Democracy and Social Science II

Professor Jeff Grynaviski

Winter 2005 (Prepared February 25, 2005)

 

 

Homework #4 Due Friday, March 5.

 

Use the dataset and codebook from the last homework assignment. You may need a calculator for this homework assignment.

 

Your assignment for this week is as follows:

 

  1. Using the following information, hand-calculate the estimates of intercept (b0), coefficient of X (b1), and R-square value (R2) from a bivariate regression of Y (the dependent variable) on X (the independent variable). Please identify the formulas of b0, b1, R (correlation), and R2.

 

Mean (X) = 20.908

Mean (Y) = 18.45833

Var (X) = 38.952

Var (Y) = 21.2806

Cov (X, Y) = 15.1791

 

  1. Perform a multiple regression with respondents’ attitudes toward homosexuality (the dependent variable) and the variables, degree, income, polviews, partyid, and agerange as the independent variables. (1) Interpret the effect of age (agerange) on public attitudes toward homosexuality (homosex) in this model. (Please do not forget to explain the role of other variables in your interpretation.) (2) Also, describe whether all the coefficients of independent variables are statistically significant (i.e., whether you can reject the null hypotheses using t-test).

 

  1. This question has three parts.

(i)              Perform a bivariate regression with respondents’ attitudes toward homosexuality (homosex) and their income (income) as the independent variable. Report and interpret the regression coefficient and its standard error.

(ii)            Now, run another bivariate regression with respondents’ attitudes toward homosexuality (homosex) and their level of education (degree) as the independent variable. Report and interpret the regression coefficient and its standard error.

(iii)          Finally, run a multiple regression including BOTH income and degree in a model. Report BOTH regression coefficients and their standard errors. Are they consistent with the coefficients and standard errors from two -- separately performed in (1) and (2) -- bivariate regressions? Are both coefficients statistically significant? How can you explain this phenomenon?