# POL222H1 Lecture 9: Explaining the Intricacies Behind the Multiple Linear Regression Model

## Document Summary

The multiple linear regression model (continued from lecture 8) When confounding variables (z) arise, the multiple linear regression (mlr) model is needed to control for them: to control for z: Divide data by different values of x and z. Calculate the conditional average (average of y) for each value of x and z. The result is how much y varies on average as x changes while holding z constant. The mlr formula: y(hat sign) = + x + z: y(hat sign) = values of y along linear regression lines, note that and z are added/subtracted together before calculating x, z = confounding variable. As z changes, the intercept shifts upwards/downwards. If the coef cients of x and z are positive ( 1 > 0/ >0), a positive z value will raise the intercept, while a negative z value will lower it.