Lesson 3: SLR Estimation & Prediction

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Introduction

A typical regression analysis involves the following steps:

  1. Model formulation
  2. Model estimation
  3. Model evaluation
  4. 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 (and we will learn further evaluation methods in Lesson 4). In 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.

Learning objectives & outcomes

Upon completion of this lesson, you should be able to do the following:

  • Distinguish between estimating a mean response (confidence interval) and predicting a new observation (prediction interval).
  • Understand the various factors that affect the width of a confidence interval for a mean response.
  • Understand why a prediction interval for a new response is wider than the corresponding confidence interval for a mean response.
  • Know the formula for a prediction interval depends strongly on the condition that the error terms are normally distributed, while the formula for the confidence interval is not so dependent on this condition for large samples.
  • Know the types of research questions that can be answered using the materials and methods of this lesson.