POL222H1 Lecture Notes - Lecture 9: Linear Regression, Confounding
Document Summary
Divide our data by different values of x. Calculate the average of y for each value of x (conditional average) How y would vary on average as x changes. Use the linear regression to model the conditional average of y given x - how y would vary on average as x changes. Conditional average of y given x is modeled as: = 0 + x. 0 is the value of when x = 0. Represents how y would vary, on average, as x changes by one unit. In terms of the predicted value of y : i = a + xi. In terms of the observed value of y: i = a + xi + ui. = values of y along the linear regression line. The part of y that can be systemically explained. Method to separate systemic component and purely random component of relationship. Most of the causal relationship between x and y there is a confounding variable involved.
