library(readxl)
library("AER")## Loading required package: car## Loading required package: carData## Loading required package: lmtest## Loading required package: zoo##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric## Loading required package: sandwich## Loading required package: survivaldata(CPS1988)
CPS1988## wage education experience ethnicity smsa region parttime
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## 2 123.46 12 1 cauc yes northeast yes
## 3 370.37 9 9 cauc yes northeast no
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## 1728 522.32 12 8 cauc yes northeast no
## 1729 158.28 14 20 cauc yes northeast no
## 1730 888.89 12 19 cauc yes northeast no
## 1731 712.25 14 42 cauc yes northeast no
## 1732 949.67 14 43 cauc no northeast no
## 1733 861.33 17 13 cauc no northeast no
## 1734 973.41 17 20 cauc no northeast no
## 1735 427.35 8 31 cauc yes northeast no
## 1736 308.64 12 2 cauc yes northeast no
## 1737 939.35 11 24 cauc yes northeast no
## 1738 498.58 12 30 cauc yes northeast no
## 1739 569.80 16 23 cauc yes northeast no
## 1740 379.87 0 49 cauc yes northeast no
## 1741 344.73 8 4 cauc yes northeast no
## 1742 123.46 13 -1 cauc yes northeast yes
## 1743 404.98 14 17 cauc yes northeast no
## 1744 522.32 12 9 cauc yes northeast no
## 1745 593.54 12 11 cauc yes northeast no
## 1746 949.67 12 34 cauc yes northeast no
## 1747 59.35 12 1 cauc yes northeast no
## 1748 833.33 12 41 cauc no northeast no
## 1749 474.83 12 6 cauc no northeast no
## 1750 2374.15 16 31 cauc yes northeast no
## 1751 854.70 12 39 cauc no northeast no
## 1752 432.10 10 34 cauc no northeast no
## 1753 427.35 10 41 cauc yes northeast no
## 1754 781.10 14 11 cauc yes northeast no
## 1755 522.32 12 18 cauc no northeast no
## 1756 216.05 10 4 cauc yes northeast no
## 1757 830.96 16 3 cauc yes northeast no
## 1758 546.06 12 12 cauc yes northeast no
## 1759 118.71 12 20 afam no northeast no
## 1760 593.54 12 16 cauc yes northeast no
## 1761 293.21 9 16 cauc yes northeast no
## 1762 343.83 17 1 cauc yes northeast no
## 1763 246.91 16 13 cauc yes northeast no
## 1764 1780.63 18 25 cauc yes northeast no
## 1765 814.81 10 18 cauc yes northeast no
## 1766 118.71 9 12 cauc yes northeast no
## 1767 385.80 12 2 cauc yes northeast no
## 1768 1187.08 16 28 cauc yes northeast no
## 1769 735.99 14 9 cauc yes northeast no
## 1770 474.83 12 40 cauc yes northeast no
## 1771 664.77 14 19 cauc no northeast no
## 1772 246.91 12 12 cauc no northeast no
## 1773 997.15 12 27 cauc no northeast no
## 1774 451.09 12 4 cauc no northeast no
## 1775 830.96 14 10 cauc yes northeast no
## 1776 683.76 9 46 cauc yes northeast no
## 1777 617.28 12 11 cauc yes northeast no
## 1778 164.20 10 25 cauc yes northeast no
## 1779 142.45 3 16 afam yes northeast no
## 1780 403.61 12 41 cauc no northeast no
## 1781 735.99 12 25 cauc yes northeast no
## 1782 227.92 12 2 cauc yes northeast no
## 1783 712.25 13 14 cauc yes northeast no
## 1784 546.74 12 28 cauc no northeast no
## 1785 379.87 10 44 cauc no northeast no
## 1786 747.86 13 18 cauc no northeast no
## 1787 51.44 14 -1 cauc no northeast yes
## 1788 1066.69 18 44 cauc no northeast no
## 1789 209.88 13 0 cauc yes northeast yes
## 1790 1175.78 18 28 cauc yes northeast no
## 1791 1495.73 10 8 cauc yes northeast no
## 1792 403.61 12 27 cauc yes northeast yes
## 1793 555.56 9 20 cauc yes northeast no
## 1794 617.28 12 33 cauc yes northeast no
## 1795 444.44 12 5 cauc yes northeast no
## 1796 1139.60 17 27 cauc yes northeast no
## 1797 451.09 12 11 cauc yes northeast no
## 1798 474.83 12 9 cauc yes northeast no
## 1799 747.86 12 19 cauc yes northeast no
## 1800 1234.57 18 20 cauc yes northeast no
## 1801 344.68 13 11 cauc yes northeast no
## 1802 593.54 16 31 cauc yes northeast no
## 1803 356.13 12 6 cauc yes northeast no
## 1804 216.05 13 43 cauc yes northeast yes
## 1805 244.44 16 7 cauc no northeast yes
## 1806 358.02 12 3 cauc no northeast no
## 1807 949.67 12 38 cauc no northeast no
## 1808 712.25 13 13 cauc no northeast no
## 1809 481.96 8 30 cauc no northeast no
## 1810 633.90 13 26 cauc yes northeast no
## 1811 740.74 11 42 cauc no northeast no
## 1812 583.33 12 41 cauc no northeast no
## 1813 246.91 13 6 cauc no northeast no
## 1814 1020.89 13 7 cauc no northeast no
## 1815 332.38 8 31 cauc no northeast no
## 1816 546.06 16 13 cauc no northeast no
## 1817 170.29 10 47 cauc no northeast no
## 1818 688.51 12 17 cauc no northeast no
## 1819 237.42 12 38 cauc no northeast no
## 1820 213.68 12 15 cauc no northeast no
## 1821 498.58 16 7 cauc yes northeast no
## 1822 636.57 12 5 cauc yes northeast no
## 1823 403.61 10 4 cauc yes northeast no
## 1824 1305.79 18 17 cauc yes northeast no
## 1825 2374.15 12 16 cauc yes northeast no
## 1826 830.96 12 24 cauc yes northeast no
## 1827 360.08 16 0 cauc yes northeast yes
## 1828 1102.33 16 32 cauc yes northeast no
## 1829 463.59 12 8 cauc yes northeast no
## 1830 398.86 12 5 cauc yes northeast yes
## 1831 712.25 14 4 cauc yes northeast no
## 1832 759.73 12 10 cauc yes northeast no
## 1833 688.51 16 9 cauc yes northeast no
## 1834 546.06 12 15 cauc yes northeast no
## 1835 427.35 12 41 afam yes northeast no
## 1836 137.17 15 2 cauc yes northeast no
## 1837 308.64 14 9 cauc yes northeast no
## 1838 1383.50 12 40 cauc yes northeast no
## 1839 412.69 12 10 cauc yes northeast no
## 1840 656.93 12 6 cauc yes northeast no
## 1841 1282.05 16 23 cauc yes northeast no
## 1842 902.18 15 36 cauc yes northeast no
## 1843 427.35 14 6 cauc yes northeast no
## 1844 451.09 18 8 cauc yes northeast no
## 1845 462.96 12 13 cauc yes northeast no
## 1846 617.28 14 6 cauc yes northeast no
## 1847 676.64 14 15 cauc yes northeast no
## 1848 747.86 12 14 cauc yes northeast no
## 1849 795.35 16 34 cauc yes northeast no
## 1850 712.25 13 18 cauc yes northeast no
## 1851 586.42 16 1 cauc yes northeast no
## 1852 1780.63 16 14 cauc yes northeast no
## 1853 1424.50 12 36 cauc yes northeast no
## 1854 1115.86 16 23 cauc yes northeast no
## 1855 925.93 16 12 cauc yes northeast no
## 1856 474.83 16 34 cauc yes northeast no
## 1857 546.06 12 22 cauc yes northeast no
## 1858 641.03 18 20 cauc yes northeast no
## 1859 806.25 16 10 cauc yes northeast no
## 1860 1412.63 18 14 cauc yes northeast no
## 1861 617.28 12 40 cauc yes northeast no
## 1862 308.64 12 48 cauc yes northeast no
## 1863 308.64 12 15 cauc yes