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- https://stats.libretexts.org/Bookshelves/Applied_Statistics/Book%3A_Quantitative_Research_Methods_for_Political_Science_Public_Policy_and_Public_Administration_(Jenkins-Smith_et_al.)/10%3A_OLS_Assumptions_and_Simple_Regression_DiagnosticsNow that you know how to run and interpret simple regression results, we return to the matter of the underlying assumptions of OLS models, and the steps we can take to determine whether those assumpti...Now that you know how to run and interpret simple regression results, we return to the matter of the underlying assumptions of OLS models, and the steps we can take to determine whether those assumptions have been violated. We begin with a quick review of the conceptual use of residuals, then turn to a set of “visual diagnostics” that can help you identify possible problems in your model. We conclude with a set of steps you can take to address model problems, should they be encountered. As with
- https://stats.libretexts.org/Bookshelves/Applied_Statistics/Book%3A_Quantitative_Research_Methods_for_Political_Science_Public_Policy_and_Public_Administration_(Jenkins-Smith_et_al.)/04%3A_ProbabilityProbability tells us how likely something is to occur. Probability concepts are also central to inferential statistics - something we will turn to shortly. Probabilities range from 0 (when there is no...Probability tells us how likely something is to occur. Probability concepts are also central to inferential statistics - something we will turn to shortly. Probabilities range from 0 (when there is no chance of the event occurring) to 1.0 (when the event will occur with certainty). If you have a probability outside the 0 - 1.0 range, you have made an error! Colloquially we often interchange probabilities and percentages, but probabilities refer to single events while percentages refer to the por
- https://stats.libretexts.org/Bookshelves/Applied_Statistics/Book%3A_Quantitative_Research_Methods_for_Political_Science_Public_Policy_and_Public_Administration_(Jenkins-Smith_et_al.)/12%3A_The_Logic_of_Multiple_Regression/12.01%3A_Theoretical_SpecificationNote that linearity is assumed in the parameters (that is, for the BsBs), therefore the expected value of the dependent variable is a linear function of the parameters, not necessarily of the variable...Note that linearity is assumed in the parameters (that is, for the BsBs), therefore the expected value of the dependent variable is a linear function of the parameters, not necessarily of the variables themselves.
- https://stats.libretexts.org/Bookshelves/Applied_Statistics/Book%3A_Quantitative_Research_Methods_for_Political_Science_Public_Policy_and_Public_Administration_(Jenkins-Smith_et_al.)/08%3A_Linear_Estimation_and_Minimizing_Error/8.03%3A_SummaryWhoa! Think of what you’ve accomplished here: You learned enough calculus to find a minima for an equation with two variables, then applied that to the equation for the ∑ϵ2∑ϵ2. You derived the error m...Whoa! Think of what you’ve accomplished here: You learned enough calculus to find a minima for an equation with two variables, then applied that to the equation for the ∑ϵ2∑ϵ2. You derived the error minimizing values for ^αα^ and ^ββ^, then used those formulae in R to calculate by hand" the OLS regression for a small dataset. Congratulate yourself – you deserve it!
- https://stats.libretexts.org/Bookshelves/Applied_Statistics/Book%3A_Quantitative_Research_Methods_for_Political_Science_Public_Policy_and_Public_Administration_(Jenkins-Smith_et_al.)/01%3A_Theories_and_Social_Science/1.02%3A_Theory_and_Empirical_ResearchIn political science and public policy, some of the things we want to measure are directly observable: how many dollars were spent on a project or how many votes the incumbent receives, but many of ou...In political science and public policy, some of the things we want to measure are directly observable: how many dollars were spent on a project or how many votes the incumbent receives, but many of our concepts are not observable: is issue X on the public’s agenda, how successful is a program, or how much do citizens trust the president.
- https://stats.libretexts.org/Bookshelves/Applied_Statistics/Book%3A_Quantitative_Research_Methods_for_Political_Science_Public_Policy_and_Public_Administration_(Jenkins-Smith_et_al.)/08%3A_Linear_Estimation_and_Minimizing_ErrorAs noted in the last chapter, the objective when estimating a linear model is to minimize the aggregate of the squared error. Specifically, when estimating a linear model, Y = A + B X + E , we seek...As noted in the last chapter, the objective when estimating a linear model is to minimize the aggregate of the squared error. Specifically, when estimating a linear model, Y = A + B X + E , we seek to find the values of ^ α and ^ β that minimize the ∑ ϵ 2 . To accomplish this, we use calculus.
