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In econometrics training you learn to use the classical linear model and never even learn the names for the parametric tests. It weirds me out that some people

In econometrics training you learn to use the classical linear model and never even learn the names for the parametric tests. It weirds me out that some people who're math-literate enough to know calculus 101 wouldn't instantly get that to test if two groups you would regress with a dummy, or to test if slopes between groups are different you would regress with an interaction effect. I remember it feeling as natural as water-is-wet by the end of the semester. This must be what it felt to learn multiplication with Roman numerals.

pas 8y ago
What does it mean to "regress with a dummy"? (Also what does regress with mean in general?) And two groups of what? Points? Also, what is an interaction effect? :o
- tomrod 8y ago
  Jargon only. Regress with a dummy means find a set of coefficients which minimize the sum of squared errors between a column (or columns) of a dependent variable from linear combinations of independent variables. The "dummy" is a 1/0 flag identifying whether the observation row belongs to a category, e.g. gender (assuming a binary classification) with Female mapped to 1. The coefficient that results from this algorithm will be the effect difference for a Female, and the intercept will represent the Male group. Simple model: dependent variable is wage, independent variable is years worked, and dummy represents female. The model is then Wage = b + m * years worked + c * 1(gender = F). The intercept term b (0 years worked) will be the average male wage with 0 years worked. b+c, the coefficient for female, will be the average female wage for 0 years worked. With the regression, you get some nice things out like confidence intervals around your coefficient estimates and more. So you can test hypotheses like whether their is a wage gap (c=0) or how large the wage gap might be (c=any number). Obviously a canned example, but this helps to introduce all but your last question. You can also test whether there is a slope effect. That is called an interaction term: you add an independent variable to the model that multiplies the gender coded variable to years worked. This would then show, if significant, that you can rule out a hypothesis that there is no wage differential between males and females for years worked (i.e. not just two parallel lines, but different slopes entirely).
  - thanatropism 8y ago
    Great reply. Thanks for spreading knowledge.

pas 8y ago

What does it mean to "regress with a dummy"? (Also what does regress with mean in general?) And two groups of what? Points? Also, what is an interaction effect? :o

tomrod 8y ago
Jargon only. Regress with a dummy means find a set of coefficients which minimize the sum of squared errors between a column (or columns) of a dependent variable from linear combinations of independent variables. The "dummy" is a 1/0 flag identifying whether the observation row belongs to a category, e.g. gender (assuming a binary classification) with Female mapped to 1. The coefficient that results from this algorithm will be the effect difference for a Female, and the intercept will represent the Male group. Simple model: dependent variable is wage, independent variable is years worked, and dummy represents female. The model is then Wage = b + m * years worked + c * 1(gender = F). The intercept term b (0 years worked) will be the average male wage with 0 years worked. b+c, the coefficient for female, will be the average female wage for 0 years worked. With the regression, you get some nice things out like confidence intervals around your coefficient estimates and more. So you can test hypotheses like whether their is a wage gap (c=0) or how large the wage gap might be (c=any number). Obviously a canned example, but this helps to introduce all but your last question. You can also test whether there is a slope effect. That is called an interaction term: you add an independent variable to the model that multiplies the gender coded variable to years worked. This would then show, if significant, that you can rule out a hypothesis that there is no wage differential between males and females for years worked (i.e. not just two parallel lines, but different slopes entirely).
- thanatropism 8y ago
  Great reply. Thanks for spreading knowledge.