Regression assumptions Return to the paper Questions? Lecture 11 Regression assumptions Return to the paper Questions?

What is error in a regression? Ideally error in this context is the combined influence on the dependent variable of a large number of excluded and hopefully irrelevant independent variables. Keep this in mind as we discuss the assumptions that must be met in conducting and interpreting regression results Those in bold are ones you should primarily concern yourself with in your project.

Basic OLS assumptions Dependent variable Independent variables Numeric at least at the interval level, continuous and unbounded. Not truncated (Not limited) Varies (non-zero variance) Normally distributed (or close to it) Independent variables Numeric at least at the interval level OR 1/0 Numeric variables normally distributed Vary (non-zero variance)

Basic OLS assumptions (cont.) The Independent variables are not (perfectly) correlated. The relationship between X and Y is expected to be linear (average error 0 everywhere) Independence of the errors No relevant independent variables have been excluded (including time and space) and No irrelevant independent variables have been included (You have more control over this why your model is important) The variables are measured without error, in particular bias (Hah!)

Basic OLS assumptions (cont.) Homoskedasticity Predicted values are as good (or bad) at all levels of the independent variable If variance is NOT constant across all values of the independent variables it is Heteroskadasticity.

Transforming variables E.g. For variables where there appears to be a logarithmic distribution of the data (e.g. population) logging the variables (=ln(X))* can make the relationship linear while preserving the interval relationships of the data. Often all variables are logged to assist in interpretation A one unit change in X results in a B change in Y A one percent change in X results in a B percent change in Y You can not take the natural log of zero, need to transform further. For more on interpretation see www.ats.ucla.edu/stat/spss/faq/spss_interpret_log.htm

N The more relevant observations (the bigger N) you have the more variation and the more powerful your results – if you just have ten countries and your model does not limit you, you likely want to add observations.

The paper Focus on presenting and describing the data that you think tells the story. KISS Use history and policy from other sources to put it in context. Use some of the methods from class to summarize data in text. E.g. “Exports of computers grew at an average annual rate of 5% in the 1990s. Despite a strong start this decade, hitting 11% growth in 2000, the sector’s exports fallen sharply and have averaged just 2% annually.”

Suggested format Introduction Trends and patterns in [Country’s] Trade States what the basic story is. Trends and patterns in [Country’s] Trade Present in simple terms how trade has changed over the past two decades. Be parsimonious. Discussion Provide the context for the data story such as key events or milestones in the story’s development. Conclusion