- https://stats.libretexts.org/Bookshelves/Applied_Statistics/Book%3A_Quantitative_Research_Methods_for_Political_Science_Public_Policy_and_Public_Administration_(Jenkins-Smith_et_al.)/06%3A_Association_of_VariablesThe last chapter focused on the characterization of distributions of a single variable. We now turn to the associations between two or more variables. This chapter explores ways to measure and visuali...The last chapter focused on the characterization of distributions of a single variable. We now turn to the associations between two or more variables. This chapter explores ways to measure and visualize associations between variables. We start with how to analyze the relations between nominal and ordinal level variables, using cross-tabulation in R. Then, for interval level variables, we examine the use of the measures of covariance and correlation between pairs of variables. Next, we examine hy
- https://stats.libretexts.org/Bookshelves/Applied_Statistics/Book%3A_Quantitative_Research_Methods_for_Political_Science_Public_Policy_and_Public_Administration_(Jenkins-Smith_et_al.)/16%3A_Logit_Regression/16.03%3A__SummaryThe estimated coefficients show the change in the log of the odds for a one unit increase in the XX variable – not the usual way to describe effects. Of particular utility are logit graphics, showing ...The estimated coefficients show the change in the log of the odds for a one unit increase in the XX variable – not the usual way to describe effects. Of particular utility are logit graphics, showing the estimated shift in YY from values of zero to one; the estimated probabilities of YY=1 for cases with specified combinations of values in the XX variables; and estimates of the ranges of probabilities for YY=1 across the ranges of values in any XX.
- https://stats.libretexts.org/Bookshelves/Applied_Statistics/Book%3A_Quantitative_Research_Methods_for_Political_Science_Public_Policy_and_Public_Administration_(Jenkins-Smith_et_al.)/17%3A_Appendix-_Basic_R/17.02%3A_Downloading_R_and_RStudioIn this section we will provide instructions to downloading R and RStudio. RStudio is an integrated development environment (IDE) that makes R a bit more user-friendly. In the class associated with th...In this section we will provide instructions to downloading R and RStudio. RStudio is an integrated development environment (IDE) that makes R a bit more user-friendly. In the class associated with this text, RStudio will primarily be used; however, it should be noted other IDEs exist for R. Additionally, R can be used without the aid of an IDE should you decide to do so.
- https://stats.libretexts.org/Bookshelves/Applied_Statistics/Book%3A_Quantitative_Research_Methods_for_Political_Science_Public_Policy_and_Public_Administration_(Jenkins-Smith_et_al.)/10%3A_OLS_Assumptions_and_Simple_Regression_Diagnostics/10.05%3A_SummaryProfessor Gaddie notes: “… instead of working to achieve better model specification through the application of theory and careful thought, in the 1960s and 1970s electoral scholars instead just threw ...Professor Gaddie notes: “… instead of working to achieve better model specification through the application of theory and careful thought, in the 1960s and 1970s electoral scholars instead just threw out the South and all senate races, creating the perception that the United States had 39 states and a unicameral legislature.”↩
- https://stats.libretexts.org/Bookshelves/Applied_Statistics/Book%3A_Quantitative_Research_Methods_for_Political_Science_Public_Policy_and_Public_Administration_(Jenkins-Smith_et_al.)/09%3A_Bi-Variate_Hypothesis_Testing_and_Model_Fit/9.03%3A_SummaryWith respect to the former, we focused on the residual standard error and its role in determining the probability that our model estimates, BB and AA, are just random departures from a population in w...With respect to the former, we focused on the residual standard error and its role in determining the probability that our model estimates, BB and AA, are just random departures from a population in which ββ and αα are zero. The question wording was as follows: On a scale from zero to ten, where zero means no risk and ten means extreme risk, how much risk do you think global warming poses for people and the environment?“↩