northeast no
## 1864 1519.47 18 16 cauc yes northeast no
## 1865 206.55 12 48 cauc yes northeast yes
## 1866 821.46 18 15 afam yes northeast no
## 1867 379.87 14 21 cauc yes northeast no
## 1868 356.13 1 50 cauc yes northeast no
## 1869 3793.83 14 6 cauc yes northeast no
## 1870 403.61 15 20 cauc yes northeast no
## 1871 617.28 16 14 cauc yes northeast no
## 1872 315.82 14 7 cauc yes northeast no
## 1873 348.21 14 9 cauc yes northeast yes
## 1874 522.32 12 6 cauc yes northeast no
## 1875 629.63 13 34 cauc yes northeast no
## 1876 332.38 13 31 cauc yes northeast no
## 1877 605.41 17 2 cauc yes northeast no
## 1878 197.53 13 16 afam yes northeast no
## 1879 481.72 10 16 cauc yes northeast no
## 1880 488.68 18 7 cauc yes northeast no
## 1881 474.83 12 21 cauc yes northeast no
## 1882 830.96 12 49 cauc yes northeast no
## 1883 712.25 15 39 cauc yes northeast no
## 1884 1068.38 18 7 cauc yes northeast no
## 1885 445.41 16 10 cauc yes northeast no
## 1886 878.44 13 26 cauc yes northeast no
## 1887 555.56 16 38 cauc yes northeast no
## 1888 797.33 12 25 cauc yes northeast no
## 1889 298.43 12 3 cauc yes northeast no
## 1890 830.96 12 13 cauc yes northeast no
## 1891 225.70 12 6 cauc yes northeast no
## 1892 854.70 16 4 cauc yes northeast no
## 1893 522.32 12 43 cauc yes northeast no
## 1894 617.28 13 18 cauc yes northeast no
## 1895 493.83 12 14 cauc yes northeast no
## 1896 474.83 15 29 cauc yes northeast no
## 1897 189.93 14 3 cauc yes northeast yes
## 1898 486.42 8 41 cauc yes northeast no
## 1899 830.96 14 12 cauc yes northeast no
## 1900 284.90 12 16 cauc yes northeast no
## 1901 356.13 12 2 cauc yes northeast no
## 1902 474.83 10 34 cauc yes northeast no
## 1903 231.48 12 46 cauc yes northeast no
## 1904 197.53 13 0 cauc yes northeast no
## 1905 150.89 11 1 cauc yes northeast no
## 1906 1452.43 18 13 cauc yes northeast no
## 1907 237.42 15 2 cauc yes northeast yes
## 1908 237.42 14 2 cauc yes northeast no
## 1909 712.25 16 15 cauc yes northeast no
## 1910 857.34 11 40 cauc yes northeast no
## 1911 670.96 12 27 cauc yes northeast no
## 1912 308.64 12 6 cauc yes northeast no
## 1913 705.70 12 44 cauc yes northeast no
## 1914 153.42 14 0 cauc yes northeast no
## 1915 688.51 10 45 cauc yes northeast no
## 1916 214.25 14 1 cauc yes northeast no
## 1917 237.42 12 6 cauc yes northeast no
## 1918 415.48 8 8 cauc yes northeast no
## 1919 427.35 12 3 cauc yes northeast no
## 1920 432.10 4 27 cauc yes northeast no
## 1921 474.83 14 8 cauc yes northeast no
## 1922 593.54 4 47 cauc yes northeast no
## 1923 759.73 12 18 cauc yes northeast no
## 1924 332.38 12 28 cauc yes northeast no
## 1925 145.06 11 8 cauc yes northeast no
## 1926 569.80 16 20 cauc yes northeast no
## 1927 1543.21 14 19 cauc yes northeast no
## 1928 261.16 10 47 cauc yes northeast no
## 1929 332.38 14 11 cauc yes northeast no
## 1930 332.38 8 43 cauc yes northeast no
## 1931 284.90 12 8 cauc yes northeast no
## 1932 522.32 16 5 cauc yes northeast no
## 1933 712.25 14 16 cauc yes northeast no
## 1934 118.71 18 13 cauc yes northeast yes
## 1935 72.02 18 11 cauc yes northeast yes
## 1936 166.19 18 5 cauc yes northeast yes
## 1937 155.51 16 1 cauc yes northeast yes
## 1938 520.99 10 29 cauc yes northeast no
## 1939 902.18 18 10 cauc yes northeast no
## 1940 866.57 12 45 cauc yes northeast no
## 1941 522.32 10 17 cauc yes northeast no
## 1942 1234.57 16 15 cauc yes northeast no
## 1943 759.73 16 8 cauc yes northeast no
## 1944 925.93 12 19 cauc yes northeast no
## 1945 997.15 14 10 cauc yes northeast no
## 1946 1044.63 13 12 cauc yes northeast no
## 1947 641.03 12 21 cauc yes northeast no
## 1948 324.89 10 13 cauc yes northeast no
## 1949 552.26 10 32 cauc yes northeast no
## 1950 142.45 12 44 cauc yes northeast yes
## 1951 593.54 12 14 cauc yes northeast no
## 1952 617.28 13 7 cauc yes northeast no
## 1953 237.42 12 2 cauc yes northeast no
## 1954 617.28 13 0 cauc yes northeast no
## 1955 142.45 14 14 cauc yes northeast no
## 1956 593.54 12 32 cauc yes northeast no
## 1957 231.48 12 4 cauc yes northeast no
## 1958 890.31 16 17 cauc yes northeast no
## 1959 949.67 16 18 cauc yes northeast no
## 1960 783.40 12 23 cauc yes northeast no
## 1961 284.90 12 11 cauc yes northeast no
## 1962 232.67 12 3 cauc yes northeast no
## 1963 82.30 12 0 cauc yes northeast yes
## 1964 379.87 9 42 cauc yes northeast no
## 1965 847.25 17 16 cauc yes northeast no
## 1966 569.80 13 8 cauc yes northeast no
## 1967 1234.57 18 32 cauc yes northeast no
## 1968 356.13 13 4 cauc yes northeast no
## 1969 113.17 13 -1 cauc yes northeast no
## 1970 1621.88 16 9 cauc yes northeast no
## 1971 664.77 12 37 cauc yes northeast no
## 1972 356.13 13 18 cauc yes northeast no
## 1973 394.28 6 31 cauc yes northeast no
## 1974 197.53 12 6 cauc yes northeast no
## 1975 547.24 12 35 cauc yes northeast no
## 1976 664.77 14 6 cauc yes northeast no
## 1977 759.73 12 10 cauc yes northeast no
## 1978 688.51 12 20 cauc yes northeast no
## 1979 427.35 12 5 cauc yes northeast no
## 1980 356.13 10 23 cauc yes northeast no
## 1981 830.96 12 17 cauc yes northeast no
## 1982 878.44 11 15 cauc yes northeast no
## 1983 987.65 17 4 cauc yes northeast yes
## 1984 785.63 11 30 cauc yes northeast no
## 1985 427.35 16 3 cauc yes northeast no
## 1986 1666.67 16 23 cauc yes northeast no
## 1987 518.52 14 0 cauc yes northeast no
## 1988 949.67 18 36 cauc yes northeast no
## 1989 949.67 12 17 cauc yes northeast no
## 1990 320.51 16 11 cauc yes northeast no
## 1991 593.54 15 29 cauc yes northeast no
## 1992 379.87 12 47 cauc yes northeast no
## 1993 807.22 16 19 cauc yes northeast no
## 1994 895.06 12 20 cauc yes northeast no
## 1995 1020.89 18 20 cauc yes northeast no
## 1996 308.64 14 0 cauc yes northeast no
## 1997 664.77 18 13 afam yes northeast no
## 1998 370.37 12 44 cauc yes northeast no
## 1999 1068.38 18 19 cauc yes northeast no
## 2000 850.97 18 8 cauc yes northeast no
## 2001 530.30 14 23 cauc yes northeast no
## 2002 339.51 12 0 cauc yes northeast no
## 2003 630.42 10 47 cauc yes northeast no
## 2004 284.90 16 19 cauc yes northeast no
## 2005 735.99 14 13 cauc yes northeast no
## 2006 712.25 18 16 cauc yes northeast no
## 2007 1258.31 16 17 cauc yes northeast no
## 2008 246.91 12 28 cauc yes northeast no
## 2009 641.03 12 22 cauc yes northeast no
## 2010 544.80 14 13 cauc yes northeast no
## 2011 356.13 12 7 cauc yes northeast no
## 