Table B-6 gives data on the number of new business incorporations (Y) and the nu
ID: 1257100 • Letter: T
Question
Table B-6 gives data on the number of new business incorporations (Y) and the number business failures (X) for the United States from 1984 to 1995. What is the average value of new business incorporations? And the variance? What is the average value of business failures? And the variance? What is the covariance between Y and X? And the correlation coefficient? TABLE B-6 NUMBER OF NEW BUSINESS INCORPORATIONS (Y) AND NUMBER OF BUSINESS FAILURES (X), UNITED STATES, 1984-1995 Are the two variables independent? If there is correlation between the two variables, does this mean that one variable causes the other variable? That is. do new incorporations cause business failures, or vice versa?Explanation / Answer
Note: Excel functions used to compute the statistic are:
1. For computing Average, function is: =AVERAGE()
2. Variance is computed using =VAR()
3. Covariance is computed using =COVAR()
4. Correlation is computed using =CORREL()
Therefore: (a), (b) & (c):
(d) Correlation between the variables is 0.07 which is very low, therefore the variables are close to being statistically independent.
(e) Statistical correlation does not signify actual causation. The correlation coefficient may be non-zero by chance also. So, this cause-and-effect inference cannot be drawn from a non-zero correlation coefficient.
Year Number of New Business (X) Number of Business Failure (Y) 1984 6,34,991 52,078 1985 6,64,235 57,253 1986 7,02,738 61,616 1987 6,85,572 61,111 1988 6,85,095 57,097 1989 6,76,565 50,361 1990 6,47,366 60,747 1991 6,28,604 88,140 1992 6,66,800 97,069 1993 7,06,537 86,133 1994 7,41,778 71,558 1995 7,66,988 71,128 Average = 6,83,939 67,858 Variance = 16947,62,129 2310,42,729 Covariance = 421,04,508 Correlation = 0.07Related Questions
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