Table P-18 contains the number of severe earthquakes (those with a Richter scale magnitude of 7 and above) per year for the years 1900-1999.

a. Use Minitab to smooth the earthquake data with moving averages of orders k = 5, 10, and 15. Describe the nature of the smoothing as the order of the moving average increases. Do you think there might be a cycle in these data? If so, provide an estimate of the length (in years) of the cycle.
b. Use Minitab to smooth the earthquake data using simple exponential smoothing. Store the residuals and generate a forecast for the number of severe earthquakes in the year 2000. Compute the residual autocorrelations. Does simple exponential smoothing provide a reasonable fit to these data? Explain.
c. Is there a seasonal component in the earthquake data? Why or why not?

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TABLE P-18 Number of Severe Earthquakes, 1900-1999 Year NumberYear Number Year Number Year Number 1927 20 19547198 14 1928 221955 1982 10 1929 19 1956 5 1983 15 1930 13 1957 341984 8 1900 1901 1902 1903 10 1904 16 193 26 1958 10 1985 15 1905 26 1906 1907 27 1908 1909 32 1910 36 1911 1912 22 1913 23 1914 22 1915 18 1916 25 191721 1918 1919 14 1920 1921 1922 1 1923 1924 18 1925 17 1926 19 1932 13 1959 151986 6 1933 14 1960 22 1987 11 1934221961 11988 8 1935 24 1962 1198 7 1936 21 1963 12 937221964 1991 11 1938 26 196522 1992 23 1939 21 1940 23 1967 1994 15 1941 24 1968 30 1995 25 194227 1969 27 1996 22 1943 411970 29 1997 20 1944 31 |1971 23 | 1998 16 1945 27 1972 201999 23 1946 1947 26 1974 21 1948 28 1975 94936 1976 25 1950 39 1977 16 1951 2197818 1952 171979 15 95322 1980 18 1966 19 1993 16 351973 16