# POL222H1 Lecture Notes - Lecture 10: Simple Linear Regression, Regression Analysis, Confounding

## Document Summary

Multiple linear regression models the conditional average of y given x and z how y would vary on average as x changes holding z constant. Conditional average of y given x and z modeled as. Yhat = values of y along the linear regression lines. B(0) = value of yhat when x=0 and z=0. B = change in yhat with respect to one unit change in x holding z constant. Same interpretation applies when z takes different values. B is slope of relationship between yhat and x when z is held constant. B represents how y would vary on average as z changes by one unit, holding the value of. Omitted variable bias b8 = b + (y x a) If z is a confounding variable, then b* not equal to b. If z is a confounding variable, then the coefficient of x would change when z is included in a linear regression model.