2012 641.03 14 17 cauc yes northeast no
## 2013 322.89 12 19 cauc yes northeast no
## 2014 902.18 12 16 cauc yes northeast no
## 2015 4748.34 12 34 cauc no northeast no
## 2016 807.22 12 25 cauc no northeast no
## 2017 1068.38 16 9 cauc yes northeast no
## 2018 759.73 12 14 cauc no northeast no
## 2019 474.83 12 21 cauc yes northeast no
## 2020 522.32 14 32 cauc yes northeast no
## 2021 569.80 12 33 cauc yes northeast no
## 2022 474.83 12 43 cauc no northeast no
## 2023 830.96 12 32 cauc yes northeast no
## 2024 246.91 14 2 cauc yes northeast yes
## 2025 296.30 14 6 cauc yes northeast no
## 2026 71.23 14 2 cauc yes northeast yes
## 2027 144.03 12 0 cauc no northeast yes
## 2028 136.30 11 1 cauc yes northeast yes
## 2029 470.31 12 16 cauc yes northeast no
## 2030 356.13 12 30 cauc yes northeast no
## 2031 278.38 11 18 cauc yes northeast no
## 2032 1424.50 12 46 cauc yes northeast yes
## 2033 854.70 12 13 cauc yes northeast no
## 2034 830.96 12 11 cauc no northeast no
## 2035 546.06 12 16 cauc no northeast no
## 2036 448.93 14 13 cauc no northeast no
## 2037 403.61 12 35 cauc yes northeast no
## 2038 427.35 12 30 cauc yes northeast no
## 2039 830.96 18 10 cauc no northeast no
## 2040 458.21 18 11 cauc no northeast no
## 2041 949.67 16 2 cauc yes northeast no
## 2042 664.77 12 13 cauc yes northeast no
## 2043 1481.48 12 5 cauc yes northeast no
## 2044 246.91 9 34 cauc yes northeast no
## 2045 819.09 15 17 cauc no northeast no
## 2046 759.73 16 12 cauc no northeast no
## 2047 593.54 12 28 cauc yes northeast no
## 2048 664.77 16 15 cauc yes northeast no
## 2049 647.52 14 24 cauc yes northeast no
## 2050 254.32 14 0 cauc yes northeast no
## 2051 156.89 13 -1 cauc yes northeast yes
## 2052 185.19 12 49 cauc no northeast yes
## 2053 363.11 10 25 cauc no northeast no
## 2054 830.96 12 23 cauc yes northeast no
## 2055 569.80 12 20 cauc yes northeast no
## 2056 142.07 12 48 afam no northeast yes
## 2057 154.32 12 0 afam no northeast yes
## 2058 593.54 16 8 cauc yes northeast no
## 2059 546.06 0 43 cauc yes northeast no
## 2060 285.13 13 6 cauc yes northeast no
## 2061 77.16 14 0 cauc yes northeast yes
## 2062 284.90 10 12 cauc yes northeast no
## 2063 395.06 10 13 cauc yes northeast no
## 2064 474.83 12 6 cauc yes northeast no
## 2065 593.54 18 2 cauc yes northeast no
## 2066 783.48 16 13 cauc yes northeast no
## 2067 451.09 12 11 afam yes northeast no
## 2068 189.93 13 5 afam no northeast no
## 2069 822.17 12 19 cauc yes northeast no
## 2070 427.35 12 11 cauc yes northeast no
## 2071 771.60 12 23 cauc yes northeast no
## 2072 776.09 14 11 cauc yes northeast no
## 2073 997.15 12 8 cauc yes northeast no
## 2074 394.01 8 41 cauc yes northeast no
## 2075 314.69 9 23 cauc yes northeast no
## 2076 617.28 13 23 cauc yes northeast no
## 2077 420.88 12 17 cauc yes northeast no
## 2078 403.12 8 31 cauc yes northeast no
## 2079 569.80 16 4 cauc yes northeast no
## 2080 617.28 18 18 cauc yes northeast no
## 2081 189.93 12 42 cauc yes northeast no
## 2082 641.03 12 23 cauc no northeast no
## 2083 593.54 16 5 cauc yes northeast no
## 2084 949.67 12 13 cauc yes northeast no
## 2085 712.25 14 26 cauc yes northeast no
## 2086 153.13 14 4 cauc yes northeast no
## 2087 280.58 13 1 cauc yes northeast no
## 2088 712.25 14 16 cauc yes northeast no
## 2089 1187.08 16 13 cauc yes northeast no
## 2090 949.67 17 12 cauc yes northeast no
## 2091 593.54 10 32 cauc yes northeast no
## 2092 346.91 10 42 cauc yes northeast no
## 2093 593.54 14 28 cauc yes northeast no
## 2094 429.72 12 6 cauc yes northeast no
## 2095 593.54 12 13 cauc yes northeast no
## 2096 617.28 11 38 cauc yes northeast no
## 2097 712.25 15 11 cauc yes northeast no
## 2098 467.71 12 31 cauc yes northeast no
## 2099 474.83 8 26 cauc yes northeast no
## 2100 759.73 16 25 cauc yes northeast no
## 2101 474.83 10 28 afam yes northeast yes
## 2102 1139.60 18 3 cauc yes northeast no
## 2103 1543.21 13 42 cauc yes northeast no
## 2104 617.28 16 14 cauc yes northeast no
## 2105 522.32 9 50 cauc yes northeast no
## 2106 487.82 12 15 cauc yes northeast no
## 2107 123.46 12 1 cauc yes northeast yes
## 2108 1234.57 16 5 cauc yes northeast no
## 2109 985.28 18 17 cauc yes northeast no
## 2110 1068.38 17 15 cauc yes northeast no
## 2111 493.83 14 3 cauc yes northeast no
## 2112 1305.79 18 30 cauc yes northeast no
## 2113 641.03 14 21 afam yes northeast no
## 2114 902.18 12 9 cauc yes northeast no
## 2115 666.67 11 48 cauc yes northeast no
## 2116 1187.08 14 21 cauc yes northeast no
## 2117 759.73 13 30 cauc yes northeast no
## 2118 760.97 12 18 afam yes northeast no
## 2119 679.01 15 8 cauc yes northeast no
## 2120 2018.04 16 14 cauc yes northeast no
## 2121 554.30 12 22 afam yes northeast no
## 2122 403.61 12 24 afam yes northeast no
## 2123 1899.34 16 12 cauc yes northeast no
## 2124 498.58 13 9 cauc yes northeast no
## 2125 543.21 12 9 cauc yes northeast no
## 2126 258.78 14 17 cauc yes northeast no
## 2127 567.90 8 31 cauc yes northeast no
## 2128 716.05 16 22 cauc yes northeast no
## 2129 1661.92 16 9 cauc yes northeast no
## 2130 1899.34 18 25 cauc yes northeast no
## 2131 1424.50 14 32 cauc yes northeast no
## 2132 474.83 12 5 cauc yes northeast no
## 2133 164.61 13 0 cauc yes northeast no
## 2134 493.83 12 6 cauc yes northeast no
## 2135 296.77 12 2 cauc yes northeast no
## 2136 151.95 12 4 cauc yes northeast no
## 2137 735.99 16 10 cauc yes northeast no
## 2138 474.83 11 37 cauc yes northeast no
## 2139 641.98 12 35 cauc yes northeast no
## 2140 830.96 16 28 cauc yes northeast no
## 2141 623.77 12 46 cauc yes northeast no
## 2142 740.74 16 37 cauc yes northeast yes
## 2143 546.06 14 4 cauc yes northeast no
## 2144 1320.04 12 31 cauc yes northeast no
## 2145 664.77 16 7 cauc yes northeast no
## 2146 854.70 12 24 cauc yes northeast no
## 2147 289.65 8 13 cauc yes northeast no
## 2148 1020.89 16 18 cauc yes northeast no
## 2149 641.03 14 17 cauc yes northeast no
## 2150 783.48 12 10 cauc yes northeast no
## 2151 569.80 12 19 cauc yes northeast no
## 2152 593.54 12 7 afam yes northeast no
## 2153 949.67 14 11 cauc yes northeast no
## 2154 712.25 12 42 cauc yes northeast no
## 2155 1187.08 18 32 cauc yes northeast no
## 2156 669.52 16 6 cauc yes northeast no
## 2157 403.61 14 5 cauc yes northeast no
## 2158 237.42 7 50 afam yes northeast no
## 2159 522.32 12 20 afam yes northeast no
## 2160 1543.21 16 