# hw6 - STATISTICS 500 – Fall 2009 Homework 6 handed out...

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Unformatted text preview: STATISTICS 500 – Fall 2009 Homework 6 - handed out Friday, 9 Oct 2009 DUE DATE: on campus Friday, 16 Oct 2009, in lecture (11 am) or by e-mailto Chuanlong, [email protected], no later than noon. off campus Monday, 5 Oct 2009, by 4 pm to Nicole Rembert, email: [email protected] or FAX: 515-294-4040 (please include cover page with Stat 500 / Nicole Rembert). 1. Regression using summary statistics – Suppose we consider the growth rate of the US economy (X) as a predictor of the proportion of the vote obtained by the Democratic candidate in presidential elections (Y). The following table gives the Democratic share of the two-party vote (ignoring third parties) and the growth rate (in %). year %Dem. growth year %Dem. growth year %Dem. growth 1916 0.5168 6.38 1944 0.5377 6.88 1972 0.3821 5.05 1920 0.3612-6.14 1948 0.5237 3.77 1976 0.5105 0.78 1924 0.4568-2.16 1952 0.4460-0.34 1980 0.4470-5.69 1928 0.4118-0.63 1956 0.4224-0.69 1984 0.4083 3.04 1932 0.5916-13.98 1960 0.5009-1.92 1988 0.4610 2.14 1936 0.6246 13.41 1964 0.6134 2.38 1940 0.5500 6.97 1968 0.4960 4.00 Two years, 1932 and 1972, are explainable anomalies (depression, Watergate). They are omitted; the following summaries are computed from the remaining data: 17 X i =1 x i = 32 . 18 17 X i =1 x 2 i = 446 . 171 17 X i =1 ( x i- ¯ x ) 2 = 385 . 256 17 X i =1 x i y i = 19 . 838 17 X i =1 y i = 8 . 288 17 X i =1 y 2 i = 4 . 121 17 X i =1 ( y i- ¯ y ) 2 = 0 . 0812 17 X i =1 ( x i- ¯ x )( y i- ¯ y ) = 4 . 149 (a) You want to use growth rate to predict the proportion of Democratic vote. Estimate b and b 1 . (b) The sum of squared residuals around the regression line is .03653. Find the t-statistic for testing the hypothesis that the slope is equal to 0. What conclusion do you draw from this?...
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hw6 - STATISTICS 500 – Fall 2009 Homework 6 handed out...

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