In one of the first statistical textbooks, Arthur Bowley (1901) used these data to illustrate an arithmetic and graphical analysis of time-series data using the total value of British and Irish exports from 1855-1899. He presented a line graph of the time-series data, supplemented by overlaid line graphs of 3-, 5- and 10-year moving averages. His goal was to show that while the initial series showed wide variability, moving averages made the series progressively smoother.
A data frame with 45 observations on the following 2 variables.
Year, from 1855-1899
total value of British and Irish exports (millions of Pounds)
Bowley, A. L. (1901). Elements of Statistics. London: P. S. King and Son, p. 151-154.
Digitized from Bowley's graph.
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data(Bowley) # plot the data with(Bowley,plot(Year, Value, type='b', ylab="Value of British and Irish Exports", main="Bowley's example of the method of smoothing curves")) # find moving averages-- use center alignment (requires width=ODD) require(gtools, warn.conflicts=FALSE) mav3<-running(Bowley$Value, width=3, align="center") mav5<-running(Bowley$Value, width=5, align="center") mav9<-running(Bowley$Value, width=9, align="center") lines(Bowley$Year[2:44], mav3, col='blue', lty=2) lines(Bowley$Year[3:43], mav5, col='green3', lty=3) lines(Bowley$Year[5:41], mav9, col='brown', lty=4) # add lowess smooth lines(lowess(Bowley), col='red', lwd=2) require(ggplot2, warn.conflicts=FALSE) qplot(Year,Value, data=Bowley)+geom_smooth()