14 cauc yes northeast no
## 2161 197.53 18 41 cauc yes northeast yes
## 2162 693.26 16 6 cauc yes northeast no
## 2163 427.35 12 45 cauc yes northeast no
## 2164 113.96 16 1 cauc yes northeast yes
## 2165 1115.86 16 29 cauc yes northeast no
## 2166 712.25 16 25 cauc yes northeast no
## 2167 316.95 12 13 cauc yes northeast no
## 2168 319.03 13 0 cauc yes northeast no
## 2169 688.51 16 11 cauc yes northeast no
## 2170 593.54 13 10 cauc yes northeast no
## 2171 546.06 17 8 cauc yes northeast no
## 2172 368.00 12 6 cauc yes northeast no
## 2173 1044.63 16 13 cauc yes northeast no
## 2174 949.67 12 47 cauc yes northeast no
## 2175 432.10 10 13 cauc yes northeast no
## 2176 414.39 12 27 cauc yes northeast no
## 2177 2469.11 18 29 cauc yes northeast no
## 2178 1187.08 14 33 cauc yes northeast no
## 2179 546.06 14 12 cauc yes northeast no
## 2180 1661.92 18 19 cauc yes northeast no
## 2181 593.54 16 5 cauc yes northeast no
## 2182 580.97 11 5 afam yes northeast yes
## 2183 408.36 12 16 cauc yes northeast no
## 2184 1899.34 18 19 cauc yes northeast no
## 2185 1187.08 14 33 cauc yes northeast no
## 2186 1068.38 12 39 cauc yes northeast no
## 2187 973.41 10 32 cauc yes northeast no
## 2188 740.74 14 25 cauc yes northeast no
## 2189 505.87 16 35 cauc yes northeast no
## 2190 332.38 16 44 cauc yes northeast no
## 2191 1163.34 12 8 cauc yes northeast no
## 2192 807.22 16 9 cauc yes northeast no
## 2193 154.32 16 4 cauc yes northeast no
## 2194 403.61 18 22 cauc yes northeast no
## 2195 434.83 13 11 cauc yes northeast no
## 2196 897.60 18 26 cauc yes northeast no
## 2197 1032.10 12 15 cauc yes northeast no
## 2198 1377.02 18 33 cauc yes northeast no
## 2199 451.09 8 37 cauc yes northeast no
## 2200 308.64 11 6 cauc yes northeast no
## 2201 345.68 12 23 cauc yes northeast no
## 2202 1282.05 18 22 cauc yes northeast no
## 2203 749.98 13 32 cauc yes northeast no
## 2204 783.48 12 23 cauc yes northeast no
## 2205 2992.51 17 12 cauc yes northeast no
## 2206 902.18 12 23 cauc yes northeast no
## 2207 727.28 17 6 cauc yes northeast no
## 2208 1044.63 15 10 cauc yes northeast no
## 2209 451.09 12 14 afam yes northeast no
## 2210 498.58 12 25 cauc yes northeast no
## 2211 688.51 12 22 cauc yes northeast no
## 2212 546.06 12 11 cauc yes northeast no
## 2213 296.30 10 7 cauc yes northeast no
## 2214 783.48 12 26 cauc yes northeast no
## 2215 65.62 13 -1 cauc yes northeast yes
## 2216 742.21 16 12 cauc yes northeast no
## 2217 403.61 8 50 cauc yes northeast no
## 2218 1234.57 12 26 cauc yes northeast no
## 2219 2057.61 16 20 cauc yes northeast no
## 2220 142.75 14 18 cauc yes northeast yes
## 2221 783.48 11 44 cauc yes northeast no
## 2222 451.09 12 40 cauc yes northeast no
## 2223 726.22 4 28 cauc yes northeast no
## 2224 712.25 12 42 cauc yes northeast no
## 2225 603.04 12 9 cauc yes northeast no
## 2226 474.83 12 38 cauc yes northeast no
## 2227 1068.38 12 35 afam yes northeast no
## 2228 177.13 14 17 afam yes northeast no
## 2229 617.28 10 9 afam yes northeast no
## 2230 664.77 12 19 cauc yes northeast no
## 2231 470.31 10 6 cauc yes northeast no
## 2232 166.19 11 4 cauc yes northeast no
## 2233 555.07 9 45 cauc yes northeast no
## 2234 2018.04 16 17 cauc yes northeast no
## 2235 546.06 14 3 afam yes northeast no
## 2236 403.61 10 38 afam yes northeast no
## 2237 1187.08 18 10 cauc yes northeast no
## 2238 533.11 12 7 cauc yes northeast no
## 2239 186.01 12 1 cauc yes northeast yes
## 2240 403.61 11 46 cauc yes northeast no
## 2241 474.43 12 13 cauc yes northeast no
## 2242 1044.63 13 13 cauc yes northeast no
## 2243 353.09 12 11 cauc yes northeast no
## 2244 2374.15 16 28 cauc yes northeast no
## 2245 830.96 18 0 cauc yes northeast no
## 2246 949.67 16 8 cauc yes northeast no
## 2247 2374.15 12 15 cauc yes northeast no
## 2248 1248.46 18 6 cauc yes northeast no
## 2249 712.25 10 47 cauc yes northeast no
## 2250 617.28 12 9 cauc yes northeast no
## 2251 949.67 16 9 cauc yes northeast no
## 2252 608.93 14 13 cauc yes northeast no
## 2253 558.50 12 10 cauc yes northeast no
## 2254 759.73 16 34 cauc yes northeast no
## 2255 427.35 11 49 cauc yes northeast no
## 2256 1358.02 14 29 afam yes northeast no
## 2257 740.74 16 6 afam yes northeast no
## 2258 1358.02 18 8 cauc yes northeast no
## 2259 830.96 12 24 cauc yes northeast no
## 2260 534.98 16 39 cauc no northeast yes
## 2261 1946.82 16 11 cauc yes northeast no
## 2262 713.51 12 20 cauc yes northeast no
## 2263 1661.92 16 15 cauc yes northeast no
## 2264 237.42 12 13 cauc yes northeast no
## 2265 724.12 16 10 cauc yes northeast no
## 2266 506.49 15 4 cauc yes northeast no
## 2267 379.87 5 46 cauc yes northeast no
## 2268 498.58 0 49 cauc yes northeast no
## 2269 228.40 12 1 cauc yes northeast yes
## 2270 142.45 12 2 cauc yes northeast no
## 2271 522.32 7 27 cauc yes northeast no
## 2272 546.06 15 7 cauc yes northeast no
## 2273 569.80 6 42 cauc yes northeast no
## 2274 830.96 16 18 cauc yes northeast no
## 2275 1543.21 18 26 cauc yes northeast no
## 2276 1661.92 16 15 cauc yes northeast no
## 2277 949.67 12 13 cauc yes northeast no
## 2278 293.94 12 27 cauc yes northeast no
## 2279 92.59 12 0 cauc yes northeast no
## 2280 1115.86 12 11 cauc yes northeast no
## 2281 759.73 16 7 cauc yes northeast no
## 2282 759.73 16 12 cauc yes northeast no
## 2283 949.67 12 9 cauc yes northeast no
## 2284 712.25 12 7 cauc yes northeast no
## 2285 854.70 14 34 cauc yes northeast no
## 2286 427.35 12 4 cauc yes northeast no
## 2287 246.91 12 0 cauc yes northeast no
## 2288 1234.57 14 25 cauc yes northeast no
## 2289 308.64 12 2 cauc yes northeast no
## 2290 641.03 11 47 cauc yes northeast no
## 2291 617.28 12 20 cauc no northeast no
## 2292 474.83 8 49 cauc no northeast no
## 2293 406.96 14 11 cauc no northeast no
## 2294 688.51 12 17 cauc no northeast no
## 2295 1172.84 12 3 cauc yes northeast no
## 2296 282.92 12 11 cauc yes northeast no
## 2297 201.80 13 12 cauc yes northeast no
## 2298 759.73 12 13 cauc yes northeast no
## 2299 1329.53 12 39 cauc yes northeast no
## 2300 1353.28 16 17 cauc yes northeast no
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## 14174 261.16 14 3 cauc yes south no
