011943371943 -42.0119433719434 32 510 543.136943371943 -33.1369433719434 33 513 539.234176319176 -26.2341763191763 34 503 527.519890604891 -24.5198906048906 35 471 508.377033462033 -37.3770334620335 36 471 503.080199485199 -32.0801994851994 37 476 515.218635778636 -39.2186357786358 38 475 510.343635778636 -35.3436357786358 39 470 500.718635778636 -30.7186357786358 40 461 492.968635778636 -31.9686357786358 41 455 485.468635778636 -30.4686357786357 42 456 485.843635778636 -29.8436357786357 43 517 538.843635778636 -21.8436357786358 44 525 555.968635778636 -30.9686357786358 45 523 552.065868725869 -29.0658687258687 46 519 540.351583011583 -21.351583011583 47 509 521.208725868726 -12.2087258687259 48 512 523.758198198198 -11.7581981981982 49 519 535.896634491634 -16.8966344916345 50 517 531.021634491634 -14.0216344916345 51 510 521.396634491634 -11.3966344916345 52 509 513.646634491634 -4.64663449163449 53 501 506.146634491634 -5.14663449163449 54 507 506.521634491634 0.478365508365511 55 569 559.521634491634 9.4783655083655 56 580 576.646634491634 3.35336550836551 57 578 572.743867438867 5.25613256113256 58 565 561.029581724582 3.97041827541827 59 547 541.886724581725 5.11327541827542 60 555 544.436196911197 10.5638030888031 61 562 556.574633204633 5.42536679536681 62 561 551.699633204633 9.3003667953668 63 555 542.074633204633 12.9253667953668 64 544 534.324633204633 9.6753667953668 65 537 526.824633204633 10.1753667953668 66 543 527.199633204633 15.8003667953668 67 594 580.199633204633 13.8003667953668 68 611 597.324633204633 13.6753667953668 69 613 593.421866151866 19.5781338481338 70 611 581.70758043758 29.2924195624195 71 594 562.564723294723 31.4352767052767 72 595 565.114195624196 29.8858043758044 73 591 577.252631917632 13.7473680823681 74 589 572.377631917632 16.6223680823681 75 584 562.752631917632 21.2473680823681 76 573 555.002631917632 17.9973680823681 77 567 547.502631917632 19.4973680823681 78 569 547.877631917632 21.1223680823681 79 621 600.877631917632 20.1223680823681 80 629 618.002631917632 10.9973680823681 81 628 614.099864864865 13.9001351351352 82 612 602.385579150579 9.61442084942083 83 595 583.242722007722 11.7572779922780 84 597 585.792194337194 11.2078056628057 85 593 597.930630630631 -4.93063063063063 86 590 593.055630630631 -3.05563063063066 87 580 583.430630630631 -3.43063063063064 88 574 575.680630630631 -1.68063063063065 89 573 568.180630630631 4.81936936936935 90 573 568.555630630631 4.44436936936936 91 620 621.55563063063 -1.55563063063065 92 626 638.68063063063 -12.6806306306306

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/22/t1195738658pr04x52dhbikwj5/1r1oa1195738607.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/22/t1195738658pr04x52dhbikwj5/1r1oa1195738607.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/22/t1195738658pr04x52dhbikwj5/2jmsp1195738607.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/22/t1195738658pr04x52dhbikwj5/2jmsp1195738607.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/22/t1195738658pr04x52dhbikwj5/3lzw01195738607.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/22/t1195738658pr04x52dhbikwj5/3lzw01195738607.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/22/t1195738658pr04x52dhbikwj5/4srs51195738607.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/22/t1195738658pr04x52dhbikwj5/4srs51195738607.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/22/t1195738658pr04x52dhbikwj5/5b03j1195738607.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/22/t1195738658pr04x52dhbikwj5/5b03j1195738607.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/22/t1195738658pr04x52dhbikwj5/6c2ev1195738607.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/22/t1195738658pr04x52dhbikwj5/6c2ev1195738607.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/22/t1195738658pr04x52dhbikwj5/7zgva1195738607.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/22/t1195738658pr04x52dhbikwj5/7zgva1195738607.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/22/t1195738658pr04x52dhbikwj5/84tdq1195738607.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/22/t1195738658pr04x52dhbikwj5/84tdq1195738607.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/22/t1195738658pr04x52dhbikwj5/9dzo41195738607.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Nov/22/t1195738658pr04x52dhbikwj5/9dzo41195738607.ps (open in new window)

Parameters:

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

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.

FreeStatistics.org is powered by