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Multiple regression

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

Title produced by software: Multiple Regression

Date of computation: Tue, 18 Dec 2007 11:50:35 -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/Dec/18/t1198002891ae2sd5ov0eg0gg2.htm/, Retrieved Tue, 18 Dec 2007 19:35:02 +0100

User-defined keywords:

Dataseries X:

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106,0 100,9 114,3 101,2 109,2 111,6 91,7 93,7 105,7 109,5 105,3 102,8 100,6 97,6 110,3 107,2 107,2 108,1 97,1 92,2 112,2 111,6 115,7 111,3 104,2 103,2 112,7 106,4 102,6 110,6 95,2 89,0 112,5 116,8 107,2 113,6 101,8 102,6 122,7 110,3 110,5 121,6 100,3 100,7 123,4 127,1 124,1 131,2 111,6 114,2 130,1 125,9 119,0 133,8 107,5 113,5 134,4 126,8 135,6 139,9 129,8 131,0 153,1 134,1 144,1 155,9 123,3 128,1 144,3 153,0 149,9 150,9 141,0 138,9 157,4 142,9 151,7 161,0 138,6 136,0 151,9

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 x[t] = + 97.4816091954023 -8.10852490421458M1[t] -9.7053913519431M2[t] + 5.66917077175697M3[t] -5.35626710454297M4[t] -3.68170498084293M5[t] + 3.99285714285713M6[t] -17.9325807334428M7[t] -18.6580186097428M8[t] -0.569170771756992M9[t] + 0.491351943076064M10[t] -1.32932402846197M11[t] + 0.654009304871374t + 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) 97.4816091954023 3.262915 29.8756 0 0 M1 -8.10852490421458 3.994623 -2.0299 0.046286 0.023143 M2 -9.7053913519431 3.993301 -2.4304 0.017725 0.008863 M3 5.66917077175697 3.992273 1.42 0.160166 0.080083 M4 -5.35626710454297 3.991538 -1.3419 0.18409 0.092045 M5 -3.68170498084293 3.991096 -0.9225 0.35954 0.17977 M6 3.99285714285713 3.990949 1.0005 0.320626 0.160313 M7 -17.9325807334428 3.991096 -4.4931 2.8e-05 1.4e-05 M8 -18.6580186097428 3.991538 -4.6744 1.4e-05 7e-06 M9 -0.569170771756992 3.992273 -0.1426 0.887053 0.443526 M10 0.491351943076064 4.142171 0.1186 0.905925 0.452962 M11 -1.32932402846197 4.141746 -0.321 0.749227 0.374614 t 0.654009304871374 0.034257 19.091 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.932272717360232 R-squared 0.86913241953423 Adjusted R-squared 0.846038140628507 F-TEST (value) 37.634100769382 F-TEST (DF numerator) 12 F-TEST (DF denominator) 68 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 7.17346853859014 Sum Squared Residuals 3499.1882594417 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 106 90.0270935960593 15.9729064039407 2 100.9 89.084236453202 11.8157635467980 3 114.3 105.112807881773 9.18719211822658 4 101.2 94.7413793103448 6.45862068965518 5 109.2 97.0699507389163 12.1300492610837 6 111.6 105.398522167488 6.20147783251231 7 91.7 84.1270935960591 7.5729064039409 8 93.7 84.0556650246305 9.64433497536948 9 105.7 102.798522167488 2.90147783251233 10 109.5 104.513054187192 4.9869458128079 11 105.3 103.346387520525 1.95361247947456 12 102.8 105.329720853859 -2.52972085385879 13 100.6 97.8752052545156 2.72479474548442 14 97.6 96.9323481116584 0.667651888341568 15 110.3 112.960919540230 -2.66091954022987 16 107.2 102.589490968801 4.6105090311987 17 107.2 104.918062397373 2.28193760262728 18 108.1 113.246633825944 -5.14663382594417 19 97.1 91.9752052545156 5.12479474548441 20 92.2 91.903776683087 0.296223316912988 21 112.2 110.646633825944 1.55336617405584 22 111.6 112.361165845649 -0.761165845648604 23 115.7 111.194499178982 4.50550082101807 24 111.3 113.177832512315 -1.87783251231528 25 104.2 105.723316912972 -1.52331691297203 26 103.2 104.780459770115 -1.58045977011492 27 112.7 120.809031198686 -8.10903119868635 28 106.4 110.437602627258 -4.03760262725778 29 102.6 112.766174055829 -10.1661740558292 30 110.6 121.094745484401 -10.4947454844007 31 95.2 99.823316912972 -4.62331691297207 32 89 99.7518883415435 -10.7518883415435 33 112.5 118.494745484401 -5.99474548440066 34 116.8 120.209277504105 -3.40927750410509 35 107.2 119.042610837438 -11.8426108374384 36 113.6 121.025944170772 -7.42594417077177 37 101.8 113.571428571429 -11.7714285714285 38 102.6 112.628571428571 -10.0285714285714 39 122.7 128.657142857143 -5.95714285714286 40 110.3 118.285714285714 -7.9857142857143 41 110.5 120.614285714286 -10.1142857142857 42 121.6 128.942857142857 -7.34285714285715 43 100.3 107.671428571429 -7.37142857142857 44 100.7 107.6 -6.9 45 123.4 126.342857142857 -2.94285714285714 46 127.1 128.057389162562 -0.957389162561581 47 124.1 126.890722495895 -2.79072249589492 48 131.2 128.874055829228 2.32594417077173 49 111.6 121.419540229885 -9.81954022988503 50 114.2 120.476683087028 -6.2766830870279 51 130.1 136.505254515599 -6.40525451559935 52 125.9 126.133825944171 -0.233825944170769 53 119 128.462397372742 -9.4623973727422 54 133.8 136.790968801314 -2.99096880131362 55 107.5 115.519540229885 -8.01954022988506 56 113.5 115.448111658456 -1.94811165845649 57 134.4 134.190968801314 0.209031198686370 58 126.8 135.905500821018 -9.10550082101806 59 135.6 134.738834154351 0.861165845648596 60 139.9 136.722167487685 3.17783251231526 61 129.8 129.267651888342 0.532348111658499 62 131 128.324794745484 2.67520525451561 63 153.1 144.353366174056 8.74663382594417 64 134.1 133.981937602627 0.118062397372728 65 144.1 136.310509031199 7.78949096880131 66 155.9 144.639080459770 11.2609195402299 67 123.3 123.367651888342 -0.0676518883415553 68 128.1 123.296223316913 4.80377668308701 69 144.3 142.039080459770 2.26091954022989 70 153 143.753612479475 9.24638752052545 71 149.9 142.586945812808 7.31305418719211 72 150.9 144.570279146141 6.32972085385876 73 141 137.115763546798 3.884236453202 74 138.9 136.172906403941 2.72709359605912 75 157.4 152.201477832512 5.19852216748769 76 142.9 141.830049261084 1.06995073891625 77 151.7 144.158620689655 7.54137931034482 78 161 152.487192118227 8.51280788177339 79 138.6 131.215763546798 7.38423645320195 80 136 131.144334975369 4.85566502463053 81 151.9 149.887192118227 2.01280788177338

Charts produced by software:

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Parameters (Session):

Parameters (R input):

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')

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Software written by Ed van Stee & Patrick Wessa

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