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s04pre1a

# s04pre1a - Prof G Jakubson Economics 321 Spring 2004...

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Prof. G. Jakubson Economics 321 March 2004 Spring 2004 PRELIMINARY EXAM #1 Correct Answers 1.a. median for African-Americans is in the range \$15-25K (5 points). Median for Caucasian's is higher (in the range \$25-35K ) (5 points). b. (10 points) – see calculations below Afr.-Amer. Class intervals thousands of families rel cum for family income Caucasian African-American freq freq < \$5,000 2,000 900 .13 .13 \$ 5,000 to < \$10,000 3,000 1,100 .16 .29 \$10,000 to < \$15,000 5,000 900 .13 .42 \$15,000 to < \$25,000 10,000 1,600 .23 .65 \$25,000 to < \$35,000 10,000 900 .13 .78 \$35,000 to < \$50,000 12,000 900 .13 .91 \$50,000 or more 14,000 600 .09 1.00 Total number of families 56,000 6,900 2.a. Z = (1/N) i Z i = [ (1/N) i X i - N X ] / s x = 0 (5 points) b. s z = (1/s x ) s x = 1. (5 points) c. Since T i is just a standardized version of Y i , its mean and variance are also 0 and 1, respectively. (5 points) d. CV(Y)/CV(X) = { |d 2 |s x / d 2 X } / {s x / X } = 1 (10 points) 3.a. Let e i = Y i - ± β 0 - β ± 1 X i . The least squares estimators solve min i (e i ) 2 (5 points) b. FOC (each worth 3 points) wrt β ± 0 : i e i = 0 wrt β ± 1 : i e i X i = 0 implications: (each worth 3 points) [Note (i) <=> (iii)] (i) mean residual = 0 (ii) e and X are uncorrelated (iii) regression line goes through the point of means Economics 321, Spring 2004 Page 1 of 4 Prelim 1 Answers c:\…\s04pre1a.doc

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Economics 321, Spring 2004 Page 2 of 4 Prelim 1 Answers c:\…\s04pre1a.doc 4. a. β 1 : change in billions of dollars of GNP due to an additional million person-hours of government labor (7 points) b. measure Y in \$M rather than \$B: intercept and slope are each multiplied by 1000.
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s04pre1a - Prof G Jakubson Economics 321 Spring 2004...

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