::Free Statistics and Forecasting Software::

All rights reserved. The non-commercial (academic) use of this software is free of charge. The only thing that is asked in return is to cite this software when results are used in publications.

This R module demonstrates with real data that gas consumption as usually measured by drivers is quite variable, and with no apparent trend, until a nonparametric smoother reveals a very distinct seasonal pattern. Ask students if they see anything in the data. The first graph you see is the raw data, and in the next graph the smoothed fit is displayed. The point of the demo is that nonparametric smoothing is easy to understand and useful, and should be taught in intro stats courses. The program can also be used to demonstrate the trial-and-error approach to choosing the degree of smoothing, by varying the parameter 'span'.

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Source code of R module

x <- c(1999.38 ,1999.39 ,1999.41 ,1999.42 ,1999.44 ,1999.45 ,1999.46 ,1999.47 ,1999.49 ,1999.5 ,1999.51 ,1999.52 ,1999.53 ,1999.54 ,1999.54 ,1999.58 ,1999.6 ,1999.64 ,1999.66 ,1999.59 ,1999.67 ,1999.68 ,1999.69 ,1999.71 ,1999.72 ,1999.73 ,1999.74 ,1999.76 ,1999.77 ,1999.78 ,1999.79 ,1999.81 ,1999.82 ,1999.84 ,1999.84 ,1999.86 ,1999.88 ,1999.89 ,1999.91 ,1999.92 ,1999.94 ,1999.95 ,1999.96 ,1999.98 ,2000 ,2000.02 ,2000.03 ,2000.04 ,2000.05 ,2000.16 ,2000.17 ,2000.19 ,2000.21 ,2000.21 ,2000.24 ,2000.25 ,2000.26 ,2000.27 ,2000.28 ,2000.29 ,2000.31 ,2000.34 ,2000.36 ,2000.36 ,2000.39 ,2000.4 ,2000.42 ,2000.43 ,2000.45 ,2000.46 ,2000.47 ,2000.51 ,2000.54 ,2000.56 ,2000.57 ,2000.59 ,2000.62 ,2000.63 ,2000.67 ,2000.67 ,2000.68 ,2000.7 ,2000.71 ,2000.73 ,2000.74 ,2000.76 ,2000.77 ,2000.78 ,2000.8 ,2000.81 ,2000.83 ,2000.84 ,2000.86 ,2000.87 ,2000.88 ,2000.88 ,2000.9 ,2000.91 ,2000.92 ,2000.93 ,2000.94 ,2000.96 ,2000.97 ,2000.98 ,2001.01 ,2001.03 ,2001.04 ,2001.06 ,2001.07 ,2001.08 ,2001.09 ,2001.12 ,2001.13 ,2001.16 ,2001.19 ,2001.2 ,2001.21 ,2001.23 ,2001.24 ,2001.26 ,2001.26 ,2001.27 ,2001.3 ,2001.31 ,2001.33 ,2001.34 ,2001.36 ,2001.36 ,2001.38 ,2001.4 ,2001.41 ,2001.43 ,2001.45 ,2001.46 ,2001.48 ,2001.5 ,2001.51 ,2001.53 ,2001.55 ,2001.57 ,2001.58 ,2001.59 ,2001.61 ,2001.62 ,2001.67 ,2001.69 ,2001.72 ,2001.73 ,2001.74 ,2001.76 ,2001.77 ,2001.78 ,2001.8 ,2001.81 ,2001.82 ,2001.84 ,2001.89 ,2001.9 ,2001.91 ,2001.92 ,2001.94 ,2001.96 ,2001.98 ,2002.01 ,2002.02 ,2002.04 ,2002.06 ,2002.07 ,2002.09 ,2002.1 ,2002.12 ,2002.14 ,2002.15 ,2002.16 ,2002.17 ,2002.19 ,2002.2 ,2002.21 ,2002.24 ,2002.24 ,2002.27 ,2002.28 ,2002.29 ,2002.31 ,2002.35 ,2002.37 ,2002.4 ,2002.34 ,2002.44 ,2002.5 ,2002.56 ,2002.6 ,2002.64 ,2002.65 ,2002.67 ,2002.69 ,2002.7 ,2002.72 ,2002.72 ,2002.74 ,2002.76 ,2002.77 ,2002.78 ,2002.8 ,2002.82 ,2002.84 ,2002.84 ,2002.87 ,2002.89 ,2002.9 ,2002.91 ,2002.92 ,2002.93 ,2002.99 ,2003.01 ,2003.04 ,2003.05 ,2003.07 ,2003.08 ,2003.1 ,2003.13 ,2003.15 ,2003.18 ,2003.19 ,2003.2 ,2003.22 ,2003.23 ,2003.24 ,2003.25 ,2003.26 ,2003.27 ,2003.29 ,2003.3 ,2003.32 ,2003.33 ,2003.34 ,2003.36 ,2003.36 ,2003.37 ,2003.39 ,2003.41 ,2003.42 ,2003.43 ,2003.46 ,2003.47 ,2003.48 ,2003.49 ,2003.51 ,2003.54 ,2003.55 ,2003.56 ,2003.58 ,2003.61 ,2003.66 ,2003.68 ,2003.68 ,2003.7 ,2003.72 ,2003.73 ,2003.74 ,2003.76 ,2003.81 ,2003.82 ,2003.84 ,2003.85 ,2003.86 ,2003.88 ,2003.88 ,2003.89 ,2003.91 ,2003.92 ,2003.94 ,2003.95 ,2003.96 ,2003.99 ,2004.02 ,2004.05 ,2004.03 ,2004.07 ,2004.08 ,2004.09 ,2004.11 ,2004.15 ,2004.17 ,2004.19 ,2004.21 ,2004.24 ,2004.26 ,2004.27 ,2004.28 ,2004.3 ,2004.31 ,2004.33 ,2004.34 ,2004.36 ,2004.38 ,2004.39 ,2004.41 ,2004.43 ,2004.44 ,2004.46 ,2004.48) y <- c(10.69 ,9.09 ,11.29 ,10.59 ,9.97 ,9.65 ,9.18 ,10.49 ,9.27 ,10.4 ,8.9 ,9.17 ,10.4 ,9.53 ,8.19 ,10.04 ,9.37 ,10.46 ,10.09 ,7.38 ,10.56 ,9.83 ,9.57 ,10.46 ,12.2 ,7.64 ,10.26 ,9.43 ,9.94 ,11.19 ,10.17 ,9.61 ,10.28 ,12.06 ,9.73 ,10.1 ,10.63 ,10.64 ,11.24 ,9.4 ,11.78 ,9.75 ,12.3 ,11.35 ,10.97 ,11.77 ,11.09 ,11.43 ,10.92 ,11.91 ,11.17 ,10.04 ,10.32 ,9.6 ,9.56 ,10.27 ,8.69 ,10.91 ,9.64 ,9.09 ,10.39 ,10.15 ,10.2 ,9.28 ,10.66 ,9.37 ,10.14 ,10.43 ,10.24 ,9.28 ,10.38 ,9.85 ,10.81 ,12.2 ,9.47 ,9.49 ,8.9 ,9.76 ,9.62 ,9.6 ,9.99 ,10.48 ,9.56 ,9.19 ,9.94 ,9.57 ,10.4 ,9.26 ,10.69 ,10.35 ,10 ,9.34 ,10.45 ,10.76 ,9.74 ,7.34 ,11.21 ,10.67 ,9.22 ,10.34 ,10.66 ,9.96 ,12.11 ,10.71 ,10.09 ,10.25 ,9.96 ,11.73 ,9.71 ,10.1 ,10.29 ,11.05 ,10.35 ,12 ,10.56 ,10.43 ,8.19 ,11.38 ,9.95 ,10.51 ,8.61 ,10.29 ,10.11 ,10.12 ,9.84 ,10.05 ,10.13 ,9.97 ,10.13 ,9.87 ,9.92 ,9.44 ,9.71 ,9.77 ,9.82 ,10.31 ,8.82 ,9.62 ,9.64 ,10.69 ,9.08 ,9.59 ,9.57 ,8.17 ,9.99 ,9.09 ,9.66 ,9.21 ,9.44 ,10.04 ,9.3 ,10.24 ,10.15 ,10.2 ,11.36 ,9.5 ,9.96 ,10.15 ,11.02 ,10.05 ,10.65 ,10.31 ,11.42 ,10.08 ,10.44 ,10.39 ,10.74 ,10.99 ,11.02 ,10.55 ,10.72 ,10.54 ,10.67 ,10.35 ,9.68 ,10.78 ,9.8 ,11.09 ,10.45 ,10.66 ,10.65 ,9.9 ,9.55 ,9.91 ,10.26 ,10.14 ,9.82 ,10.27 ,10.12 ,9.52 ,9.05 ,10.26 ,9.4 ,8.99 ,8.98 ,9.49 ,10.42 ,9.31 ,9.13 ,9.71 ,10.3 ,9.75 ,9.05 ,10.91 ,10.09 ,11.15 ,10.69 ,10.36 ,10.56 ,10.52 ,10.32 ,9.78 ,12.11 ,10.75 ,11.12 ,10.32 ,12.33 ,10.03 ,11.4 ,12.47 ,13.57 ,10.2 ,10.2 ,10.84 ,9.61 ,10.35 ,10 ,9.76 ,10.3 ,9.86 ,10.52 ,10.49 ,10.14 ,10.11 ,6.86 ,9.58 ,10.17 ,8.9 ,10.54 ,9.49 ,10.23 ,9.04 ,10.47 ,11.88 ,10.55 ,8.86 ,11.71 ,9.88 ,9.07 ,9.63 ,10.5 ,10.16 ,7.65 ,8.56 ,10.51 ,8.9 ,9.7 ,9.83 ,9.73 ,9.03 ,10.18 ,9.45 ,11.27 ,10.35 ,10.76 ,11.2 ,11.08 ,9.17 ,12.67 ,11.09 ,10.32 ,10.71 ,10.88 ,8.44 ,10.15 ,10.06 ,9.76 ,12.45 ,10.02 ,8.89 ,10.66 ,10.71 ,10.52 ,10.58 ,10.15 ,11.1 ,9.96 ,11.31 ,9.51 ,6.98 ,10.55 ,7.22 ,10.16 ,8.03 ,9.77 ,10.36 ,9.63 ,10.6 ,9.6 ,8.75 ,10.32 ,10.23) merc.df <- as.data.frame(cbind(x,y)) colnames(merc.df) <- c("date1","lp100km") span <- as.numeric(par1) if (par2 == "TRUE") smooth <- TRUE else smooth <- FALSE x=merc.df$date1 y=merc.df$lp100km yl=loess(y~x,span=span) bitmap(file="noloessplot.png") plot(yl,col="darkgreen",type="p",main="5 years gas consumption, 1999-2004 (raw data)",xlab="decimal date",ylab="litres per 100 km") dev.off() if (smooth==TRUE) { bitmap(file="loessplot.png") plot(yl,col="darkgreen",type="p",main="5 years gas consumption, 1999-2004 (incl. LOESS)",xlab="decimal date",ylab="litres per 100 km") mn=mean(yl$y) lines(yl$x,yl$fitted,col="red",lwd=3) lines(yl$x,mn*rep(1,length(yl$x)),col="black",lwd=3) dev.off() bitmap(file="resplot.png") plot(yl$x,yl$residuals,col="darkgreen",ylab="residuals from smooth",xlab="decimal date",main="Residuals of (Data - Smooth)") lines(yl$x,0*rep(1,length(yl$x)),col="black",lwd=3) rl=loess(yl$residuals~yl$x,span=span) lines(rl$x,rl$fitted,col="red",lwd=3) dev.off() }

Cite this software as:

Weldon Larry, (2017), Time Series Smoothing Example (v1.0.4) in Free Statistics Software (v1.2.1), Office for Research Development and Education, URL https://www.wessa.net/rwasp_gas.wasp/

The R code is based on :

Weldon Larry, Stat Ed Programs for Demos in R, Simon Fraser University, URL http://www.stat.sfu.ca/~weldon/title.doc

Weldon Larry, R Programs for Statistics Education, Simon Fraser University, URL http://www.stat.sfu.ca/~weldon/Programs

Weldon Larry, Instructions for using R programs for Statistics Education, Simon Fraser University, URL http://www.stat.sfu.ca/~weldon/instructions.doc

To cite Wessa.net in publications use:
Wessa, P. (2024), Free Statistics Software, Office for Research Development and Education,
version 1.2.1, URL https://www.wessa.net/

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