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ARM technique consultation regression analysis aantekeningen
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Lecture notes from the technique consultation on regression analysis. Written in 2024, mostly in English.
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Advanced Research Methods part B – Technique consultation RegressionAnalysis
Choosing the reference category by dummy variables
Why do we use dummy variables in a multiple regression analysis?
- Regression analysis requires metrically scaled variables (zowel voor de
onafhankelijke als de afhankelijke variabele)
- To be able to incorporate non-metrically scaled variables, we create dummies that
does not make them metrically scaled, maar hierdoor kan je ze wel opnemen in een
regressive analyse
- One dummy is left out and serves as reference category
- Je maakt bijvoorbeeld 3 dummy’s en je neemt er 2 van deze op in de analyse. Je
interpreteert daardoor de Beta altijd in relatie tot de reference category (in
comparison to)
Does it matter which category becomes the reference category while using a dummy?
- Mathematically: no
- Sometimes there are theoretical reasons to use a particular reference category er
kan een categorie zijn waartegen je alle andere categorieën mee wil vergelijken
- If not, you can use the one with the largest sample size
- You can run several models to get all comparisons
Error terms
- The individual error terms have a mean of zero. This is an assumption, because with
multiple regression we cannot formally assess the error, we assume that individual
error terms have a mean of zero
- We cannot formally assess this (omdat we niet de data hebben), but we know our
measures might not be always completely right, we might not have all variables in the
model, therefore we assume that overall we are kind of right
- That is why we check the residuals (the deviation between the predicted value and
the actual value)
What is a residual? How do you detect influential observations?
Residual: error in predicting our sample data
Influential observations detection: through residual plots and partial regression plots
A: null-plot. Het is niet based en niet heteroscedactic
B: non-linearity. Je moet misschien polynomial terms meenemen
C: heteroscedasticity. De variance van de errors is klein in het begin en groot aan het einde
D: heteroscedasticity
E: time-based dependence.
F: event-based dependence
G: non-linearity
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