Multiple regression (no seiz, no linear)

*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: Thu, 16 Dec 2010 12:27:59 +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/Dec/16/t1292502405x2ze2fv9e4hnfml.htm/, Retrieved Thu, 16 Dec 2010 13:27:04 +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/Dec/16/t1292502405x2ze2fv9e4hnfml.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:

» Textbox « » Textfile « » CSV «

300 2,26 302 2,57 400 3,07 392 2,76 373 2,51 379 2,87 303 3,14 324 3,11 353 3,16 392 2,47 327 2,57 376 2,89 329 2,63 359 2,38 413 1,69 338 1,96 422 2,19 390 1,87 370 1,60 367 1,63 406 1,22 418 1,21 346 1,49 350 1,64 330 1,66 318 1,77 382 1,82 337 1,78 372 1,28 422 1,29 428 1,37 426 1,12 396 1,51 458 2,24 315 2,94 337 3,09 386 3,46 352 3,64 383 4,39 439 4,15 397 5,21 453 5,80 363 5,91 365 5,39 474 5,46 373 4,72 403 3,14 384 2,63 364 2,32 361 1,93 419 0,62 352 0,60 363 -0,37 410 -1,10 361 -1,68 383 -0,78 342 -1,19 369 -0,79 361 -0,12 317 0,26 386 0,62 318 0,70 407 1,66 393 1,80 404 2,27 498 2,46 438 2,57

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 5 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 R Framework error message The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'. Multiple Linear Regression - Estimated Regression Equation Aantal_vergunningen[t] = + 368.989826033592 + 3.83095798756888`Inflatie `[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) 368.989826033592 8.515119 43.3335 0 0 `Inflatie ` 3.83095798756888 3.196042 1.1987 0.235013 0.117507 Multiple Linear Regression - Regression Statistics Multiple R 0.14705866243018 R-squared 0.0216262501957536 Adjusted R-squared 0.00657434635261145 F-TEST (value) 1.43677839169871 F-TEST (DF numerator) 1 F-TEST (DF denominator) 65 p-value 0.235013299229688 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 42.0088356064701 Sum Squared Residuals 114708.247485743 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 300 377.647791085498 -77.6477910854981 2 302 378.835388061644 -76.8353880616444 3 400 380.750867055429 19.2491329445712 4 392 379.563270079282 12.4367299207175 5 373 378.60553058239 -5.60553058239026 6 379 379.984675457915 -0.984675457915051 7 303 381.019034114559 -78.0190341145587 8 324 380.904105374932 -56.9041053749316 9 353 381.09565327431 -28.0956532743100 10 392 378.452292262888 13.5477077371125 11 327 378.835388061644 -51.8353880616444 12 376 380.061294617666 -4.06129461766643 13 329 379.065245540899 -50.0652455408985 14 359 378.107506044006 -19.1075060440063 15 413 375.464145032584 37.5358549674162 16 338 376.498503689227 -38.4985036892274 17 422 377.379624026368 44.6203759736318 18 390 376.153717470346 13.8462825296538 19 370 375.119358813703 -5.11935881370258 20 367 375.234287553330 -8.23428755332964 21 406 373.663594778426 32.3364052215736 22 418 373.625285198551 44.3747148014493 23 346 374.69795343507 -28.69795343507 24 350 375.272597133205 -25.2725971332053 25 330 375.349216292957 -45.3492162929567 26 318 375.770621671589 -57.7706216715893 27 382 375.962169570968 6.03783042903227 28 337 375.808931251465 -38.808931251465 29 372 373.893452257681 -1.89345225768054 30 422 373.931761837556 48.0682381624438 31 428 374.238238476562 53.7617615234383 32 426 373.280498979670 52.7195010203305 33 396 374.774572594821 21.2254274051786 34 458 377.571171925747 80.4288280742533 35 315 380.252842517045 -65.2528425170449 36 337 380.82748621518 -43.8274862151802 37 386 382.244940670581 3.75505932941931 38 352 382.934513108343 -30.9345131083431 39 383 385.80773159902 -2.80773159901975 40 439 384.888301682003 54.1116983179968 41 397 388.949117148826 8.05088285117377 42 453 391.209382361492 61.7906176385081 43 363 391.630787740124 -28.6307877401244 44 365 389.638689586589 -24.6386895865886 45 474 389.906856645718 84.0931433542816 46 373 387.071947734918 -14.0719477349175 47 403 381.019034114559 21.9809658854413 48 384 379.065245540899 4.93475445910148 49 364 377.877648564752 -13.8776485647522 50 361 376.3835749496 -15.3835749496003 51 419 371.365019985885 47.6349800141149 52 352 371.288400826134 -19.2884008261337 53 363 367.572371578192 -4.57237157819189 54 410 364.775772247267 45.2242277527334 55 361 362.553816614477 -1.55381661447666 56 383 366.001678803289 16.9983211967114 57 342 364.430986028385 -22.4309860283854 58 369 365.963369223413 3.03663077658704 59 361 368.530111075084 -7.5301110750841 60 317 369.98587511036 -52.9858751103603 61 386 371.365019985885 14.6349800141149 62 318 371.671496624891 -53.6714966248906 63 407 375.349216292957 31.6507837070433 64 393 375.885550411216 17.1144495887836 65 404 377.686100665374 26.3138993346263 66 498 378.413982683012 119.586017316988 67 438 378.835388061644 59.1646119383556

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/16/t1292502405x2ze2fv9e4hnfml/1q5iq1292502473.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/16/t1292502405x2ze2fv9e4hnfml/1q5iq1292502473.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/16/t1292502405x2ze2fv9e4hnfml/2q5iq1292502473.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/16/t1292502405x2ze2fv9e4hnfml/2q5iq1292502473.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/16/t1292502405x2ze2fv9e4hnfml/31xib1292502473.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/16/t1292502405x2ze2fv9e4hnfml/31xib1292502473.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/16/t1292502405x2ze2fv9e4hnfml/41xib1292502473.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/16/t1292502405x2ze2fv9e4hnfml/41xib1292502473.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/16/t1292502405x2ze2fv9e4hnfml/51xib1292502473.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/16/t1292502405x2ze2fv9e4hnfml/51xib1292502473.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/16/t1292502405x2ze2fv9e4hnfml/61xib1292502473.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/16/t1292502405x2ze2fv9e4hnfml/61xib1292502473.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/16/t1292502405x2ze2fv9e4hnfml/7bohd1292502473.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/16/t1292502405x2ze2fv9e4hnfml/7bohd1292502473.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/16/t1292502405x2ze2fv9e4hnfml/8mxgh1292502473.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/16/t1292502405x2ze2fv9e4hnfml/8mxgh1292502473.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/16/t1292502405x2ze2fv9e4hnfml/9mxgh1292502473.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/16/t1292502405x2ze2fv9e4hnfml/9mxgh1292502473.ps (open in new window)

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) 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