## 14175 123.46 11 2 cauc yes south yes
## 14176 271.60 6 27 cauc yes south no
## 14177 641.03 11 32 afam yes south no
## 14178 1419.75 18 18 cauc yes south no
## 14179 1115.86 18 13 cauc yes south no
## 14180 284.90 12 8 afam yes south no
## 14181 201.56 12 7 afam yes south no
## 14182 1305.79 18 13 cauc yes south no
## 14183 1210.83 18 16 cauc yes south no
## 14184 985.28 18 19 cauc yes south no
## 14185 949.67 16 20 cauc yes south no
## 14186 529.10 17 5 cauc yes south yes
## 14187 1424.50 16 15 cauc yes south no
## 14188 332.38 14 12 afam yes south no
## 14189 368.00 12 8 afam yes south no
## 14190 949.67 18 15 cauc yes south no
## 14191 322.06 11 33 afam yes south yes
## 14192 426.52 8 31 afam yes south yes
## 14193 375.00 16 32 cauc yes south no
## 14194 2374.15 18 11 cauc yes south no
## 14195 1804.37 18 29 cauc yes south no
## 14196 522.32 18 11 cauc yes south no
## 14197 427.35 16 12 cauc yes south no
## 14198 1305.79 18 2 cauc yes south no
## 14199 650.52 16 8 afam yes south no
## 14200 474.83 18 10 cauc yes south no
## 14201 1637.14 18 22 cauc yes south no
## 14202 1020.89 18 6 cauc yes south no
## 14203 268.28 14 12 afam yes south no
## 14204 997.15 18 9 afam yes south no
## 14205 356.13 15 12 cauc yes south no
## 14206 197.53 14 2 afam yes south no
## 14207 337.54 15 1 afam yes south no
## 14208 664.77 12 40 afam yes south no
## 14209 384.62 12 18 afam yes south no
## 14210 246.91 12 2 afam yes south no
## 14211 451.09 12 10 afam yes south no
## 14212 925.93 18 18 afam yes south no
## 14213 82.72 12 1 afam yes south yes
## 14214 185.19 18 18 cauc yes south yes
## 14215 209.88 18 13 cauc yes south no
## 14216 118.71 16 1 cauc yes south no
## 14217 375.38 10 20 afam yes south no
## 14218 558.31 8 30 afam yes south no
## 14219 172.48 11 4 afam yes south no
## 14220 393.04 14 20 afam yes south no
## 14221 284.90 11 29 afam yes south no
## 14222 320.51 9 20 afam yes south no
## 14223 493.83 11 17 afam yes south no
## 14224 284.90 12 7 afam yes south no
## 14225 462.96 15 13 afam yes south no
## 14226 569.80 17 17 cauc yes south no
## 14227 403.61 12 8 afam yes south no
## 14228 427.35 10 32 afam yes south no
## 14229 427.35 14 2 afam yes south no
## 14230 501.54 18 1 cauc yes south no
## 14231 593.54 15 17 afam yes south no
## 14232 617.28 14 18 cauc yes south no
## 14233 379.87 10 47 afam yes south no
## 14234 451.09 12 37 afam yes south no
## 14235 546.06 12 35 afam yes south no
## 14236 212.16 16 6 afam yes south yes
## 14237 157.02 14 -1 afam yes south yes
## 14238 664.77 18 6 cauc yes south no
## 14239 493.83 16 3 cauc yes south no
## 14240 510.45 16 2 cauc yes south no
## 14241 385.80 16 2 cauc yes south no
## 14242 451.09 16 1 cauc yes south no
## 14243 1234.57 13 37 afam yes south no
## 14244 3009.26 18 1 afam yes south no
## 14245 546.06 16 13 cauc yes south no
## 14246 735.99 16 2 cauc yes south no
## 14247 823.05 18 0 cauc yes south no
## 14248 664.77 15 14 cauc yes south no
## 14249 1899.34 18 19 cauc yes south no
## 14250 1305.79 13 26 cauc yes south no
## 14251 462.96 12 28 afam yes south no
## 14252 1405.72 8 54 afam yes south no
## 14253 1020.89 17 20 cauc yes south no
## 14254 451.09 15 18 cauc yes south no
## 14255 641.03 18 8 cauc yes south no
## 14256 1132.48 18 4 cauc yes south no
## 14257 298.88 11 12 afam yes south yes
## 14258 356.13 12 28 afam yes south no
## 14259 498.58 12 2 afam yes south no
## 14260 617.28 17 3 cauc yes south no
## 14261 1566.95 16 8 cauc yes south no
## 14262 413.11 18 22 cauc yes south no
## 14263 664.77 18 28 afam yes south no
## 14264 308.64 14 23 afam yes south no
## 14265 1187.08 18 3 cauc yes south no
## 14266 902.18 16 11 afam yes south no
## 14267 1590.69 18 23 cauc yes south no
## 14268 1780.63 18 28 cauc yes south no
## 14269 1543.21 18 18 cauc yes south no
## 14270 1068.38 15 2 cauc yes south no
## 14271 1208.45 16 24 cauc yes south no
## 14272 864.20 12 32 cauc yes south no
## 14273 1377.02 18 20 cauc yes south no
## 14274 308.64 18 3 afam yes south no
## 14275 775.90 16 29 cauc yes south no
## 14276 261.16 14 7 afam yes south no
## 14277 185.19 10 43 afam yes south no
## 14278 664.77 12 24 afam yes south no
## 14279 664.77 15 29 afam yes south no
## 14280 427.35 14 7 afam yes south no
## 14281 732.38 16 14 afam yes south no
## 14282 878.44 10 31 afam yes south no
## 14283 1483.86 13 30 afam yes south no
## 14284 854.70 12 19 afam yes south no
## 14285 197.53 9 11 afam yes south no
## [ reached 'max' / getOption("max.print") -- omitted 13870 rows ]google drive
Trong một số trường hợp chúng ta có thể không sử dụng hết các biến số hoặc tất cả các quan sát trong 1 file dữ liệu, chúng ta có thể trích dữ liệu từ 1 dataframe có sẵn bằng những câu lệnh đơn giản, trong nội dung này chúng ta sử dụng bộ số liệu CPS1988.csv để làm ví dụ minh họa. Trước hết chúng ta sơ bộ file dữ liệu có tên CPS1988.csv bằng câu lệnh sau:
CPS1988 <- read.csv(“crab.csv”, header = TRUE): đọc file có tên CPS1988.csv trong thư mục D:/PhanmemR và đặt tên CPS1988.
CPS1988: câu lệnh cho biết chi tiết các biến của đối tượng CPS1988.
Có thể trích xuất ra một dataframe con bằng cách chỉ định cụ thể quan sát nào muốn lấy theo vị trí của hàng. Câu lệnh như sau:
CPS1988 <- read.csv(“crab.csv”, header = TRUE): đọc file có tên CPS1988.csv trong thư mục D:/PhanmemR và đặt tên CPS1988.
CPS1 <- CPS1988[c(1, 3, 100),]: trích xuất các quan sát dòng 1, 3, 100 của đối tượng CPS1988 và đặt tên CPS1.
CPS2 <- CPS1988[c(1: 3, 10, 100),]:trích xuất các quan sát dòng từ 1 đến dòng 3, dòng 10, dòng 100 của đối tượng CPS1988 và đặt tên CPS2.
Kết quả của hai câu lệnh trên:
# Đọc flie CPS1988 và đặt tên CPS1988
CPS1 <- CPS1988[c(1, 3, 100),]# Trích xuất quan sát từ dòng 1, 3, 100
CPS1 #xem 6 giá trị đầu tiên của CPS1## wage education experience ethnicity smsa region parttime
## 1 354.94 7 45 cauc yes northeast no
## 3 370.37 9 9 cauc yes northeast no
## 100 688.51 18 16 cauc no northeast no## Trích xuất quan sát từ dòng 1 đến 3, dòng 10, dòng 100
CPS2 <- CPS1988[c(1:3, 10,100),]
CPS2 #xem 6 giá trị đầu tiên của CPS2## wage education experience ethnicity smsa region parttime
## 1 354.94 7 45 cauc yes northeast no
## 2 123.46 12 1 cauc yes northeast yes
## 3 370.37 9 9 cauc yes northeast no
## 10 1643.83 14 18 cauc yes northeast no
## 100 688.51 18 16 cauc no northeast noTrong một số trường hợp chúng ta chỉ quan tâm đến một số biến chứ không phải toàn bộ các biến. Đểtrích xuất dữliệu theo cột ta thực hiện lệnh sau:
CPS1988 <- read.csv(“crab.csv”, header =TRUE): đọc file có tên CPS1988.csv trong thư mục D:/PhanmemR và đặt tên CPS1988.
