ahi computation 3

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 04:37:50 -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/t1200397034hll0cfkrgmxmcuu.htm/, Retrieved Tue, 15 Jan 2008 12:37:14 +0100

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

106 87 1 65.3 170 2.2 70 1 65.73 165 62.3 75 1 69.44 168 14.7 79 1 73.74 170 5 64.5 1 74.31 157 74.4 75 0 70.53 146 66.1 70 0 69.42 149 22 67 1 69.77 159 3.4 52 0 65.47 151 0.3 67.2 1 66.2 174 53.2 47 0 70.46 156 0 46.4 0 74.44 151.5 57.2 76 0 69.28 146 9.2 71.6 1 67.67 157 15.9 63.8 1 67.22 171.5 17.6 48.2 1 64.85 150 21 64.5 1 71.35 170 7.6 75.9 1 72.28 164.5 71.6 80 1 71.87 163 12.9 56 1 67.34 162.5 10.5 75.5 0 73.5 161 25.7 77 1 64.91 166.5 26.8 88 0 68.13 160 7.3 48 0 72.5 147 17.1 73 1 72.36 162.5 27.3 72 1 70.59 161 16.5 64 1 74.76 163.5 5.4 76 0 65.63 161 5.6 67.4 1 67.04 172.5 36.5 73.7 1 66.72 169.5 1.1 59.2 0 65.8 158 3.9 53 0 72.44 153.5 34.2 41.9 1 71.83 165.5 40.3 65.5 1 72.67 153.5 15.6 63 1 69.56 157.5 15.5 54 0 67 145.5 52.9 77.7 0 68.86 156 1.6 47.6 0 71.25 163 14.2 53.1 1 69.88 159 7.5 55.5 1 67.18 167 2 64 1 67.47 157.5 71.4 75.6 1 73.2 156 3.2 57 0 69.6 156.5 20 63 0 71.24 148.5 2.8 59.5 1 73.83 162.5 15.3 84.5 1 66.07 164 8 59.9 0 70.68 152 36.6 60 1 74.01 157.5 3.8 64 0 68.53 148 25.5 54 0 66.72 145.5 3.2 53.8 0 72.69 154.5 33.1 84 1 67.46 166.5 42 63.2 0 73.81 157 16.2 54.3 1 72.96 150 0 60 0 71.65 152 22.7 68 1 72.79 171 36.4 74 1 73.83 165.5 69 74 1 66.74 165 11.2 68.5 1 65.62 168.5 12.5 76 0 66.18 154 51.7 83 0 67.78 156.5 3.6 62.5 0 68.84 152 22.2 57 1 65.27 164.5 39.2 85 1 72.84 161 27.9 50 1 75.36 162 58.8 53 1 76.88 169 1 57 0 76.51 150 4.7 46 1 80.63 146 25.6 65.4 1 75.27 165 5.3 71.4 1 81.19 165.5 38.7 41 1 81.3 164 31.6 66 1 77.77 163 19.3 69.5 1 75.51 167.5 26.5 59 1 78.64 166 12.8 80 1 80.68 167.5 18.3 72 1 77.4 162 13.2 73 0 80.71 165 36 66.4 0 83.16 145 34.1 37 0 87.99 139 71.5 70 1 72.21 164 43.3 75 1 70.24 167 47.7 54 1 66.06 163 74.9 76.2 1 68.67 162.5 0.9 74.9 1 68.77 159.5 35.9 98 1 68.07 169 45.8 86.5 0 67.33 152.5 54.2 72.8 1 69.47 165 34 65 1 70.81 166 7.9 50 1 73.17 163 54.5 81 1 71.28 167.5 8.2 52 0 69.47 157.5 49.3 68 1 65.31 160 46.9 58.5 1 70.23 162 16.8 65.5 1 73.23 164.5 2.8 62.5 0 68.67 150 60.9 64 1 72.66 167 5.6 55.7 0 74.79 155 6.6 84 1 73.04 173.5 22.9 63.7 1 69.95 173 51.1 65 0 67.51 156 23.3 87.5 0 67.5 149.5 11.5 79 1 71.32 167 79.1 58.5 0 71.23 146 53.6 75 1 67.49 166 1.5 52.5 0 68.62 151.5 40.4 57.5 1 72.53 164 25.4 70 1 66.67 160 6.7 72 1 66.19 152.5 76 88 1 78.4 160 0.6 58 1 75.67 163 43.4 73 1 76.07 168 13 56 1 82.88 165.5 27.8 49 0 77.14 147 6.5 54.7 0 77.31 158 7.1 67 1 76.58 168 6 47 0 82.86 154.5 6.5 47 0 76.64 147

