Inference in Regression

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Overview

  1. 13.1 Inference About the Slope of the Regression Line
  2. 13.2 Confidence Intervals and Prediction Intervals
  3. 13.3 Multiple Regression
  4. Chapter 13 Formulas and Vocabulary
  5. Chapter 13 Review Exercises
  6. Chapter 13 Quiz

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image How Fair Is the Scoring in Scrabble?

Scrabble1 is a game in which the players choose letters randomly from a pool of letter tiles and take turns building words. Each letter tile is worth a specific number of points. For example, the letter A is worth 1 point, and the letter Z is worth 10 points. Do you think the way the various letters are valued is fair? Do you dread picking up the letter Z so much that you think it should be worth 25 points instead of 10? Do you think there are too many I's, perhaps, and not enough T's?

We can use regression analysis, the topic of this chapter, to help us find out why it often seems that there are too many I's and not enough T's. Regression can also help us understand why we would rather pick up an H tile instead of a V tile, even though each tile is worth 4 points. We can compare the distribution of letter points in Scrabble to the number of letter tiles in the game and to the frequency distribution of letters in the English language. To see more, check out this chapter's Case Study, How Fair Is the Scoring in Scrabble? (page 728).

THE BIG PICTURE

Where we are coming from and where we are headed …

  • In Chapter 4, we were introduced to regression analysis using descriptive methods.
  • Then, in Chapters 8–12, we learned about inference.
  • Here, in Chapter 13, “Inference in Regression,” we learn how to apply inference to regression analysis, such as the test for the relationship between and .
  • Where do you go from here? That's up to you. The world is overflowing with data and needs people like you who understand the statistical techniques and methods for uncovering the knowledge locked in the data. This course in statistics has tried to provide you with these tools. Here's hoping that your new expertise as a data analyst will help you achieve success in the Information Age.