week 2 - introducing categorical predictors into a multiple regression model

Question 1

what is the raw data of multiple regression

Answer 1

• continuous or categorical predictors
• Intercept = value of the outcome variable when all continuous predictors are at zero and categorical predictors are at their reference level
• Interpretation for continuous coefficients = A one unit increase in X1 gives a change in Y by the amount of b1
• Interpretation for categorical coefficients = A change to another category within X2 gives a change in Y by the amount of b2

Question 2

what are examples of categorical variables

Answer 2

• sex or smoker

Question 3

how does R manage categorical variables

Answer 3

• uses dummy or treatment coding
• level coded as 0 = variable reference level
• this is part of the intercept term

Question 4

why would you change the reference level of a variable

Answer 4

• hypothesis means a different reference level makes it easier to interpret
• useful for more than two levels

Question 5

what does mean centring mean in relation to continuous predictors

Answer 5

• the intercept now represents the average value when all continuous predictors are at their average value
• subtract the mean value of a variable from every observation in that variable

Question 6

what is meant by standardising

Answer 6

• taking centred variable and divide each observation by one standard deviation of the variable
• allows for direct comparison of the coefficients for continuous and binary predictors

Question 7

what about categorical variables with more than two levels

Answer 7

• each levels coefficient is the difference between the reference level and one other level (dummy/treatment coding)
• each levels coefficient is the difference of the level from the intercept (sum coding)

Question 8

what is ordered variables

Answer 8

• use ordinal regression model
• each level of the coefficient is the difference between those levels or levels below them

Question 9

what is dummy coding

Answer 9

• reference level becomes hidden in the intercept for the categorical level and one other level
• switching from one level of the categorical predictor to the second level is the same as moving along one unit of a predictor variable

Question 10

what is sum coding

Answer 10

• intercept now reflects 0 rather than the reference level
• switching between one level to the second is same as moving along two units of a continuous predictor

Question 11

what are standardising variables

Answer 11

• centre a predictor and then divide the observation by the standard deviation of the variable
• each standardised variable now predicts the change in the outcome variable for a one standard deviation increase in the predictor variables