econ310_f09_ps10_ans

econ310_f09_ps10_ans - Econ 310: Problem Set #10 Solutions...

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Andres Aradillas-Lopez 1. Exercise 10.6 (a) The variables x and y are reversed: Slope gives the change in y for a change in x. (b) The population regression line has intercept β 0 and slope β 1 (not b 0 and b 1 ). (c) The estimate ˆ μ y = b 0 + b 1 x * is more accurate when x * is closed to ¯ x , so the width of the conFdence interval grows with ( x * ¯ x ) 2 . 2. Exercise 10.8 The table below gives two sets of answers: those found with critical values from table D, and those found with software. In each case, the margin of error is t * SE b 1 = 6 . 31 t * , with df = n 2. df b 1 t * Interval t * Interval (a) 23 12.1 2.069 -0.9554 to 25.1554 2.0687 -0.9532 to 25.1532 (b) 23 6.1 2.069 -6.9554 to 19.1554 2.0687 -6.9532 to 19.1532 (c) 98 12.1 1.990* -0.4569 to 24.6569 1.9845 -0.4220 to 24.6220 *Note that for (c), if we use Table D, we take df = 80. 3. Exercise 10.10 (a) The plot (below) shows a strong linear relationship with no striking outliers. (b) The regression line (shown on the plot) is ˆ y = 1059 + 1 . 3930 x . (c) In the plot (below), it appears that for large x values, many residuals are negative. (d) A stemplot or histogram suggests a slight left skew. (e) To test for a relationship, we test H 0 : β 1 = 0 vs. H a : β 1 n = 0 (or equivalently, use ρ in place of β 1 ). (f) The test statistic and P-value are given in the Minitab output below: t . = 15
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econ310_f09_ps10_ans - Econ 310: Problem Set #10 Solutions...

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