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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 03:22:42 -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/t1195467485csuvyghgpe2hejb.htm/, Retrieved Mon, 19 Nov 2007 11:18:33 +0100

User-defined keywords:

groep 1 ws6 vraag 3

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 1 103,6 1 94,1 1 98,7 1 119,5 1 112,7 1 104,4 1 124,7 1 89,1 1 97 1 121,6 1 118,8 1 114 1 111,5 1 97,2 1 102,5 1 113,4 1 109,8 1 104,9 1 126,1 1 80 1 96,8 1 117,2 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] = + 104.252941176471 + 8.92531969309463x[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) 104.252941176471 2.146267 48.5741 0 0 x 8.92531969309463 2.830414 3.1534 0.002292 0.001146 Multiple Linear Regression - Regression Statistics Multiple R 0.336257132538942 R-squared 0.113068859183312 Adjusted R-squared 0.101697947121559 F-TEST (value) 9.94369304496108 F-TEST (DF numerator) 1 F-TEST (DF denominator) 78 p-value 0.00229171634194392 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 12.5147825240803 Sum Squared Residuals 12216.3429667519 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 97.3 104.252941176471 -6.95294117647088 2 101 104.252941176471 -3.25294117647057 3 113.2 104.252941176471 8.94705882352942 4 101 104.252941176471 -3.25294117647058 5 105.7 104.252941176471 1.44705882352942 6 113.9 104.252941176471 9.64705882352943 7 86.4 104.252941176471 -17.8529411764706 8 96.5 104.252941176471 -7.75294117647058 9 103.3 104.252941176471 -0.952941176470584 10 114.9 104.252941176471 10.6470588235294 11 105.8 104.252941176471 1.54705882352942 12 94.2 104.252941176471 -10.0529411764706 13 98.4 104.252941176471 -5.85294117647058 14 99.4 104.252941176471 -4.85294117647058 15 108.8 104.252941176471 4.54705882352942 16 112.6 104.252941176471 8.34705882352941 17 104.4 104.252941176471 0.147058823529425 18 112.2 104.252941176471 7.94705882352942 19 81.1 104.252941176471 -23.1529411764706 20 97.1 104.252941176471 -7.15294117647059 21 112.6 104.252941176471 8.34705882352941 22 113.8 104.252941176471 9.54705882352942 23 107.8 104.252941176471 3.54705882352942 24 103.2 104.252941176471 -1.05294117647058 25 103.3 104.252941176471 -0.952941176470584 26 101.2 104.252941176471 -3.05294117647058 27 107.7 104.252941176471 3.44705882352942 28 110.4 104.252941176471 6.14705882352942 29 101.9 104.252941176471 -2.35294117647058 30 115.9 104.252941176471 11.6470588235294 31 89.9 104.252941176471 -14.3529411764706 32 88.6 104.252941176471 -15.6529411764706 33 117.2 104.252941176471 12.9470588235294 34 123.9 104.252941176471 19.6470588235294 35 100 113.178260869565 -13.1782608695652 36 103.6 113.178260869565 -9.57826086956522 37 94.1 113.178260869565 -19.0782608695652 38 98.7 113.178260869565 -14.4782608695652 39 119.5 113.178260869565 6.32173913043478 40 112.7 113.178260869565 -0.478260869565215 41 104.4 113.178260869565 -8.77826086956521 42 124.7 113.178260869565 11.5217391304348 43 89.1 113.178260869565 -24.0782608695652 44 97 113.178260869565 -16.1782608695652 45 121.6 113.178260869565 8.42173913043478 46 118.8 113.178260869565 5.62173913043478 47 114 113.178260869565 0.821739130434782 48 111.5 113.178260869565 -1.67826086956522 49 97.2 113.178260869565 -15.9782608695652 50 102.5 113.178260869565 -10.6782608695652 51 113.4 113.178260869565 0.221739130434788 52 109.8 113.178260869565 -3.37826086956522 53 104.9 113.178260869565 -8.27826086956521 54 126.1 113.178260869565 12.9217391304348 55 80 113.178260869565 -33.1782608695652 56 96.8 113.178260869565 -16.3782608695652 57 117.2 113.178260869565 4.02173913043479 58 112.3 113.178260869565 -0.87826086956522 59 117.3 113.178260869565 4.12173913043478 60 111.1 113.178260869565 -2.07826086956522 61 102.2 113.178260869565 -10.9782608695652 62 104.3 113.178260869565 -8.87826086956522 63 122.9 113.178260869565 9.72173913043479 64 107.6 113.178260869565 -5.57826086956522 65 121.3 113.178260869565 8.12173913043478 66 131.5 113.178260869565 18.3217391304348 67 89 113.178260869565 -24.1782608695652 68 104.4 113.178260869565 -8.77826086956521 69 128.9 113.178260869565 15.7217391304348 70 135.9 113.178260869565 22.7217391304348 71 133.3 113.178260869565 20.1217391304348 72 121.3 113.178260869565 8.12173913043478 73 120.5 113.178260869565 7.32173913043478 74 120.4 113.178260869565 7.22173913043479 75 137.9 113.178260869565 24.7217391304348 76 126.1 113.178260869565 12.9217391304348 77 133.2 113.178260869565 20.0217391304348 78 146.6 113.178260869565 33.4217391304348 79 103.4 113.178260869565 -9.77826086956521 80 117.2 113.178260869565 4.02173913043479

Charts produced by software:

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Parameters:

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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