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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: Tue, 18 Dec 2007 12:42:27 -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/t1198005964fvdd37aai93k2nt.htm/, Retrieved Tue, 18 Dec 2007 20:26:15 +0100

User-defined keywords:

Dataseries X:

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8.1 359 8.3 304.6 8.2 297.7 8.1 303.3 7.7 304.7 7.6 331.3 7.7 318.8 8.2 306.8 8.4 331.1 8.4 284.1 8.6 259.7 8.4 335.8 8.5 338.5 8.7 310.3 8.7 322.1 8.6 289.3 7.4 300.8 7.3 360.6 7.4 327.3 9 304.1 9.2 362 9.2 287.8 8.5 286.1 8.3 358.2 8.3 346 8.6 329.9 8.6 334.3 8.5 303.7 8.1 307.6 8.1 351.7 8 324.6 8.6 311.9 8.7 361.5 8.7 271.1 8.6 286.5 8.4 352.8 8.4 322.4 8.7 335 8.7 322.2 8.5 313.6 8.3 323.3 8.3 379.1 8.3 315.6 8.1 353.6 8.2 371.7 8.1 282.9 8.1 298.8 7.9 361.8 7.7 365.9 8.1 357.6 8 335.4 7.7 340.1 7.8 337.8 7.6 389.6 7.4 342.5 7.7 354.6 7.8 391.6 7.5 317.7 7.2 312.8 7 356.2

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] = + 389.155925196851 -7.52559055118119Y[t] + 2.2411400918632M1[t] -15.1986056430446M2[t] -21.3065403543307M3[t] -35.5175459317585M4[t] -34.5052050524935M5[t] + 11.8458366141732M6[t] -25.6715862860892M7[t] -21.6841666666666M8[t] + 16.0825049212599M9[t] -60.0464534120734M10[t] -62.0079708005249M11[t] + 0.666911089238846t + 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) 389.155925196851 34.929166 11.1413 0 0 Y -7.52559055118119 4.119764 -1.8267 0.074237 0.037119 M1 2.2411400918632 7.657875 0.2927 0.771099 0.38555 M2 -15.1986056430446 7.799657 -1.9486 0.057455 0.028728 M3 -21.3065403543307 7.76483 -2.744 0.008626 0.004313 M4 -35.5175459317585 7.663006 -4.6349 3e-05 1.5e-05 M5 -34.5052050524935 7.655622 -4.5072 4.5e-05 2.2e-05 M6 11.8458366141732 7.686258 1.5412 0.130127 0.065063 M7 -25.6715862860892 7.686879 -3.3397 0.00167 0.000835 M8 -21.6841666666666 7.678863 -2.8239 0.00699 0.003495 M9 16.0825049212599 7.792141 2.0639 0.044691 0.022345 M10 -60.0464534120734 7.728294 -7.7697 0 0 M11 -62.0079708005249 7.62264 -8.1347 0 0 t 0.666911089238846 0.099146 6.7266 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.933813178790619 R-squared 0.87200705288304 Adjusted R-squared 0.835835133045638 F-TEST (value) 24.1072925297536 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 3.33066907387547e-16 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 11.9874974471114 Sum Squared Residuals 6610.20437204716 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 359 331.106692913387 27.8933070866129 2 304.6 312.82874015748 -8.22874015748024 3 297.7 308.140275590551 -10.4402755905512 4 303.3 295.34874015748 7.9512598425197 5 304.7 300.038228346457 4.66177165354334 6 331.3 347.808740157480 -16.5087401574803 7 318.8 310.205669291339 8.59433070866145 8 306.8 311.097204724409 -4.29720472440946 9 331.1 348.025669291339 -16.9256692913386 10 284.1 272.563622047244 11.5363779527559 11 259.7 269.763897637795 -10.0638976377952 12 335.8 333.943897637795 1.85610236220474 13 338.5 336.099389763779 2.40061023622085 14 310.3 317.821437007874 -7.52143700787398 15 322.1 312.380413385827 9.71958661417329 16 289.3 299.588877952756 -10.2888779527559 17 300.8 310.298838582677 -9.4988385826772 18 360.6 358.069350393701 2.53064960629918 19 327.3 320.466279527559 6.8337204724409 20 304.1 313.079665354331 -8.97966535433061 21 362 350.00812992126 11.9918700787402 22 287.8 274.546082677165 13.2539173228348 23 286.1 278.519389763779 7.58061023622051 24 358.2 342.699389763779 15.5006102362205 25 346 345.607440944882 0.392559055118447 26 329.9 326.576929133858 3.32307086614171 27 334.3 321.135905511811 13.164094488189 28 303.7 308.34437007874 -4.64437007874015 29 307.6 313.033858267717 -5.43385826771652 30 351.7 360.051811023622 -8.35181102362206 31 324.6 323.953858267717 0.646141732283486 32 311.9 324.092834645669 -12.1928346456693 33 361.5 361.773858267716 -0.273858267716511 34 271.1 286.311811023622 -15.211811023622 35 286.5 285.769763779528 0.730236220472475 36 352.8 349.949763779528 2.85023622047248 37 322.4 352.857814960630 -30.4578149606296 38 335 333.827303149606 1.17269685039369 39 322.2 328.386279527559 -6.18627952755905 40 313.6 316.347303149606 -2.74730314960627 41 323.3 319.531673228346 3.76832677165357 42 379.1 366.549625984252 12.5503740157481 43 315.6 329.699114173228 -14.0991141732283 44 353.6 335.858562992126 17.741437007874 45 371.7 373.539586614173 -1.83958661417327 46 282.9 298.830098425197 -15.9300984251969 47 298.8 297.535492125984 1.26450787401573 48 361.8 361.715492125984 0.0845078740157477 49 365.9 366.128661417323 -0.228661417322606 50 357.6 346.345590551181 11.2544094488188 51 335.4 341.657125984252 -6.25712598425205 52 340.1 330.370708661417 9.72929133858261 53 337.8 331.297401574803 6.50259842519681 54 389.6 379.820472440945 9.77952755905507 55 342.5 344.475078740158 -1.97507874015756 56 354.6 346.871732283465 7.72826771653537 57 391.6 384.552755905512 7.04724409448812 58 317.7 311.348385826772 6.35161417322822 59 312.8 312.311456692914 0.488543307086506 60 356.2 376.491456692914 -20.2914566929135

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 = 2 ; 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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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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