Lesson 6: MLR Assumptions, Estimation & Prediction
Overview of this Lesson
This lesson extends the methods from Lesson 4 to the context of multiple linear regression. How do we evaluate a model? How do we know if the model we are using is good? One way to consider these questions is to assess whether the assumptions underlying the multiple linear regression model seem reasonable when applied to the dataset in question. Since the assumptions relate to the (population) prediction errors, we do this through the study of the (sample) estimated errors, the residuals.
Next, we focus our efforts on using a multiple linear regression model to answer two specific research questions, namely:
 What is the average response for a given set of values of the predictors x_{1}, x_{2}, ...?
 What is the value of the response likely to be for a given set of values of the predictors x_{1}, x_{2}, ...?
In particular, we will learn how to calculate and interpret:
 A confidence interval for estimating the mean response for a given set of values of the predictors x_{1}, x_{2}, ....
 A prediction interval for predicting a new response for a given set of values of the predictors x_{1}, x_{2}, ....
Key Learning Goals for this Lesson: 
