Answer the following questions, showing your work. In other words, where you have to perform calculations to arrive at an answer, show those calculations, demonstrating that you understood how to arrive at the answer. Do not simply write the answer. Do not rely on calculations from a spreadsheet. If you do not provide calculations, you will not be given credit for the problems even if you provide the correct answers. Please ensure that your homework is neat and easy to follow, i.e., well-done and presented in a professional manner. (1) Neatly present all of the calculations that we did in class on Monday, Oct. 23, for the regression of vote share on gdp growth. Present (a) the coefficient estimate, b, of the association between gdp and vote-share; (b) present the constant of the regression; (c) present both calculations of R-Squared, (d) present the calculation of the standard error of the regression; (e) present the calculation of the standard error of the coefficient; (f) present the hypothesis test (all five steps). (2) For (2), use the following data: year twopartysh inflation 1916 1920 1924 1928 1932 1936 1940 55 1944 1948 1952 1956 1960 1964 1968 1972 1976 1980 1984 1988 1992 1996 2000 2004 2008 2012 2016 2020 52 Know that twopartysh is the share of the two-party vote won by the presidents party and that inflation refers to the degree to which inflation has increased over a period prior to the election. Two party vote-share is the dependent variable. Inflation is the independent variable. (2a) Write the population regression function for this model. (2b) Explain why inflation might influence the two party share of the vote won by the incumbents party. (2c) Based on your explanation in (2b), state a research (and null) hypothesis for the coefficient for the independent variable, inflation. (2d) Estimate a coefficient, b, for parameter, Beta, of the independent variable. (Make sure to include all of your calculations in a table like the one that we used in class to compute the coefficient estimate for GDP growth). In addition, show all of your work for all of the following questions: (2e) Calculate the constant, a, for the parameter, Alpha. (2f) Calculate the R-Squared statistic for your model. (2g) Calculate the standard error of the regression. (2h) Calculate the standard error of the coefficient, b. (2i) Develop a research hypothesis for beta based on the explanation that higher levels of inflation are bad, politically, for the presidents party. Given this observation, what should the expectation of the research hypothesis be for the sign of beta? Should it be positive? Negative? Why? Using the 5 steps of the critical value approach to hypothesis testing, test a research hypothesis (alpha = .05). (2j) Bonus: Construct a 99% confidence interval for your coefficient estimate.
