PW1 Flashcards
(33 cards)
What is a quantitative variable
- A variable measured in natural units and satisfies cardinality
What is a continuous variable and give two examples
- A variable that can have an infinite number of different values between two points
- Time, Age
What is a count variable and give two examples
- A variable that takes specific values indicating a counting of some kind
- Number of visits to the hospital, Number of pens
What is a Categorical variable and give two examples
- A variable that expresses some sort of qualitative trait of the objects studied
- Eye color: blue, brown, hazel, Smoking status: smoker, non-smoker
What is a Nominal variable
- A nominal variable takes on levels that have no numerical value/interpretation
What is an Ordinal variable
- A variable that has an arbritrary numeric scale where the distance is not possible to establish, so order matters
Whats the difference between a Binary variable and a Many Category variable
- A binary variable only has two levels where as a many category variable will take more than two levels
Give two examples of a nominal binary and many catagories variable
- Binary: Health status & Ethnicity
- Many Categories: Type of bycicle, Ethnicity
Give two examples of an ordinary binary and many categories variable
- Binary: Mark(Pass/Fail), Student Status(Under/Postgrad)
- Many Categories: Health Status(Poor, Fair, Good), Rating Question(1 to 5)
What does the slope of a linear regression represent
- The slope is the effect on the average y of a unitary change in x
How does interpretation of the slope change as extra explanatory variables are added to a regression
- It doesn’t, each variable is interpreted individually and instead of a line a plane is fitted
How do Dummy variables work in a regression
- The variable will take the value of 1 if a condition is satisfied & 0 if not
What does the reference level mean for a Dummy variable
- The level that takes the value of zero is often called the reference level
- This is because this is the level that the other level is compared to
How is the coefficient for a Dummy variable interpreted for a basic regression model
- b1 is the difference in the average y of D(1) compared to D(0)
- Shows the difference in Average y when we compare D = 1 to the level D = 0
How can we derive the effect of a Dummy variable
- We can take expectations of the regression model and take the difference of when D = 1 and D = 0
- We assume E(X|u) = 0
How are Categorical variables used in a regression model
- In a similar way to dummys, where multiple variables are in the model but are compared to the same reference level
What are interaction effects and why are the important
- They capture the effect of two variables working in combination
- We can have interactions between continuous variables, Dummys and both combined
How does the interpretation of x change when the model is Log-Level
- Log(y) = b0 + b1 * x + u
- A unitary change in x implies a (100 * b1) percentage change in y
- Known as semi-elasticites
How does the interpretation of x change when the model is Log-Log
- Log(y) = b0 + b1 * Log(x) + u
- A percentage change in x results in a b1 percentage change in y
- Known as common elasticity
How does the interpretation of x change when the model is Level-Log
- y = b0 + b1 * log(x) + u
- A percentage change in x results in a b1/100 change in y
What is MLR 1
- MLR1: Linearity in Parameters
- The model can be written as y = b0 + b1 * x + etc
What is MLR 2
- MLR2: Random sampling from the population
- There is no sample selection, the observations are randomly extracted from the population
What is MLR 3
- MLR3: No perfect collinearity in the sample
- None of the independent variables in the sample have an exact linear relationship
- Independent variables can be correlated, but not perfectly correlated
What is MLR4
- MLR4: E(u|x1,…,xk) = E(u) = 0
- Under MLR4, we have exogenous explanatory variables