Text written by user:

This model 2

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] = + 61.5198389564695 + 0.71698916920363weight[t] + 10.0572486368983sex[t] + 0.119109062022995age[t] -0.608987531164776height[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) 61.5198389564695 66.972904 0.9186 0.36029 0.180145 weight 0.71698916920363 0.186978 3.8346 0.000208 0.000104 sex 10.0572486368983 5.882887 1.7096 0.090113 0.045057 age 0.119109062022995 0.445398 0.2674 0.789637 0.394818 height -0.608987531164776 0.380946 -1.5986 0.112723 0.056362 Multiple Linear Regression - Regression Statistics Multiple R 0.378964915955848 R-squared 0.143614407525423 Adjusted R-squared 0.113029207794188 F-TEST (value) 4.69555238440238 F-TEST (DF numerator) 4 F-TEST (DF denominator) 112 p-value 0.00153379659481434 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 21.6102713221872 Sum Squared Residuals 52304.4285812773 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 106 38.2050867661734 67.7949132338266 2 2.2 29.1124254422054 -26.9124254422054 3 62.3 31.3123033148346 30.9876966851654 4 14.7 33.4744538960184 -18.7744538960184 5 5 31.062841013061 -26.062841013061 6 74.4 34.7826092411664 39.6173907588336 7 66.1 29.2384897428084 36.8615102571916 8 22 31.0965837321561 -9.09658373215611 9 3.4 14.6442288398227 -11.2442288398227 10 0.3 21.6799492471031 -21.3799492471031 11 53.2 8.60869955747538 44.5913004425246 12 0 11.3930040130462 -11.3930040130462 13 57.2 35.3507120828413 21.8492879171587 14 9.2 35.3625799425741 -26.1625799425741 15 15.9 20.8861461429862 -4.98614614298616 16 17.6 22.5120585464577 -4.91205854645771 17 21 22.7934402843308 -1.79344028433084 18 7.6 34.4273196623399 -26.8273196623399 19 71.6 38.2316218373925 33.3683781626075 20 12.9 20.7888114911236 -7.88881149112359 21 10.5 26.3600447725049 -15.8600447725049 22 25.7 33.1201988990248 -7.42019889902484 23 26.8 35.2917812556515 -8.49178125565153 24 7.3 15.0495589936889 -7.7495589936889 25 17.1 33.5755548589407 -16.4755548589407 26 27.3 33.5612239467036 -6.26122394670356 27 16.5 26.7995265537985 -10.2995265537985 28 5.4 25.7811510389857 -20.3811510389857 29 5.6 22.8368799897903 -17.2368799897903 30 36.5 29.1427594494202 7.35724055057985 31 1.1 15.5829441304030 -14.4829441304030 32 3.9 14.6689393434146 -10.7689393434146 33 34.2 9.38710130034133 24.8128986996587 34 40.3 33.7159476796236 6.58405232037638 35 15.6 29.1170954490639 -13.5170954490639 36 15.5 19.6098754645314 -4.10987546453137 37 52.9 30.42969255279 22.4703074472100 38 1.6 4.8700764998423 -3.2700764998423 39 14.2 21.1435362770482 -6.94353627704818 40 7.5 17.6708155663566 -10.1708155663566 41 2 29.5851466786395 -27.5851466786395 42 71.4 39.4981972635405 31.9018027364595 43 3.2 15.3716636905895 -12.1716636905895 44 20 24.7408378168472 -4.74083781684721 45 2.8 24.0712913958655 -21.2712913958655 46 15.3 40.1582530079107 -24.8582530079107 47 8 20.3200139585064 -12.3200139585064 48 36.6 27.4961632674554 9.10383673254464 49 3.8 25.4395351935509 -21.6395351935509 50 