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Q3_WS8_Rik_Tim_Giel

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

Title produced by software: Multiple Regression

Date of computation: Fri, 16 Nov 2007 08:39:10 -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/16/t1195227699tmsphp3lww82tgd.htm/, Retrieved Fri, 16 Nov 2007 16:41:48 +0100

User-defined keywords:

woningen, rente, workshop 8, Q3

Dataseries X:

» Textbox « » Textfile « » CSV «

3481 0 3592 0 3472 0 2312 0 3322 0 4348 0 3603 0 2700 0 2640 0 2918 0 3181 0 4151 0 4024 0 3431 0 3870 1 2618 0 3577 0 5268 0 3833 0 3442 0 3217 0 3401 0 3973 0 4628 0 4489 0 4130 0 4687 0 3179 0 4280 0 4214 0 4154 0 3938 0 3129 1 3588 1 4169 1 4349 1 4696 1 4714 1 4892 1 3373 1 4453 1 5174 1 4916 1 4690 1 3841 1 4325 1 4559 1 5370 1 4693 0 5177 0 4860 0 3368 0 4796 0 4979 0 5082 0 4815 0 3709 0 3985 0 4117 0 4022 0 4136 0 4341 0

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 Won[t] = + 3620.3186440678 + 287.457627118644`Rente `[t] -76.996233521657M1[t] -120.682297551789M2[t] + 44.3745762711868M3[t] -1305.68662900188M4[t] -211.439359698682M5[t] + 478.207909604521M6[t] -22.1448210922781M7[t] -444.097551789077M8[t] -1132.74180790960M9[t] -817.894538606403M10[t] -482.847269303201M11[t] + 21.3527306967985t + 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) 3620.3186440678 185.880156 19.4766 0 0 `Rente ` 287.457627118644 108.312037 2.654 0.010757 0.005378 M1 -76.996233521657 218.275426 -0.3527 0.725822 0.362911 M2 -120.682297551789 218.20768 -0.5531 0.582788 0.291394 M3 44.3745762711868 227.68678 0.1949 0.846299 0.42315 M4 -1305.68662900188 227.945405 -5.7281 1e-06 0 M5 -211.439359698682 227.777231 -0.9283 0.357911 0.178955 M6 478.207909604521 227.639862 2.1007 0.040943 0.020471 M7 -22.1448210922781 227.533356 -0.0973 0.922873 0.461437 M8 -444.097551789077 227.457755 -1.9524 0.056731 0.028366 M9 -1132.74180790960 226.570857 -4.9995 8e-06 4e-06 M10 -817.894538606403 226.493158 -3.6111 0.000727 0.000364 M11 -482.847269303201 226.446526 -2.1323 0.038128 0.019064 t 21.3527306967985 2.653396 8.0473 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.898934045452476 R-squared 0.808082418073554 Adjusted R-squared 0.756104739635142 F-TEST (value) 15.5467200989178 F-TEST (DF numerator) 13 F-TEST (DF denominator) 48 p-value 5.49782441794378e-13 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 358.018814833736 Sum Squared Residuals 6152518.64519774 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 3481 3564.67514124294 -83.6751412429386 2 3592 3542.34180790960 49.6581920903955 3 3472 3728.75141242938 -256.751412429379 4 2312 2400.04293785311 -88.042937853107 5 3322 3515.64293785311 -193.642937853107 6 4348 4226.64293785311 121.357062146893 7 3603 3747.64293785311 -144.642937853107 8 2700 3347.04293785311 -647.042937853108 9 2640 2679.75141242938 -39.7514124293791 10 2918 3015.95141242938 -97.9514124293785 11 3181 3372.35141242938 -191.351412429378 12 4151 3876.55141242938 274.448587570621 13 4024 3820.90790960452 203.092090395481 14 3431 3798.57457627119 -367.574576271187 15 3870 4272.44180790960 -402.441807909605 16 2618 2656.27570621469 -38.2757062146893 17 3577 3771.87570621469 -194.875706214689 18 5268 4482.87570621469 785.12429378531 19 3833 4003.87570621469 -170.875706214689 20 3442 3603.27570621469 -161.275706214689 21 3217 2935.98418079096 281.01581920904 22 3401 3272.18418079096 128.815819209040 23 3973 3628.58418079096 344.415819209039 24 4628 4132.78418079096 495.215819209039 25 4489 4077.1406779661 411.859322033898 26 4130 4054.80734463277 75.192655367232 27 4687 4241.21694915254 445.783050847458 28 3179 2912.50847457627 266.491525423729 29 4280 4028.10847457627 251.891525423729 30 4214 4739.10847457627 -525.108474576272 31 4154 4260.10847457627 -106.108474576271 32 3938 3859.50847457627 78.491525423729 33 3129 3479.67457627119 -350.674576271186 34 3588 3815.87457627119 -227.874576271186 35 4169 4172.27457627119 -3.2745762711867 36 4349 4676.47457627119 -327.474576271186 37 4696 4620.83107344633 75.1689265536724 38 4714 4598.497740113 115.502259887006 39 4892 4784.90734463277 107.092655367232 40 3373 3456.1988700565 -83.1988700564972 41 4453 4571.7988700565 -118.798870056497 42 5174 5282.7988700565 -108.798870056497 43 4916 4803.7988700565 112.201129943503 44 4690 4403.19887005650 286.801129943503 45 3841 3735.90734463277 105.092655367232 46 4325 4072.10734463277 252.892655367232 47 4559 4428.50734463277 130.492655367231 48 5370 4932.70734463277 437.292655367232 49 4693 4589.60621468927 103.393785310735 50 5177 4567.27288135593 609.727118644068 51 4860 4753.68248587571 106.317514124294 52 3368 3424.97401129944 -56.9740112994351 53 4796 4540.57401129943 255.425988700565 54 4979 5251.57401129944 -272.574011299435 55 5082 4772.57401129944 309.425988700565 56 4815 4371.97401129944 443.025988700565 57 3709 3704.68248587571 4.31751412429412 58 3985 4040.88248587571 -55.8824858757062 59 4117 4397.28248587571 -280.282485875707 60 4022 4901.48248587571 -879.482485875706 61 4136 4845.83898305085 -709.838983050848 62 4341 4823.50564971751 -482.505649717514

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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