Homework SourseNew business incorporations Y a What is the average value of
New business incorporations
(Y)
a. What is the average value of new business incorporations? And the variance?
b) What is the average value of business failures? And the variance?
c) What is the covariance between Y and X? And the correlation coefficient? Explain.
d) Are the two variables independent? Explain.
| Year or month | New business incorporations (Y) | Number of failures (X) |
| 1955 | 139915.00 | 10969.00 |
| 1956 | 141163.00 | 12686.00 |
| 1957 | 137112.00 | 13739.00 |
| 1958 | 150781.00 | 14964.00 |
| 1959 | 193067.00 | 14053.00 |
| 1960 | 182713.00 | 15445.00 |
| 1961 | 181535.00 | 17075.00 |
| 1962 | 182057.00 | 15782.00 |
| 1963 | 186404.00 | 14374.00 |
| 1964 | 197724.00 | 13501.00 |
| 1965 | 203897.00 | 13514.00 |
| 1966 | 200010.00 | 13061.00 |
| 1967 | 206569.00 | 12364.00 |
| 1968 | 233635.00 | 9636.00 |
| 1969 | 274267.00 | 9154.00 |
| 1970 | 264209.00 | 10748.00 |
| 1971 | 287577.00 | 10326.00 |
| 1972 | 316601.00 | 9566.00 |
| 1973 | 329358.00 | 9345.00 |
| 1974 | 319149.00 | 9915.00 |
| 1975 | 326345.00 | 11432.00 |
| 1976 | 375766.00 | 9628.00 |
| 1977 | 436170.00 | 7919.00 |
| 1978 | 478019.00 | 6619.00 |
| 1979 | 524565.00 | 7564.00 |
| 1980 | 533520.00 | 11742.00 |
| 1981 | 581242.00 | 16794.00 |
| 1982 | 566942.00 | 24908.00 |
| 1983 | 600420.00 | 31334.00 |
| 1984 | 634991.00 | 52078.00 |
| 1985 | 664235.00 | 57253.00 |
| 1986 | 702738.00 | 61616.00 |
| 1987 | 685572.00 | 61111.00 |
| 1988 | 685095.00 | 57097.00 |
| 1989 | 676565.00 | 50361.00 |
| 1990 | 647366.00 | 60747.00 |
| 1991 | 628604.00 | 88140.00 |
| 1992 | 666800.00 | 97069.00 |
| 1993 | 706537.00 | 86133.00 |
| 1994 | 741778.00 | 71558.00 |
| 1995 | 766988.00 | 71128.00 |
| 1996 | 786482.00 | 71931.00 |
| 1997 | 798779.00 | 83384.00 |
Solution
above value are computed using excel
d)
the two values are dependent
| 1958 | 150781 | 14964 |
| 1959 | 193067 | 14053 |
| 1960 | 182713 | 15445 |
| 1961 | 181535 | 17075 |
| 1962 | 182057 | 15782 |
| 1963 | 186404 | 14374 |
| 1964 | 197724 | 13501 |
| 1965 | 203897 | 13514 |
| 1966 | 200010 | 13061 |
| 1967 | 206569 | 12364 |
| 1968 | 233635 | 9636 |
| 1969 | 274267 | 9154 |
| 1970 | 264209 | 10748 |
| 1971 | 287577 | 10326 |
| 1972 | 316601 | 9566 |
| 1973 | 329358 | 9345 |
| 1974 | 319149 | 9915 |
| 1975 | 326345 | 11432 |
| 1976 | 375766 | 9628 |
| 1977 | 436170 | 7919 |
| 1978 | 478019 | 6619 |
| 1979 | 524565 | 7564 |
| 1980 | 533520 | 11742 |
| 1981 | 581242 | 16794 |
| 1982 | 566942 | 24908 |
| 1983 | 600420 | 31334 |
| 1984 | 634991 | 52078 |
| 1985 | 664235 | 57253 |
| 1986 | 702738 | 61616 |
| 1987 | 685572 | 61111 |
| 1988 | 685095 | 57097 |
| 1989 | 676565 | 50361 |
| 1990 | 647366 | 60747 |
| 1991 | 628604 | 88140 |
| 1992 | 666800 | 97069 |
| 1993 | 706537 | 86133 |
| 1994 | 741778 | 71558 |
| 1995 | 766988 | 71128 |
| 1996 | 786482 | 71931 |
| 1997 | 798779 | 83384 |
| 1955 | 139915 | 10969 |
| 1956 | 141163 | 12686 |
| 1957 | 137112 | 13739 |
| mean | 431238.651162791 | 31343.3255813953 |
| variance | 49924284285.0644 | 775154693.010276 |
| covariance | 5078669718.25311 | |
| correlation | 0.8163940974 | |
