What is a predictor in regression?
An observed variable used as input to explain or predict the response variable.
What is another name for a predictor?
Explanatory variable, independent variable, covariate, or feature.
What is the response variable?
The outcome variable the model is trying to explain or predict.
What is the model (design) matrix?
A numeric matrix whose rows are observations and whose columns correspond to model parameters.
What do the rows of the model matrix represent?
Individual observations.
What do the columns of the model matrix represent?
Model parameters (one per column).
Does the model matrix contain parameter values?
No, it contains predictor-derived numeric values used to estimate parameters.
What equation defines fitted values using the model matrix?
ŷ = Xβ̂
Where do predictors come from?
The raw dataset.
Where do parameters come from?
They are estimated by the regression model.
Is the intercept a predictor?
No, it is a parameter.
How is the intercept represented in the model matrix?
As a column of ones.
Can one predictor create multiple columns in the model matrix?
Yes, especially for categorical predictors or polynomial terms.
If a factor has k levels, how many parameters does it add?
k − 1 parameters (with an intercept).
What is a model term?
A specific way a predictor enters the model, such as a transformation or interaction.
What is the hat matrix?
The matrix that maps observed responses y to fitted values ŷ.
What is the formula for the hat matrix?
H = X (XᵀX)⁻¹ Xᵀ
What does the diagonal of the hat matrix represent?
Leverage values.
What does the trace of the hat matrix equal?
The number of estimated parameters (rank of X).
Can you compute the hat matrix without specifying a model?
No, because the hat matrix depends on the design matrix.
