17.871 Spring 2007 Problem Set #3 Work together, write up individually, and show your work. Handed out: May 3, 2007 Due: May 10, 2007 1. (20 points) Does the incumbent president do better in New York State when the Yankees win more games? Variables vote_i: incumbent president's vote share in New York State counties pct: the Yankees winning percentage over the election-year season incterms: the number of terms the president has served in office gnp4: per capita GNP growth in the election-year year: year of the presidential election (Each row in the data set is a New York state county year.) . sum vote_i pct incterms gnp4 year Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- vote_i | 1302 .4913937 .1586309 .16 .86 pct | 1361 .5830786 .0585386 .41 .71 incterms | 1302 2 1.069456 1 5 gnp4 | 1302 2.041905 4.912677 -14.96 11.57 year | 1361 1960.025 24.17222 1920 2000 . regress vote_i pct incterms gnp4 year if year > 1919 Source | SS df MS Number of obs = 1302 -------------+------------------------------ F( 4, 1297) = 129.37 Model | 9.33695094 4 2.33423773 Prob > F = 0.0000 Residual | 23.4011068 1297 .018042488 R-squared = 0.2852 -------------+------------------------------ Adj R-squared = 0.2830 Total | 32.7380578 1301 .025163765 Root MSE = .13432 ------------------------------------------------------------------------------ vote_i | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- pct | .2090739 .0855564 a. b. .0412299 .376918 incterms | -.0758338 .0036583 -20.73 0.000 e. e. gnp4 | .006453 .0008453 7.63 0.000 .0081113 .0047948 year | .0006841 .0001934 3.54 0.000 .0003047 .0010635 _cons | -.8065863 .4117455 -1.96 0.050 -1.614347 .0011739 ------------------------------------------------------------------------------ a. Calculate the missing statistic. b. Calculate the missing statistic. c. Interpret the coefficient for Yankee winning percentage (pct). d. Interpret the coefficient for incumbent terms (incterms). e. Calculate the missing confidence interval. f. Interpret the confidence interval in e. g. Calculate the 90% confidence interval in e.h. Pretend that the regression results above (coefficients and standard errors) were from a model with only 20 degrees of freedom. Calculate b. and e. i. Do you believe that citizens of New York State vote more for the incumbent president when the Yankees win more games? What additional graphs or analyses would you like to see? j. What does this model predict about the change in the incumbent president's winning percentage between 1920 and the year 3000? Believable? 2. (10 points) Understanding interactions. . g postwar = year > 1945 . g pctXpostwar = pct * postwar . regress vote_i pct incterms gnp4 year postwar pctXpostwar Source | SS df MS Number of obs = 1302 -------------+------------------------------ F( 6, 1295) = 109.38 Model | 11.0111805 6 1.83519675 Prob > F = 0.0000 Residual | 21.7268773 1295 .016777511 R-squared = 0.3363 -------------+------------------------------ Adj R-squared = 0.3333 Total | 32.7380578 1301 .025163765 Root MSE = .12953 ------------------------------------------------------------------------------ vote_i | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- pct | .3116188 .1380185 2.26 0.024 .0408545 .582383 incterms | -.0855107 .0036936 -23.15 0.000 -.0927569 -.0782646 gnp4 | -.0062222 .0008759 -7.10 0.000 -.0079406 -.0045038 year | -.0020971 .0003352 -6.26 0.000 -.0027547 -.0014395 postwar | .4466541 .0992433 4.50 0.000 .2519587 .6413494 pctXpostwar | -.5048986 .1591314 -3.17 0.002 -.8170821 -.1927151 _cons | 4.497279 .6683988 6.73 0.000 3.186016 5.808542 ------------------------------------------------------------------------------ a. Interpret the coefficient on prewar Yankee winning percentage. b. What is the effect of Yankee winning percentage postwar. (Hint: You need to calculate this using the interactions.) c. From the model, predict the county vote share for the incumbent president for Erie County in 1936. Here's the relevant row: name vote_i pct incterms gp4 year postwar ERIE .52 .66 1 11.57 1936 0 d. From the model, predict the average county vote share for the incumbent president for Erie County in 2000. Here's the relevant row: name vote_i pct incterms gp4 year postwar ERIE .47 .54 2 1.95 2000 1 e. What does this model predict about the change in the incumbent president's winning percentage between 1920 and the year 3000? Why might the coefficient on year change from the model in question 1? (Hint: think about what changes between the models.) 3. (Infinite points) True or False: Yankees
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