CPS3 <- CPS1988[c(2:4)]:lấy cột từ 2 đến cột 4 của đối tượng CPS1988 và đặt tên CPS3
head(CPS3):xem 6 quan sát đầu tiên của đối tượng CPS3.
CPS3 <- CPS1988[c(2:4)] #Trích xuất từ cột 2 đến cột 4 và đặt tên CPS3
head(CPS3) #xem 6 giá trị đầu tiên của CPS3## education experience ethnicity
## 1 7 45 cauc
## 2 12 1 cauc
## 3 9 9 cauc
## 4 11 46 cauc
## 5 12 36 cauc
## 6 16 22 caucĐể trích xuất dữ liệu theo hàng và cột ta thực hiện câu lệnh:
CPS1988 <- read.csv(“crab.csv”, header = TRUE): câu lệnh đọc file có tên CPS1988.csv trong thư mục D:/PhanmemR và đặt tên CPS1988.
CPS4 <-CPS1988[c(1, 3, 5, 7), c(2:4)]: câu lệnh trích xuất dữ liệu từ cột 2 đến cột 4, dòng 2 đến dòng 4 của đối tượng CPS1988 và đặt tên CPS4.
head(CPS4): câu lệnh xem 6 quan sát đầu tiên của CPS4.
CPS4 <- CPS1988[c(1,3,5,7), c(2:4)]
head(CPS4)## education experience ethnicity
## 1 7 45 cauc
## 3 9 9 cauc
## 5 12 36 cauc
## 7 8 51 caucKết quả câu lệnh trên tạo ra một dataframe gồm các dòng 1, 3, 5, 7 và chỉ lấy các biến ở cột 2, 3, 4 từ dataframe gốc ban đầu.
Trong nhiều tình huống, chúng ta cần trích xuất dữ liệu cho các quan sát theo một tiêu chí nào đó. Chẳng hạn, từ tập dữ liệu CPS1988.csv chúng ta muốn trích xuất tất cả các quan sát ứng với parttime = yes mà thôi với tên gọi CPS5 chẳng hạn, ta thực hiện câu lệnh sau:
CPS1988 <- read.csv(“crab.csv”, header = TRUE): đọc file có tên CPS1988.csv trong thư mục D:/PhanmemR và đặt tên CPS1988.
CPS5 <- subset(CPS1988, parttime == “yes”): trích xuất các quan sát của biến parttime = yes trong đối tượng CPS1988 và đặt tên CPS5.
CPS5 <- subset(CPS1988, parttime=="yes")
dim(CPS5)## [1] 2524 7head(CPS5)## wage education experience ethnicity smsa region parttime
## 2 123.46 12 1 cauc yes northeast yes
## 38 166.67 12 51 cauc no northeast yes
## 41 222.93 11 41 cauc no northeast yes
## 43 277.78 11 40 cauc yes northeast yes
## 55 284.90 16 2 cauc yes northeast yes
## 64 109.04 12 1 cauc yes northeast yesKết quả câu lệnh cho thấy, có 2524 quan sát có làm bán thời gian được trích xuất.
Tương tự, chúng ta cũng có thể trích xuất dữ liệu theo một số tiêu chí nào đó.
Ví dụ, cũng từ dữ liệu CPS1988 ta trích xuất dữ liệu cho các quan sát các tiêu chí mà: (1) ứng với parttime = yes, và (2) có education ≥ 3 với đặt tên CPS6, ta thực hiện câu lệnh sau:
CPS6 <- subset(CPS1988, parttime == “yes” & education == 5): trích xuất các quan sát của biến parttime = yes và các quan sát của biến education = 5 trong đối tượng CPS1988 với tên CPS6.
head(CPS6): câu lệnh xem 6 quan sát đầu tiên của CPS6.
CPS6 <- subset(CPS1988, parttime == "yes" & education == 5)
head(CPS6)## wage education experience ethnicity smsa region parttime
## 8024 118.71 5 56 afam yes midwest yes
## 15108 98.24 5 46 afam yes south yes
## 16841 130.58 5 56 afam no south yes
## 17806 178.33 5 13 cauc yes south yes
## 20135 74.07 5 56 cauc yes south yes
## 21488 115.74 5 53 cauc yes south yesHoặc chúng ta cũng có thể trích xuất dữ liệu cho các quan sát trong CPS1988 theo các tiêu chí (1) ứng với education < 2 hoặc (2) experience > 50 và đặt tên CPS7, ta thực hiện câu lệnh:
CPS7 <- subset(CPS1988, parttime == “yes” | experience > 50): câu lệnh trích xuất các quan sát của biến parttime = yes hoặc các quan sát của biến experience > 50 trong đối tượng CPS1988 và đặt tên CPS7. head(CPS7): câu lệnh xem 6 quan sát đầu tiên của CPS7.
CPS7 <- subset(CPS1988, parttime == "yes"| experience > 50)
head(CPS7)## wage education experience ethnicity smsa region parttime
## 2 123.46 12 1 cauc yes northeast yes
## 7 284.90 8 51 cauc yes northeast no
## 38 166.67 12 51 cauc no northeast yes
## 41 222.93 11 41 cauc no northeast yes
## 43 277.78 11 40 cauc yes northeast yes
## 55 284.90 16 2 cauc yes northeast yesTrong mục này chúng ta sử dụng dữ liệu của file afterlife.xlsx trong thư mục D:/PhanmemR đểlàm ví dụ minh họa.
Trước tiên chúng ta mô tả sơ bộ về file dữ liệu afterlife.xlsx bằng câu lệnh sau:
af<-read.xlsx(“afterlife.xlsx”, sheetIndex =1, header =TRUE):đọc file afterlife.xlsx và đặt tên af.
af: câu lệnh cho biết chi tiết đối tượng af.
Đọc flie afterlife.xlsx và đặt tên af
af <- read_xlsx(“afterlife.xlsx”, sheetIndex = 1, header = T)
head(af) # xem 6 quan sát đầu
Dữliệu file afterlife.xlsx có hai biến định tính.
Biến thứ nhất: Sex (giới tính) được mã hóa như sau: 1 là nam và 2 là nữ.
Biến thứ 2: Believe (niềm tin) của người được khảo sát “Sau khi chết có tồn tại một thế giới khác” được mã hóa như sau: 1: Tin là có, khẳng định chắc chắn. 2: Tin là có, nhưng, nhưng không chắc chắn. 3: Tin là không có, nhưng không chắc chắn. 4: Tin là không có, khẳng định chắc chắn. 5. Dữliệu bị khuyết. 6. Không thể chọn. 7. Không trả lời.
Trong dữ liệu này chúng ta chỉ giữ lại những quan sát mà biến Believe < 5, sau đó thay những quan sát có giá trị 1 và 2 của biến Believe thành giá trị 1 (những quan sát Tin là có), đồng thời những quan sát có giá trị 3 và 4 của biến Believe thành giá trị 0 (những quan sát Tin là không có).
Đểthực hiện công việc trên ta thực hiện các lệnh sau:
af<-read.xlsx(“afterlife.xlsx”, sheetIndex =1, header =TRUE):đọc file tên afterlife.xlsx và đặt tên af.
afmahoa<-subset(af, Believe <5):câu lệnh trích xuất những quan sát mà giá trịcủa biến Believe <5 và đặt tên afmahoa.
afmahoa\(Believe[afmahoa\)Believe <=2] <-1: câu lệnh thay những giá trịquan sát ≤2 trong cột Believe của afmahoa bằng 1.
afmahoa\(Believe[afmahoa\)Believe >2] <-0:câu lệnh thay những giá trịquan sát >2 trong cột Believe của afmahoa bằng 0.
Đọc file afterlife.xlsx và đặt tên af
af <- read.xlsx(afterlife.xlsx”, sheetIndex = 1,header = T)
Chỉ giữ lại những quan sát mà giá trị biến Believe < 5 và đặt tên afmahoa
afmahoa <- subset(af, Believe < 5)
dim(afmahoa) # Số quan sát của afmahoa
afmahoa\(Believe[afmahoa\)Believe <=2] <-1
Trong cột biến Believe của afmahoa thay những giá trị <=2 bằng 1
afmahoa\(Believe[afmahoa\)Believe >2] <-0
Trong cột biến Believe của afmahoa thay những giá trị >2 bằng 0
head(afmahoa) #xem 6 quan sát đầu afmahoa
Sau khi thực hiện các câu lệnh trên, kết quả cho thấy đối tượng afmahoa chỉ còn 1260 quan sát, biến Believe chỉ nhận một trong hai giá trị: 0, 1.
