Lesson 4: SLR Assumptions, Estimation & Prediction
Overview of this Lesson
A typical regression analysis involves the following steps:
- Model formulation
- Model estimation
- Model evaluation
- Model use
So far, we have learned how to formulate and estimate a simple linear regression model. We have also learned about some methods for evaluating the model. The first part of this lesson continues the topic of evaluating the model.
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 simple 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.
We focus in this lesson on graphical residual analysis. When we revisit this topic in the context of multiple linear regression in Lesson 6 we'll also study some statistical tests for assessing the assumptions. We'll consider various remedies for when linear regression model assumptions fail throughout the rest of the course, but particularly in Lesson 7.
In the second part of this lesson, we focus our efforts on using the model to answer two specific research questions, namely:
- What is the average response for a given value of the predictor x?
- What is the value of the response likely to be for a given value of the predictor x?
In particular, we will learn how to calculate and interpret:
- A confidence interval for estimating the mean response for a given value of the predictor x.
- A prediction interval for predicting a new response for a given value of the predictor x.
|Key Learning Goals for this Lesson:|