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

Title produced by software: Multiple Regression

Date of computation: Mon, 19 Nov 2007 11:02:20 -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/19/t1195494936ritknomo2lx48ex.htm/, Retrieved Mon, 19 Nov 2007 18:55:46 +0100

User-defined keywords:

Q3 Totale productie

Dataseries X:

» Textbox « » Textfile « » CSV «

106,7 0 110,2 0 125,9 0 100,1 0 106,4 0 114,8 0 81,3 0 87 0 104,2 0 108 0 105 0 94,5 0 92 0 95,9 0 108,8 0 103,4 0 102,1 0 110,1 0 83,2 0 82,7 0 106,8 0 113,7 0 102,5 0 96,6 0 92,1 0 95,6 0 102,3 0 98,6 0 98,2 0 104,5 0 84 0 73,8 0 103,9 0 106 0 97,2 0 102,6 0 89 0 93,8 0 116,7 0 106,8 0 98,5 0 118,7 0 90 0 91,9 0 113,3 1 113,1 1 104,1 1 108,7 1 96,7 1 101 1 116,9 1 105,8 1 99 1 129,4 1 83 1 88,9 1 115,9 1 104,2 1 113,4 1 112,2 1 100,8 1 107,3 1 126,6 1 102,9 1 117,9 1 128,8 1 87,5 1 93,8 1 122,7 1 126,2 1 124,6 1 116,7 1 115,2 1 111,1 1 129,9 1 113,3 1 118,5 1 133,5 1 102,1 1 102,4 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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation y[t] = + 97.6433333333333 + 5.88291666666667x[t] -5.31647321428578M1[t] -2.22675595238096M2[t] + 13.6915327380952M3[t] -0.161607142857151M4[t] + 1.11382440476191M5[t] + 15.1749702380952M6[t] -17.6067410714286M7[t] -16.3741666666667M8[t] + 6.24751488095237M9[t] + 6.87056547619047M10[t] + 2.69361607142857M11[t] + 0.110282738095238t + 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) 97.6433333333333 3.106726 31.4297 0 0 x 5.88291666666667 2.959403 1.9879 0.050977 0.025488 M1 -5.31647321428578 3.647896 -1.4574 0.149746 0.074873 M2 -2.22675595238096 3.646073 -0.6107 0.543478 0.271739 M3 13.6915327380952 3.645367 3.7559 0.000368 0.000184 M4 -0.161607142857151 3.645781 -0.0443 0.964777 0.482389 M5 1.11382440476191 3.647312 0.3054 0.761036 0.380518 M6 15.1749702380952 3.649961 4.1576 9.5e-05 4.7e-05 M7 -17.6067410714286 3.653724 -4.8188 9e-06 4e-06 M8 -16.3741666666667 3.658598 -4.4755 3.1e-05 1.5e-05 M9 6.24751488095237 3.786236 1.6501 0.103682 0.051841 M10 6.87056547619047 3.783542 1.8159 0.073927 0.036963 M11 2.69361607142857 3.781925 0.7122 0.47883 0.239415 t 0.110282738095238 0.063862 1.7269 0.088863 0.044432 Multiple Linear Regression - Regression Statistics Multiple R 0.882316047395406 R-squared 0.778481607491453 Adjusted R-squared 0.73484919684583 F-TEST (value) 17.8418197842467 F-TEST (DF numerator) 13 F-TEST (DF denominator) 66 p-value 1.11022302462516e-16 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 6.54955267493152 Sum Squared Residuals 2831.17825595237 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 106.7 92.4371428571432 14.2628571428568 2 110.2 95.6371428571429 14.5628571428571 3 125.9 111.665714285714 14.2342857142858 4 100.1 97.9228571428571 2.17714285714287 5 106.4 99.3085714285714 7.09142857142859 6 114.8 113.48 1.32000000000003 7 81.3 80.8085714285714 0.491428571428584 8 87 82.1514285714286 4.84857142857144 9 104.2 104.883392857143 -0.683392857142873 10 108 105.616726190476 2.38327380952379 11 105 101.550059523810 3.44994047619049 12 94.5 