POL222 - week 10

Difference between simple and multiple linear regression

Simple regression: estimates the relationship between Y and X only

Multiple regression: estimates the relationship between Y and X while holding Z constant (controlling for confounders)

Condition and Compare Method

Divide observations into X–Z groups, compute conditional means of Y, and compare across X within the same Z

Not feasible when X and Z take many values or when there are multiple confounders

Ordinary Least Squares

finds the line that minimizes the total sum of squared residuals, where each residual = observed Y minus predicted Y (uᵢ = Yᵢ – Ŷᵢ)

Regression tables

list coefficients for each variable (e.g., X and Z), allow easy comparison between simple and multiple models to detect confounding and understand the effect of X on Y