problem-1.27

problem-1.27  We first add names to uspop.
> names(uspop) = seq(1790, 1970, by=10)
> uspop
> uspop                         # uspop is a time series
Time Series:
Start = 1790
End = 1970
...
> d = diff(uspop)
> names(d) = seq(1800, 1960, by=10) # add names
> d
...
 1800  1810  1820  1830  1840  1850  1860  1870  1880  1890
 1.38  1.93  2.40  3.26  4.20  6.10  8.20  8.40 10.40 12.70
 1900  1910  1920  1930  1940  1950  1960  1970
13.10 16.00 13.70 17.10  8.90 19.60 28.00 23.90
    
Scanning across we see that 1960 had the largest increase. To see if the numbers are always increasing we can call diff() again:
> d2 = diff(d)
> names(d2) = seq(1810, 1970, by=10)
> d2
...
 1810  1820  1830  1840  1850  1860  1870  1880  1890  1900
 0.55  0.47  0.86  0.94  1.90  2.10  0.20  2.00  2.30  0.40
 1910  1920  1930  1940  1950  1960  1970
 2.90 -2.30  3.40 -8.20 10.70  8.40 -4.10

The drop in population increase occurred during the times of World War I, the Great Depression, and the Vietnam War.