98.9667261904762 -4.46672619047619 13 92 93.7605357142857 -1.76053571428566 14 95.9 96.9605357142857 -1.06053571428570 15 108.8 112.989107142857 -4.18910714285714 16 103.4 99.24625 4.15375000000001 17 102.1 100.631964285714 1.46803571428571 18 110.1 114.803392857143 -4.70339285714286 19 83.2 82.1319642857143 1.06803571428572 20 82.7 83.4748214285714 -0.77482142857143 21 106.8 106.206785714286 0.59321428571429 22 113.7 106.940119047619 6.75988095238096 23 102.5 102.873452380952 -0.373452380952379 24 96.6 100.290119047619 -3.69011904761905 25 92.1 95.0839285714285 -2.98392857142852 26 95.6 98.2839285714286 -2.68392857142857 27 102.3 114.3125 -12.0125 28 98.6 100.569642857143 -1.96964285714286 29 98.2 101.955357142857 -3.75535714285714 30 104.5 116.126785714286 -11.6267857142857 31 84 83.4553571428571 0.544642857142854 32 73.8 84.7982142857143 -10.9982142857143 33 103.9 107.530178571429 -3.63017857142856 34 106 108.263511904762 -2.2635119047619 35 97.2 104.196845238095 -6.99684523809523 36 102.6 101.613511904762 0.986488095238083 37 89 96.4073214285714 -7.40732142857138 38 93.8 99.6073214285714 -5.80732142857143 39 116.7 115.635892857143 1.06410714285714 40 106.8 101.893035714286 4.90696428571428 41 98.5 103.27875 -4.77875 42 118.7 117.450178571429 1.24982142857142 43 90 84.77875 5.22125 44 91.9 86.1216071428571 5.77839285714286 45 113.3 114.736488095238 -1.43648809523809 46 113.1 115.469821428571 -2.36982142857143 47 104.1 111.403154761905 -7.30315476190477 48 108.7 108.819821428571 -0.119821428571430 49 96.7 103.613630952381 -6.9136309523809 50 101 106.813630952381 -5.81363095238095 51 116.9 122.842202380952 -5.94220238095238 52 105.8 109.099345238095 -3.29934523809524 53 99 110.485059523810 -11.4850595238095 54 129.4 124.656488095238 4.7435119047619 55 83 91.9850595238095 -8.98505952380953 56 88.9 93.3279166666667 -4.42791666666666 57 115.9 116.059880952381 -0.159880952380947 58 104.2 116.793214285714 -12.5932142857143 59 113.4 112.726547619048 0.673452380952381 60 112.2 110.143214285714 2.05678571428571 61 100.8 104.937023809524 -4.13702380952377 62 107.3 108.137023809524 -0.837023809523818 63 126.6 124.165595238095 2.43440476190474 64 102.9 110.422738095238 -7.5227380952381 65 117.9 111.808452380952 6.09154761904762 66 128.8 125.979880952381 2.82011904761905 67 87.5 93.3084523809524 -5.80845238095238 68 93.8 94.6513095238095 -0.851309523809535 69 122.7 117.383273809524 5.31672619047619 70 126.2 118.116607142857 8.08339285714285 71 124.6 114.049940476190 10.5500595238095 72 116.7 111.466607142857 5.23339285714285 73 115.2 106.260416666667 8.93958333333338 74 111.1 109.460416666667 1.63958333333332 75 129.9 125.488988095238 4.41101190476189 76 113.3 111.746130952381 1.55386904761904 77 118.5 113.131845238095 5.36815476190475 78 133.5 127.303273809524 6.19672619047617 79 102.1 94.6318452380953 7.46815476190475 80 102.4 95.9747023809524 6.42529761904761

Charts produced by software:

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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

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