B.13. Table B-6 gives data on the number of new business incorporations (Y) and the number of business failures (X) for the United States from 1984 to 1995. 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? (X) + var (Y) sr= -0.8 (X+Y) 2X=16, s2Y9Y= 3x2 + 2Y = ax + bY X>4Y = 0.6X-4 Y = 3X +2 E(X) = 8 and var (X) = 4 E(XY) = a 4X=1 a 2Y = 1 XIYi f(xi, Yi) X = 20 NUMBER OF NEW BUSINESS INCORPORATIONS (Y) AND NUMBER OF BUSINESS FAILURES (X), UNITED STATES, 1984-1995 YEAR Y X 1984 634,991 52,078 1985 664, 235 57,253 1986 702, 738 61,616 1987 685,572 61,111 1988 685,095 57,097 1989 676,565 Source: Economic Report of the President, 2004, Table B-96, p. 395. TABLE B-6 d. Are the two variables independent? e. 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?
B.13. Table B-6 gives data on the number of new business incorporations (Y) and the number of business failures (X) for the United States from 1984 to 1995. 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? (X) + var (Y) sr= -0.8 (X+Y) 2X=16, s2Y9Y= 3x2 + 2Y = ax + bY X>4Y = 0.6X-4 Y = 3X +2 E(X) = 8 and var (X) = 4 E(XY) = a 4X=1 a 2Y = 1 XIYi f(xi, Yi) X = 20 NUMBER OF NEW BUSINESS INCORPORATIONS (Y) AND NUMBER OF BUSINESS FAILURES (X), UNITED STATES, 1984-1995 YEAR Y X 1984 634,991 52,078 1985 664, 235 57,253 1986 702, 738 61,616 1987 685,572 61,111 1988 685,095 57,097 1989 676,565 Source: Economic Report of the President, 2004, Table B-96, p. 395. TABLE B-6 d. Are the two variables independent? e. 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?
MATLAB: An Introduction with Applications
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Author:Amos Gilat
Publisher:Amos Gilat
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Transcribed Image Text:B.13. Table B-6 gives data on the number of new business incorporations (Y) and the number of business failures (X) for the
United States from 1984 to 1995. 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? (X) + var (Y) sr= -0.8 (X+Y) 2X = 16, s2Y = 9Y = 3X2 + 2Y = ax + bY = X>4Y = 0.6X-4 Y = 3X
+2 E(X) = 8 and var (X) = 4 E(XY) = a 4X=1 a 2 Y = 1 XIYi f(XI, YI) X = 20 NUMBER OF NEW BUSINESS
INCORPORATIONS (Y) AND NUMBER OF BUSINESS FAILURES (X), UNITED STATES, 1984-1995 YEAR Y X
1984 634,991 52,078 1985 664,235 57,253 1986 702, 738 61,616 1987 685,572 61, 111 1988 685,095 57,097 1989 676,565
Source: Economic Report of the President, 2004, Table B-96, p. 395. TABLE B-6 d. Are the two variables independent? e. 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?
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