ahi computation 1

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 04:18:39 -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/t1200395762spwspmzml31gh0f.htm/, Retrieved Tue, 15 Jan 2008 12:16:02 +0100

User-defined keywords:

Dataseries X:

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106 87 1 65.3 2.2 70 1 65.73 62.3 75 1 69.44 14.7 79 1 73.74 5 64.5 1 74.31 74.4 75 0 70.53 66.1 70 0 69.42 22 67 1 69.77 3.4 52 0 65.47 0.3 67.2 1 66.2 53.2 47 0 70.46 0 46.4 0 74.44 57.2 76 0 69.28 9.2 71.6 1 67.67 15.9 63.8 1 67.22 17.6 48.2 1 64.85 21 64.5 1 71.35 7.6 75.9 1 72.28 71.6 80 1 71.87 12.9 56 1 67.34 10.5 75.5 0 73.5 25.7 77 1 64.91 26.8 88 0 68.13 7.3 48 0 72.5 17.1 73 1 72.36 27.3 72 1 70.59 16.5 64 1 74.76 5.4 76 0 65.63 5.6 67.4 1 67.04 36.5 73.7 1 66.72 1.1 59.2 0 65.8 3.9 53 0 72.44 34.2 41.9 1 71.83 40.3 65.5 1 72.67 15.6 63 1 69.56 15.5 54 0 67 52.9 77.7 0 68.86 1.6 47.6 0 71.25 14.2 53.1 1 69.88 7.5 55.5 1 67.18 2 64 1 67.47 71.4 75.6 1 73.2 3.2 57 0 69.6 20 63 0 71.24 2.8 59.5 1 73.83 15.3 84.5 1 66.07 8 59.9 0 70.68 36.6 60 1 74.01 3.8 64 0 68.53 25.5 54 0 66.72 3.2 53.8 0 72.69 33.1 84 1 67.46 42 63.2 0 73.81 16.2 54.3 1 72.96 0 60 0 71.65 22.7 68 1 72.79 36.4 74 1 73.83 69 74 1 66.74 11.2 68.5 1 65.62 12.5 76 0 66.18 51.7 83 0 67.78 3.6 62.5 0 68.84 22.2 57 1 65.27 39.2 85 1 72.84 27.9 50 1 75.36 58.8 53 1 76.88 1 57 0 76.51 4.7 46 1 80.63 25.6 65.4 1 75.27 5.3 71.4 1 81.19 38.7 41 1 81.3 31.6 66 1 77.77 19.3 69.5 1 75.51 26.5 59 1 78.64 12.8 80 1 80.68 18.3 72 1 77.4 13.2 73 0 80.71 36 66.4 0 83.16 34.1 37 0 87.99 71.5 70 1 72.21 43.3 75 1 70.24 47.7 54 1 66.06 74.9 76.2 1 68.67 0.9 74.9 1 68.77 35.9 98 1 68.07 45.8 86.5 0 67.33 54.2 72.8 1 69.47 34 65 1 70.81 7.9 50 1 73.17 54.5 81 1 71.28 8.2 52 0 69.47 49.3 68 1 65.31 46.9 58.5 1 70.23 16.8 65.5 1 73.23 2.8 62.5 0 68.67 60.9 64 1 72.66 5.6 55.7 0 74.79 6.6 84 1 73.04 22.9 63.7 1 69.95 51.1 65 0 67.51 23.3 87.5 0 67.5 11.5 79 1 71.32 79.1 58.5 0 71.23 53.6 75 1 67.49 1.5 52.5 0 68.62 40.4 57.5 1 72.53 25.4 70 1 66.67 6.7 72 1 66.19 76 88 1 78.4 0.6 58 1 75.67 43.4 73 1 76.07 13 56 1 82.88 27.8 49 0 77.14 6.5 54.7 0 77.31 7.1 67 1 76.58 6 47 0 82.86 6.5 47 0 76.64

Text written by user:

This is model 1

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] = -27.7993617757784 + 0.636634723316394weight[t] + 3.6296660508344sex[t] + 0.138881643908525age[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) -27.7993617757784 37.180281 -0.7477 0.4562 0.2281 weight 0.636634723316394 0.18133 3.5109 0.000643 0.000321 sex 3.6296660508344 4.323899 0.8394 0.402993 0.201497 age 0.138881643908525 0.448281 0.3098 0.757276 0.378638 Multiple Linear Regression - Regression Statistics Multiple R 0.352240964423445 R-squared 0.124073697017958 Adjusted R-squared 0.100819016407816 F-TEST (value) 5.33542898730859 F-TEST (DF numerator) 3 F-TEST (DF denominator) 113 p-value 0.00178719413098405 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 21.7585082448743 Sum Squared Residuals 53497.8929577759 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 106 40.2864965508089 65.7135034491911 2 2.2 29.5234253613109 -27.3234253613109 3 62.3 33.2218498767935 29.0781501232065 4 14.7 36.3655798388657 -21.6655798388657 5 5 27.2135388878059 -22.2135388878059 6 74.4 29.7435648178194 44.6564351821806 7 66.1 26.4062325764990 39.693767423501 8 22 28.1746030327522 -6.17460303275217 9 3.4 14.3982250633652 -10.9982250633652 10 0.3 27.8061225086620 -27.5061225086620 11 53.2 11.9080708498868 41.2919291501132 12 0 12.0788389586529 -12.0788389586529 13 57.2 30.2065974862501 26.9934025137499 14 9.2 30.8114713077997 -21.6114713077997 15 15.9 25.783223726173 -9.88322372617298 16 17.6 15.5225725463740 2.07742745362598 17 21 26.8024492218367 -5.80244922183666 18 7.6 34.1892449964785 -26.5892449964785 19 71.6 36.7425058880732 34.8574941119268 20 12.9 20.8341386815741 -7.93413868157412 21 10.5 30.4743606618859 -19.9743606618859 22 25.7 33.8659854765207 -8.16598547652068 23 26.8 37.6865002755521 -10.8865002755521 24 7.3 12.8280241267766 -5.52802412677656 25 17.1 32.3541148303736 -15.2541148303736 26 27.3 31.4716595973391 -4.17165959733914 27 16.5 26.9577182659065 -10.4577182659065 28 5.4 29.699679485984 -24.2996794859840 29 5.6 28.0501100342085 -22.4501100342085 30 36.5 32.016466665051 4.48353333494899 31 1.1 19.0278260137331 -17.9278260137331 32 3.9 16.0028648447240 -12.1028648447240 33 34.2 12.4811676639622 21.7188323360378 34 40.3 27.6224077151123 12.6775922848877 35 15.6 25.5988989942658 -9.9988989942658 36 15.5 15.8839834251780 -0.383983425178034 37 52.9 31.2305462254464 21.6694537745536 38 1.6 12.3997681825644 -10.7997681825644 39 14.2 19.3406573594842 -5.14065735948423 40 7.5 20.4936002568906 -12.9936002568906 41 2 25.9452710818134 -23.9452710818134 42 71.4 34.1260256918794 37.2739743081206 43 3.2 18.1549798692894 -14.9549798692894 44 20 22.2025541051977 -2.20255410519773 45 2.8 23.9637020821478 -21.1637020821478 46 15.3 38.8018486083275 -23.5018486083275 47 8 20.1512127423281 -12.1512127423281 48 36.6 24.3070181397096 12.2929818602904 49 3.8 22.4628195735220 -18.6628195735220 50 25.5 15.8450965648836 9.65490343511635 51 3.2 16.5468930343543 -13.3468930343543 52 33.1 38.6765767317022 -5.57657673170218 53 42 22.6868068747059 19.3131931252941 54 16.2 20.5323744907022 -4.33237449070216 55 0 20.3495914092510 -20.3495914092510 56 22.7 29.2306603206723 -6.53066032067232 57 36.4 33.1949055702355 3.20509442976445 58 69 32.2102347149241 36.7897652850759 59 11.2 28.5531962955064 -17.3531962955064 60 12.5 29.7760643901337 -17.2760643901337 61 51.7 34.4547180836021 17.2452819163979 62 3.6 21.5509207981591 -17.9509207981591 63 22.2 21.1832884019999 1.01671159800013 64 39.2 40.0603946992464 -0.860394699246439 65 27.9 18.1281611258221 9.77183887417787 66 58.8 20.2491653945123 38.5508346054877 67 1 19.1146520286973 -18.1146520286973 68 4.7 16.3135284959545 -11.6135284959545 69 25.6 27.9198365169428 -2.31983651694283 70 5.3 32.5618241887797 -27.2618241887797 71 38.7 13.2234055807912 25.4765944192088 72 31.6 28.649021460704 2.95097853929602 73 19.3 30.5633704770781 -11.2633704770781 74 26.5 24.3134054276896 2.18659457231036 75 12.8 37.9660531709073 -25.1660531709073 76 18.3 32.4174435923562 -14.1174435923562 77 13.2 29.8841105061754 -16.6841105061754 78 36 26.0225813598631 9.9774186401369 79 34.1 7.97631883443929 26.1236811655607 80 71.5 30.4233784138382 41.0766215861618 81 43.3 33.3329551919203 9.96704480807966 82 47.7 19.3831007307384 28.3168992692616 83 74.9 33.8788726789636 41.0211273210364 84 0.9 33.0651357030432 -32.1651357030432 85 35.9 47.6741806609159 -11.7741806609159 86 45.8 36.6204428754507 9.17955712454934 87 54.2 31.8254199348147 22.3745800651853 88 34 27.0457704957843 6.95422950421575 89 7.9 17.8240103256625 -9.92401032566246 90 54.5 37.2972004414836 17.2027995585164 91 8.2 14.9537516389993 -6.75375163899931 92 49.3 28.1918256242365 21.1081743757635 93 46.9 22.8270934407607 24.0729065592393 94 16.8 27.7001814357011 -10.9001814357011 95 2.8 21.5273109186946 -18.7273109186946 96 60.9 26.6660668136986 34.2339331863014 97 5.6 18.0481504608633 -12.4481504608633 98 6.6 39.4515363047118 -32.8515363047118 99 22.9 26.0987071417116 -3.19870714171161 100 51.1 22.9577950200517 28.1422049799483 101 23.3 37.2806874782315 -13.9806874782315 102 11.5 36.0294862606071 -24.5294862606071 103 79.1 19.3363090338349 59.7636909661651 104 53.6 32.9510306711719 20.6489693288281 105 1.5 15.1540196033353 -13.6540196033353 106 40.4 22.5098864984340 17.8901135015660 107 25.4 29.6539741065849 -4.25397410658493 108 6.7 30.8605803641416 -24.1605803641416 109 76 42.742480809327 33.257519190673 110 0.6 23.2642922219649 -22.6642922219649 111 43.4 32.8693657292743 10.5306342707258 112 13 22.9923594279126 -9.9923594279126 113 27.8 14.1090696778285 13.6909303221715 114 6.5 17.7614974801964 -11.2614974801964 115 7.1 29.1203870277692 -22.0203870277692 116 6 13.6302032343525 -7.63020323435249 117 6.5 12.7663594092415 -6.26635940924146

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) 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')

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

Software written by Ed van Stee & Patrick Wessa

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• 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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