Cấu trúc xác suất cho các bảng ngẫu nhiên
Dữliệu định tính là tần số suất hiện các biểu hiện của các biến. Cho X và Y là hai biến định tính, X có k biểu hiện: \(A_1,A_2,...,A_k\) và Y có m biểu hiện: \(B_1,B_2,...,B_m\). Chúng ta có thể sử dụng một bảng gồm k hàng và m cột để thể hiện kết quả có thể xảy ra từ việc khảo sát:
Bảng này được gọi là bảng ngẫu nhiên hai chiều 𝑘×𝑚, trong đó \(n_ij\) là số lần quan sát được cặp thuộc tính (\(A_i, B_j\)), còn gọi là tần số của (\(A_i, B_j\)). Một bảng ngẫu nhiên hai biến được gọi là bảng hai chiều; một bảng ngẫu nhiên 3 biến gọi là bảng ngẫu nhiên 3 chiều.Trong mục này, chúng ta sử dụng bộ dữ liệu afmahoa (bộ dữ liệu đã xửlý được mã hóa từ file dữ liệu afterlife.xlsx) để làm ví dụ.
Lập bảng tần số và tần suất cho biến Sex
Đểlập bảng tần số và tần suất cho biến Sex, ta thực hiện câu lệnh sau:
af<-read.xlsx(“afterlife.xlsx”, sheetIndex =1, header =TRUE): đọc file afterlife.xlsx và đặt tên af.
afmahoa<-subset(af, Believe <5): câu lệnh trích xuất những quan sát mà giá trị của biến Believe <5 và đặt tên afmahoa.
table(afmahoa$Sex)*: câu lệnh lập bảng tần số cho biến Sex.
table(afmahoa\(Sex/(sum(afmahoa\)Sex))*: câu lệnh lập bảng tần suất cho biến Sex.
head(afmahoa) # Xem 6 quan sát đầu afmahoa
table(afmahoa$Sex)
Kết quả trên được trình bày lại như sau:
Lập bảng tần suất cho biến Sex
table(afmahoa\(Sex)/sum(table(afmahoa\)Sex))
Chúng ta có thể trình bày kết quả trên như sau:
Bằng các câu lệnh tương tự chúng ta có thểlập bảng tần số và tần suất cho biến Believe và ta được kết quả.
head(afmahoa) # Xem 5 quan sát đầu afmahoa
lập bảng tần suất cho biến Believe và kết quả
table(afmahoa\(Believe)/sum(table(afmahoa\)Believe))
Kết quả trên được trình bày như sau:
Để tạo bảng hai chiều chúng ta sử dụng câu lệnh sau:
table(afmahoa\(Sex, afmahoa\)Believe): câu lệnh tạo bảng hai chiều cho 2 biến Sex và Believe.
table(afmahoa\(Sex, afmahoa\)Believe) # Bảng hai chiều
Kết quả câu lệnh trên được trình bày lại như sau:
Để tính OddsRatio của hàng 1 và hàng 2 trong bảng hai chiều, ta thực hiện câu lệnh sau:
B1. install.packages(“DescTools”): cài đặt gói DescTools.
B2. library(DecsTools): gọi gói DescTools.
B3. OddsRatio(data, conf.level =NULL, y =NULL, method = “wald”): câu lệnh tính giá trị OddsRatio; trong đó: data là bảng hai chiều; conf.level: độ tin cậy mặc nhiên 95%; y là véc tơ các giá trị cần tính giá trị OddsRatio; method =“wald”: phương pháp wald.
Ta lấy ví dụ sau để minh họa cho việc tính OddsRatio như sau:
Ta thực hiện các lệnh sau:
B1. library(DecsTools): gọi packages DescTools.
B2. v<-c(189, 104, 10845, 10933): câu lệnh tạo véc tơ v.
B3.data<-matrix(v, 2): câu lệnh tạo ma trận cấp 2 (bảng 2 chiều) và đặt tên data.data: câu lệnh xem data.
B4. y<-c(189, 104): câu lệnh tạo véc tơ y.
B5. OddsRatio(data, conf.level =NULL, y =NULL, method = “wald”): câu lệnh tính OddsRatio
library(DescTools) # Gọi Package DecsTools
v <- c(189, 104, 10845, 10933) # Tạo vector v
x <- matrix(v, 2, 2) # Tạo ma trận cấp 2 đặt tên x
y <- c(189,104) # Vector y là những người nhồi máu cơ tim
OddsRatio(x,conf.level = 0.95, y = NULL, method = “wald”)
Kết quả tỷ lệ chênh (OddsRatio) là 1,832054. Giá trị này cho chúng ta biết tỷ lệ người bị bệnh nhồi máu cơ tim đối với nhóm người dùng Placebo (giả dược) cao hơn 83,2% so với nhóm người sử dụng thuốc Aspirin.
Công thức ước lượng
\(f-\sqrt[u_{\frac{\alpha}{2}}]{\frac{f(1-f)}{n}} ≤ p ≤ f + \sqrt[u_{\frac{\alpha}{2}}]{\frac{f(1-f)}{n}}\)
Để làm bài toán ước lượng tỷ lệ bằng R, ta thực hiện câu lệnh sau:
B1. install.packages(“DescTools”): cài đặt gói DescTools.
B2. library(DecsTools): gọi gói DescTools.
B3. BinomCI(k, n, conf.level = NULL, method = “wald”): câu lệnh ước lượng tỷ lệ một tổng thể; trong đó, k: số phần tử có tính chất A, n: số phần tử mẫu, conf.level = NULL: độ tin cậy mặc định là 95%, method = wald: phương pháp wald.
Chúng ta lấy dữ liệu từ file có tên afterlife.xlsx dể minh họa cho các câu lệnh trên.
Để ước lượng tỷ lệ những người tin rằng “Tồn tại một thế giới khác sau khi chết” ta làm như sau:
library(“DescTools”) library(readxl) af <- read_excel(“~/PTDLĐT/afterlife.xlsx”)
Trích xuất biến Believe trong af và đặt tên af1 af1 <- af$Believe Trích xuất những giá trị nhỏ hơn 5 của biến Believe trong af1 af2 <- af1[af1<5] k <- length(af2[af2< 3]) # Tổng tần số những người tin của biến Believe n <- length(af2) # Tổng tần số của biến Believe (cỡ mẫu)
câu lệnh ước lượng và kết quả BinomCI(k, n, conf.level = 0.95, method = “wald”)
Ta được khoảng ước lượng tỷ lệ những người tin “Tồn tại thế gới khác sau khi chết” với độ tin cậy 95% là: 0.6341672 ≤ p ≤ 0.6864677
Khi cỡ mẫu n khá lớn, chúng ta có công thức ước lượng khoảng tin cậy với độ tin cậy \(\gamma\) = 1 − \(\alpha\), cho sự sai khác về tỷ lệ: \(p_{1} − p_{2}\) là:
\(((f_{1} - f_{2}) - u_{\frac{\alpha}{2}} (f_{1} - f_{2}) + u_{\frac{\alpha}{2}} (f_{1} - f_{2}) )\)
với: \((f_{1} - f_{2}) = \sqrt{\frac{f_{1}(1-f_{1})}{n_{1}} + \frac{f_{2}(1-f_{2})}{n_{2}}}\)
Để thực hiện ước lượng sự khác biệt tỷ lệ hai tổng thể bằng R, ta thực hiện các câu lênh sau:
B1. install.packages(“DescTools”): câu lệnh cài đặt gói DescTools.
B2. library(DecsTools): câu lệnh gọi gói DescTools.
B3. BinomDiffCI(k2, n2, k1, n1, conf.level = NULL, method = “wald”): câu lệnh ước lượng sự khác biệt hai tỷ lệ tổng thể, ki: số phần tử có tính chất A của mẫu i, ni: số phần tử mẫu thứ i, conf.level = NULL: độ tin cậy mặc định là 95%, method = wald: phương pháp wald.
