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multiple linear regression

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

Title produced by software: Multiple Regression

Date of computation: Thu, 29 Nov 2007 03:14:06 -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/29/t1196330652iz2ygnt6wxvi4sw.htm/, Retrieved Thu, 29 Nov 2007 11:04:36 +0100

User-defined keywords:

Dataseries X:

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15859,4 0 15258,9 0 15498,6 0 15106,5 0 15023,6 0 12083,0 0 15761,3 0 16942,6 0 15070,3 0 13659,6 0 14768,9 0 14725,1 0 15998,1 0 15370,6 0 14956,9 0 15469,7 0 15101,8 0 11703,7 0 16283,6 0 16726,5 0 14968,9 0 14861,0 0 14583,3 0 15305,8 0 17903,9 0 16379,4 0 15420,3 0 17870,5 0 15912,8 0 13866,5 0 17823,2 0 17872,0 0 17422,0 0 16704,5 0 15991,2 0 16583,6 0 19123,5 0 17838,7 0 17209,4 0 18586,5 0 16258,1 0 15141,6 1 19202,1 1 17746,5 1 19090,1 1 18040,3 1 17515,5 1 17751,8 1 21072,4 1 17170,0 1 19439,5 1 19795,4 1 17574,9 1 16165,4 1 19464,6 1 19932,1 1 19961,2 1 17343,4 1 18924,2 1 18574,1 1 21350,6 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] = + 13685.7137142857 + 533.767678571429`x `[t] + 2372.27384722223M1[t] + 669.098873015872M2[t] + 695.828339285715M3[t] + 1481.91780555556M4[t] + 15.7472718253972M5[t] -2347.89679761905M6[t] + 1492.33266865079M7[t] + 1554.62213492063M8[t] + 938.491601190476M9[t] -316.938932539682M10[t] -156.769466269840M11[t] + 74.6905337301586t + 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) 13685.7137142857 365.566705 37.437 0 0 `x ` 533.767678571429 316.963171 1.684 0.098812 0.049406 M1 2372.27384722223 403.195795 5.8837 0 0 M2 669.098873015872 423.004094 1.5818 0.120407 0.060204 M3 695.828339285715 422.438844 1.6472 0.106194 0.053097 M4 1481.91780555556 422.040557 3.5113 0.000996 0.000498 M5 15.7472718253972 421.809707 0.0373 0.970378 0.485189 M6 -2347.89679761905 423.145504 -5.5487 1e-06 1e-06 M7 1492.33266865079 422.224628 3.5345 0.000929 0.000465 M8 1554.62213492063 421.469687 3.6886 0.000584 0.000292 M9 938.491601190476 420.881575 2.2298 0.030574 0.015287 M10 -316.938932539682 420.460991 -0.7538 0.454736 0.227368 M11 -156.769466269840 420.208439 -0.3731 0.71077 0.355385 t 74.6905337301586 8.412551 8.8785 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.956265506678066 R-squared 0.914443719262259 Adjusted R-squared 0.89077921607948 F-TEST (value) 38.6419994622027 F-TEST (DF numerator) 13 F-TEST (DF denominator) 47 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 664.27471898456 Sum Squared Residuals 20739262.4072547 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 15859.4 16132.6780952381 -273.278095238068 2 15258.9 14504.1936547619 754.706345238095 3 15498.6 14605.6136547619 892.986345238093 4 15106.5 15466.3936547619 -359.893654761904 5 15023.6 14074.9136547619 948.686345238094 6 12083 11785.9601190476 297.039880952375 7 15761.3 15700.8801190476 60.4198809523804 8 16942.6 15837.8601190476 1104.73988095237 9 15070.3 15296.4201190476 -226.120119047622 10 13659.6 14115.6801190476 -456.080119047619 11 14768.9 14350.5401190476 418.359880952379 12 14725.1 14582.0001190476 143.099880952381 13 15998.1 17028.9645 -1030.86450000001 14 15370.6 15400.4800595238 -29.8800595238116 15 14956.9 15501.9000595238 -545.000059523811 16 15469.7 16362.6800595238 -892.98005952381 17 15101.8 14971.2000595238 130.599940476189 18 11703.7 12682.2465238095 -978.546523809523 19 16283.6 16597.1665238095 -313.566523809523 20 16726.5 16734.1465238095 -7.64652380952321 21 14968.9 16192.7065238095 -1223.80652380952 22 14861 15011.9665238095 -150.966523809524 23 14583.3 15246.8265238095 -663.526523809525 24 15305.8 15478.2865238095 -172.486523809524 25 17903.9 17925.2509047619 -21.3509047619098 26 16379.4 16296.7664642857 82.6335357142855 27 15420.3 16398.1864642857 -977.886464285715 28 17870.5 17258.9664642857 611.533535714285 29 15912.8 15867.4864642857 45.3135357142852 30 13866.5 13578.5329285714 287.967071428574 31 17823.2 17493.4529285714 329.747071428573 32 17872 17630.4329285714 241.567071428574 33 17422 17088.9929285714 333.007071428573 34 16704.5 15908.2529285714 796.247071428572 35 15991.2 16143.1129285714 -151.912928571427 36 16583.6 16374.5729285714 209.027071428572 37 19123.5 18821.5373095238 301.962690476186 38 17838.7 17193.0528690476 645.647130952383 39 17209.4 17294.4728690476 -85.0728690476161 40 18586.5 18155.2528690476 431.247130952381 41 16258.1 16763.7728690476 -505.672869047617 42 15141.6 15008.5870119048 133.012988095239 43 19202.1 18923.5070119048 278.592988095236 44 17746.5 19060.4870119048 -1313.98701190476 45 19090.1 18519.0470119048 571.052988095237 46 18040.3 17338.3070119048 701.992988095237 47 17515.5 17573.1670119048 -57.6670119047625 48 17751.8 17804.6270119048 -52.827011904762 49 21072.4 20251.5913928571 820.808607142853 50 17170 18623.1069523810 -1453.10695238095 51 19439.5 18724.5269523810 714.973047619049 52 19795.4 19585.3069523810 210.093047619048 53 17574.9 18193.8269523810 -618.926952380951 54 16165.4 15904.8734166667 260.526583333335 55 19464.6 19819.7934166667 -355.193416666667 56 19932.1 19956.7734166667 -24.6734166666659 57 19961.2 19415.3334166667 545.866583333336 58 17343.4 18234.5934166667 -891.193416666664 59 18924.2 18469.4534166667 454.746583333335 60 18574.1 18700.9134166667 -126.813416666666 61 21350.6 21147.8777976191 202.722202380946

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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