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Paper, regressie

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

Title produced by software: Multiple Regression

Date of computation: Tue, 04 Dec 2007 08:16:00 -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/04/t1196780637ld649yc09n7b3yl.htm/, Retrieved Tue, 04 Dec 2007 16:04:07 +0100

User-defined keywords:

Paper, regressie

Dataseries X:

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97,3 0 101 0 113,2 0 101 0 105,7 0 113,9 0 86,4 0 96,5 0 103,3 0 114,9 0 105,8 0 94,2 0 98,4 0 99,4 0 108,8 0 112,6 0 104,4 0 112,2 0 81,1 0 97,1 0 112,6 0 113,8 0 107,8 0 103,2 0 103,3 0 101,2 0 107,7 0 110,4 0 101,9 0 115,9 0 89,9 0 88,6 0 117,2 0 123,9 0 100 0 103,6 0 94,1 0 98,7 0 119,5 0 112,7 0 104,4 0 124,7 0 89,1 0 97 0 121,6 0 118,8 0 114 0 111,5 0 97,2 0 102,5 0 113,4 0 109,8 0 104,9 0 126,1 0 80 0 96,8 0 117,2 1 112,3 1 117,3 1 111,1 1 102,2 1 104,3 1 122,9 1 107,6 1 121,3 1 131,5 1 89 1 104,4 1 128,9 1 135,9 1 133,3 1 121,3 1 120,5 1 120,4 1 137,9 1 126,1 1 133,2 1 146,6 1 103,4 1 117,2 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation y[t] = + 102.811458333333 + 14.015625`x `[t] -4.95877976190481M1[t] -2.8873511904762M2[t] + 10.8126488095238M3[t] + 4.64122023809525M4[t] + 4.01264880952381M5[t] + 17.5983630952381M6[t] -18.4016369047619M7[t] -7.15877976190477M8[t] + 9.31666666666667M9[t] + 12.45M10[t] + 5.55M11[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) 102.811458333333 2.755055 37.3174 0 0 `x ` 14.015625 1.616498 8.6704 0 0 M1 -4.95877976190481 3.682804 -1.3465 0.182689 0.091345 M2 -2.8873511904762 3.682804 -0.784 0.435798 0.217899 M3 10.8126488095238 3.682804 2.936 0.004552 0.002276 M4 4.64122023809525 3.682804 1.2602 0.211954 0.105977 M5 4.01264880952381 3.682804 1.0896 0.279809 0.139904 M6 17.5983630952381 3.682804 4.7785 1e-05 5e-06 M7 -18.4016369047619 3.682804 -4.9966 4e-06 2e-06 M8 -7.15877976190477 3.682804 -1.9438 0.056116 0.028058 M9 9.31666666666667 3.820992 2.4383 0.017415 0.008708 M10 12.45 3.820992 3.2583 0.001762 0.000881 M11 5.55 3.820992 1.4525 0.151029 0.075515 Multiple Linear Regression - Regression Statistics Multiple R 0.887097759577947 R-squared 0.786942435048213 Adjusted R-squared 0.748782871176251 F-TEST (value) 20.6224169041520 F-TEST (DF numerator) 12 F-TEST (DF denominator) 67 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 6.61815196016258 Sum Squared Residuals 2934.59566964286 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 97.3 97.8526785714288 -0.552678571428839 2 101 99.9241071428571 1.07589285714286 3 113.2 113.624107142857 -0.424107142857127 4 101 107.452678571429 -6.45267857142857 5 105.7 106.824107142857 -1.12410714285713 6 113.9 120.409821428571 -6.50982142857144 7 86.4 84.4098214285714 1.99017857142858 8 96.5 95.6526785714286 0.847321428571432 9 103.3 112.128125 -8.82812499999999 10 114.9 115.261458333333 -0.361458333333306 11 105.8 108.361458333333 -2.56145833333333 12 94.2 102.811458333333 -8.61145833333333 13 98.4 97.8526785714285 0.547321428571477 14 99.4 99.9241071428571 -0.524107142857133 15 108.8 113.624107142857 -4.82410714285715 16 112.6 107.452678571429 5.14732142857142 17 104.4 106.824107142857 -2.42410714285714 18 112.2 120.409821428571 -8.20982142857142 19 81.1 84.4098214285714 -3.30982142857143 20 97.1 95.6526785714286 1.44732142857143 21 112.6 112.128125 0.471874999999988 22 113.8 115.261458333333 -1.46145833333334 23 107.8 108.361458333333 -0.561458333333333 24 103.2 102.811458333333 0.388541666666675 25 103.3 97.8526785714285 5.44732142857147 26 101.2 99.9241071428571 1.27589285714286 27 107.7 113.624107142857 -5.92410714285714 28 110.4 107.452678571429 2.94732142857143 29 101.9 106.824107142857 -4.92410714285714 30 115.9 120.409821428571 -4.50982142857142 31 89.9 84.4098214285714 5.49017857142858 32 88.6 95.6526785714286 -7.05267857142858 33 117.2 112.128125 5.071875 34 123.9 115.261458333333 8.63854166666667 35 100 108.361458333333 -8.36145833333333 36 103.6 102.811458333333 0.788541666666666 37 94.1 97.8526785714285 -3.75267857142853 38 98.7 99.9241071428571 -1.22410714285714 39 119.5 113.624107142857 5.87589285714285 40 112.7 107.452678571429 5.24732142857143 41 104.4 106.824107142857 -2.42410714285714 42 124.7 120.409821428571 4.29017857142858 43 89.1 84.4098214285714 4.69017857142857 44 97 95.6526785714286 1.34732142857143 45 121.6 112.128125 9.47187499999999 46 118.8 115.261458333333 3.53854166666666 47 114 108.361458333333 5.63854166666667 48 111.5 102.811458333333 8.68854166666667 49 97.2 97.8526785714285 -0.652678571428523 50 102.5 99.9241071428571 2.57589285714286 51 113.4 113.624107142857 -0.224107142857142 52 109.8 107.452678571429 2.34732142857142 53 104.9 106.824107142857 -1.92410714285714 54 126.1 120.409821428571 5.69017857142857 55 80 84.4098214285714 -4.40982142857143 56 96.8 95.6526785714286 1.14732142857143 57 117.2 126.14375 -8.94375 58 112.3 129.277083333333 -16.9770833333333 59 117.3 122.377083333333 -5.07708333333334 60 111.1 116.827083333333 -5.72708333333334 61 102.2 111.868303571429 -9.66830357142853 62 104.3 113.939732142857 -9.63973214285715 63 122.9 127.639732142857 -4.73973214285714 64 107.6 121.468303571429 -13.8683035714286 65 121.3 120.839732142857 0.460267857142848 66 131.5 134.425446428571 -2.92544642857143 67 89 98.4254464285714 -9.42544642857143 68 104.4 109.668303571429 -5.26830357142857 69 128.9 126.14375 2.75625 70 135.9 129.277083333333 6.62291666666667 71 133.3 122.377083333333 10.9229166666667 72 121.3 116.827083333333 4.47291666666666 73 120.5 111.868303571429 8.63169642857147 74 120.4 113.939732142857 6.46026785714286 75 137.9 127.639732142857 10.2602678571429 76 126.1 121.468303571429 4.63169642857142 77 133.2 120.839732142857 12.3602678571428 78 146.6 134.425446428571 12.1745535714286 79 103.4 98.4254464285714 4.97455357142857 80 117.2 109.668303571429 7.53169642857143

Charts produced by software:

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Parameters:

par1 = 1 ; par2 = Include Monthly 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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