25.5 19.5765249271649 5.92347507283507 51 3.2 14.6633204131185 -11.4633204131185 52 33.1 38.4428511916089 -5.34285119160888 53 42 20.0139519251864 21.9860480748136 54 16.2 27.8516669716063 -11.6516669716063 55 0 20.5072486655890 -20.5072486655890 56 22.7 24.8654318946919 -2.16543189469188 57 36.4 32.6406717558238 3.75932824417616 58 69 32.1006822716632 36.8993177283368 59 11.2 25.8923833325008 -14.6923833325008 60 12.5 30.1095737412518 -17.6095737412518 61 51.7 33.7966035970020 17.9033964029980 62 3.6 21.9650251243135 -18.3650251243135 63 22.2 20.0412698396101 2.15873016038993 64 39.2 43.1500785359025 -3.95007853590249 65 27.9 17.7466249189086 10.1533750810914 66 58.8 15.8157254826410 42.984274517359 67 1 20.1531262617395 -19.1531262617395 68 4.7 25.2501734975917 -20.5501734975917 69 25.6 26.9505757155681 -1.35057571556812 70 5.3 31.6531426123837 -26.3531426123836 71 38.7 10.7832551621630 27.916744837837 72 31.6 28.8965169344773 2.70348306552266 73 19.3 28.3963486562766 -9.09634865627658 74 26.5 22.1542550405176 4.34574495948239 75 12.8 36.5405287835736 -23.7405287835736 76 18.3 33.7633691279154 -15.4633691279154 77 13.2 22.9903980620225 -9.79039806202248 78 36 30.7298373705304 5.27016262946962 79 34.1 13.8795777525034 20.2204222474966 80 71.5 30.4932396952792 41.0067603047208 81 43.3 32.0165780956178 11.2834219043822 82 47.7 18.8978797877445 28.8021202122555 83 74.9 35.4304077615275 39.4695922384725 84 0.9 36.3371953412594 -35.4371953412594 85 35.9 47.0308872603818 -11.1308872603818 86 45.8 38.6884167359635 7.11158326403649 87 54.2 31.5654630079416 22.6345369920584 88 34 25.5235661000993 8.47643389990066 89 7.9 16.8767885419135 -8.97678854191347 90 54.5 36.1378927697611 18.3621072302389 91 8.2 11.1622461353436 -2.9622461353436 92 49.3 30.6733589535724 18.6266410464276 93 46.9 23.2300033689615 23.6699966310385 94 16.8 27.0837859115440 -10.2837859115440 95 2.8 23.1627516460991 -20.3627516460991 96 60.9 24.4179411644735 36.4820588355265 97 5.6 15.9712350992713 -10.3712350992713 98 6.6 34.8445670395438 -28.2445670395438 99 22.9 20.2261336686414 2.67386633135858 100 51.1 21.1631328701729 29.9368671298271 101 23.3 41.2526170392054 -17.9526170392054 102 11.5 35.0131725594171 -23.5131725594171 103 79.1 23.0356642927226 56.0643357072774 104 53.6 32.2980157062193 21.3019842937807 105 1.5 15.0734232042145 -13.5734232042145 106 40.4 21.5689899800812 18.8310100199188 107 25.4 32.2693256163309 -6.86932561633094 108 6.7 38.213538088703 -31.513538088703 109 76 46.572279959526 29.427720040474 110 0.6 22.9104745506 -22.3104745506 111 43.4 30.6680180576398 12.7319819423602 112 13 20.8128037214666 -7.8128037214666 113 27.8 16.3192142106792 11.4807857893208 114 6.5 13.7274381728713 -7.2274381728713 115 7.1 26.4268286640497 -19.3268286640497 116 6 10.9991332233077 -4.99913322330768 117 6.5 14.8256813412605 -8.32568134126047

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')

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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