Linear Regression Modelling Flashcards
What are the two main types of variables
- Qualitative and Catagorical
How can Quantitative variables be distinguished
- Continuous and Discrete
How can Categorical variables be distinguished
- Nominal and Ordinal
How can Nominal and Ordinal variables be distinguished
- Many Catagories and Binary
How can Discrete variables be distinguished
- Counts and Intervals
What is a quantitative variable
- Variables that are measured in natural units and satisfy cardinality
What is a continuous variable and give an example
- A quantitative variable that can have an infinite number of values between two different points
- Age, Height, Time
What is a count variable and give an example
- A discrete variable that take specific (usually integer) values that indicate a counting of some kind
- No of kids, No of trips to the hospital
What is a catagorical variable and give an example
- Catagorical variables usually express some sort of qualitative trait of the objects studied, that can be used as labels or catagories
- They can take a limited, fixed number of possible values
- Eye Color: Blue, Green, Hazel, Brown etc
What is a Nominal Variable, Binary Nominal Variable and a Many Catagories Nominal Variable and give examples
- A nominal variable takes on levels that have no numerical value/interpretation. There is no natural order or sequence in their interpretation or presentation
- A binary variable is a variable that can only take two values, often called a dummy variable. Eg, Health Status: Healthy, Non-Healthy
- A many catagories variable can take more than two values. Eg, Ethnicity: Black, White, Asian
What is an Ordinal variable, Binary ordinal variable and a many catagories ordinal variable and give examples
- Ordinal variables have an arbritary numeric scale where the exact numeric distance particular is not possible to establish, hence they indicate a ranking over a set of data points. Order matters
- Binary Ordinal variables can only take two values. Eg Mark: Pass or Fail
- Multiple Catagories Ordinal can take multiple values. Eg: Rating from 1 to 5
What does simple linear regression show
- Models the relationship between a dependant variable y and an independent variable x
- It fits a straight line through the set of n points in such a way that minimises the sum of squared residuals
What form does a linear regression line usually take
- yi = b0 + b1 * xi + ui
What do we assume for an estimated model
- E(u|x) = 0
- y hat i = b hat 0 + b hat 1 * xi
- Such model explains changes in y with respect to changes in x
How do we interpret a simple linear regression model
- b0 is the intercept, where x = 0
- b1 is the slope of the line ∆y/ ∆x or alternatively b1 = ∂y/∂x (marginal effect)
How do we interpret the slope of a linear regression model
- The slope is the effect on y of a unitary change in x. More precisely, the slope is the effect on the average y of a unitary change in x
How does the model change when an extra variable is added
- A two variable model changes from a line to a plane
How is a multiple regression model interpreted
- The marginal effect of x is b1, the marginal effect of z is b2. The constant is still the value for y when x = 0, z = 0.
How does a dummy variable work
- Will take the value of 1 if a condition is satisfied and 0 if it is not met
- The level that takes the value of zero is often called the base/reference level