Chúng ta lấy dữ liệu từ file có tên afterlife.xlsx dể minh họa cho các câu lệnh trên. Bài toán: ước lượng sự khác biệt tỷ lệ Nam và Nữ tin “Tồn tại thế giới khác sau khi chết”
af1 <- subset(af, Believe<5) table(af1) n1 <- table(af1\(Sex)[1] n2 <- table(af1\)Sex)[2] k1 <- table(af1\(Sex,af1\)Believe)[1,1]+table(af1\(Sex,af1\)Believe)[1,2] k2 <- table(af1\(Sex,af1\)Believe)[2,1]+table(af1\(Sex,af1\)Believe)[2,2] BinomDiffCI(k2, n2, k1, n1, conf.level = 0.95, method = “wald”)
Kết quả khoảng ước lượng sự khác biệt tỷ lệ Nam và Nữ tin “Tồn tại thế gới khác sau khi chết” với độ tin cậy 95% là: −0,01499184 ≤ \(p_{1} − p_{2}\) ≤ 0,09168869
Bài toán: Giả sử X và Y là hai biến quan sát định danh. Qua điều tra, biến X có kthuộc tính (hay k dấu hiệu): \(A_1\), \(A_2\),…, \(A_k\); biến Y có m thuộc tính: \(B_1\), \(B_2\),…, \(B_m\), nhận được bảng sau, với \(n_ij\) là sốlần xuất hiện cặp (\(A_i\), \(B_j\)), và \(\sum_{i,j} n_ij=n\)
Với mức ý nghĩa \(\alpha\), hãy xác minh xem X và Y có độc lập hay không. Việc xác minh này được gọi là kiểm định về tính độc lập.
Giảthuyết \(H_0\): X và Y độc lập nhau,
Tiêu chuẩn bác giả thuyết \(H_0\):
\(𝜒^2\)=\(n*{\sum_{i=1}^{k}*\sum_{j=1}^{m}*[((n_ij/n)-((n_i+\)
Hoặc p-value = Prob(chi-square) < \(\alpha\)
Để thực hiện kiểm định tính độc lập cho hai biến định danh bằng R ta làm như sau.
B1. Nhập dữ liệu (bảng ngẫu nhiên) cho đề bài.
B2. Thực hiện kiểm định tính độc lập 2 biến định danh bởi câu lệnh: chisq.test( ).
Chúng ta minh họa kiểm định trên thông qua ví dụsau:
Để xác minh xem sự ủng hộ của người dân trong nước về một sắc thuế mới có phụ thuộc vào mức thu nhập của họ hay không, tiến hành điều tra ngẫu nhiên 1000 công dân, người ta có số liệu sau:
Với mức ý nghĩa 5%, dựa vào điều tra, hãy cho kết luận về việc này.
Gọi Y là thái độ của công dân đối với sắc thuế mới, với 2 thuộc tính: “ủng hộ”, “phản đối”; X là mức thu nhập của công dân, với 3 thuộc tính: “thấp”, “trung bình”, “cao”. Bài toán ở đây là kiểm định về tính độc lập của X và Y:
Giả thuyết \(H_0\): X,Y độc lập; đối thuyết \(H_1\): X,Y không độc lập
Ta tiến hành kiểm định tính độc lập X và Y bằng R theo các bước trên ta được kết quả như sau:
kiểm định sự độc lập 2 biến định danh
ungho <- c(182,213,203) # tạo vector có tên ủng hộ
phandoi <- c(154,138,110) # tạo vector có tên phản đối
data <- as.data.frame(rbind(ungho, phandoi)) # tạo bảng ngẫu nhiên 2x3
name(data) <- c(‘Thap’, ‘trung binh’, ‘cao’) # đặt tên cho bảng ngẫu nhiên
data # bảng ngẫu nhiên
chisq.test(data) # câu lệnh thực hiện kiểm định
Từ bảng kết quả trên, ta có p-value = 0,01947 < 0,05: Bác bỏ \(H_0\),
Kết luận, sự ủng hộ của người dân trong nước về một sắc thuế mới có phụ thuộc vào mức thu nhập của họ,với mức ý nghĩa 5%.
Chú ý:Đối với bài toán này, trên Eviews thao tác như sau:
-Nhập dữ liệu của X và của Y
-Từ cửa số Group,chọn: View → wayTabulation → OK
-Căn cứ vào cột Prob. (p-value) Của một trong hai thống kê: Pearson hoặc Liklihood ratio đểkết luận.
Nếu p-value < \(\alpha\) thì bác \(H_0\),(X và Y độc lập)
Với ví dụ trên, Eviws cho kết quả:
Khi biến dòng X và biến cột Y là thứ tự, một liên kết “xu hướng” là khá phổbiến. Đó là khi mức X tăng lên, các phản ứng đối với Y có xu hướng tăng lên các cấp độ cao hơn, hoặc các phản ứng đối với Ycó khuynh hướng giảm xuống các cấp độ thấp hơn. Người ta có thể sử dụng một tham số để mô tả mối liên kết xu hướng thứ bậc như vậy. Phân tích phổ biến nhất là cho điểm và định tính mức độ của xu hướng tuyến tính hoặc tương quan.
Phần tiếp theo trình bày một thống kê kiểm định nhạy cảm với các xu hướng tuyến tính tích cực hoặc tiêu cực trong mối quan hệ giữa Xvà Y. Nó sử dụng các thông tin quan trong dữ liệu.
-Tiến hành gán các điểm số \(u_1 \le u_2 \le ... \le u_k\) cho các hàng, và \(v_1 \le v_2 \le ... \le v_m\) cho các cột. Điểm có cùng thứ tự như các cấp độ định tính và được cho là đơn điệu. Nguyên tắc gán điểm là: điểm số phản ánh khoảng cách giữa các loại, với khoảng cách lớn hơn giữa các loại được sắp xếp xa nhau hơn. Khi đó bảng thống kê k x mcó dạng:
Giả thuyết \(H_0\): X và Y độc lập (thống kê)
Tiêu chuẩn bác giả thuyết \(H_0\)
\(M^2 \ge X_1 ^2(\alpha); (M^2 = (n-1)r^2\)
hoặc p-value = Prob(chi-square)<\(\alpha\)
Để thực hiện kiểm định tính độc lập cho biến định tính có thang đo thứ bậc ta thực hiện các bước sau:
B1. Cài đặt và gọi packages (“vcdExtra”)
B2. Thực hiện kiểm định bằng câu lệnh: CMHtest(data, rscores =c(), cscores =c()),trong đó data: bảng ngẫu nhiên, rscores = c() là điểm cho tương ứng theo biến X (hàng), cscores = c() là điểm cho tương ứng theo biến Y (cột). Chúng ta minh họa kiểm định trên bằng ví dụ sau: Theo dõi ngẫu nhiên một số sản phẩm về chất lượng: Loại 1, Loại 2, Loại 3 được sản xuất ởcác ca: ngày, đêm, có kết quả sau:
Với mức ý nghĩa 5%, có thể cho rằng chất lượng sản phẩm phụ thuộc vào ca sản xuất hay không?
Ta cần kiểm định về tính độc lập của X (ca sản xuất) và Y (chất lượng sản phẩm), giả thuyết \(H_0\): X và Y độc lập nhau. Đối với X, ta gán 0 cho ca đêm, 1 cho ca ngày. Đối với Y ta sử dụng điểm midrank: Loại 3 được gán số 5,5; loại 2 được gán số 24,5;loại 1 được gán số 97,5.
Các bước kiểm định tính độc lập cho 𝑋và 𝑌được thực hiện như sau:
kIEM DINH SU DOC LAP CHO 2 BIEN DINH TINH CO THANG DO THU BAC
cadem <- c(81,15,9) #tạo vector có tên ca đêm
cangay <- c(118,28,10) # tạo vector có tên ca ngay
Tạo bảng ngẫu nhiên 2x3
data <- as.matrix(rbind(cadem,cangay))
deta # bảng ngẫu nhiên
câu lệnh kiểm định X =(0,1), Y(97.5, 24.5, 5.5)
CMHtest(data, rscores = c(0,1), cscore = c(97.5, 24.5, 5.5))
Từ bảng kết quảtrên ta có p-value = 0,87260 > 0,05: Chấp nhận \(H_0\),
Kết luận, chất lượng sản phẩm không phụ thuộc vào ca sản xuất, với mức ý nghĩa 5%.