Correlation and Regression

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Overview

  1. 4.1 Scatterplots and Correlation
  2. 4.2 Introduction to Regression
  3. 4.3 Further Topics in Regression Analysis
  4. Chapter 4 Formulas and Vocabulary
  5. Chapter 4 Review Exercises
  6. Chapter 4 Quiz

187

image Measuring the Human Body

Many more measurements can be made of the human body than height and weight alone. The Chapter 4 Case Study examines 18 measurements of the bodies of 260 females and 247 males who are physically active, with data obtained from a study reported in the Journal of Statistics Education.1 Two large data sets are used: body_females and body_males.

  • In Section 4.1, we visit the case study data in a series of Your Turn exercises, where we do the following for the heights and weights of the women in the data set body_females:
    • Construct a scatterplot.
    • Characterize the relationship between height and weight.
    • Calculate the correlation coefficient for the height and weight of the women.
  • We work with the large data set body_males in the Section 4.1 exercises, by repeating the analysis done for the women earlier and comparing the results.
  • In Section 4.2, we continue to apply regression techniques to the case study data, in a series of Your Turn exercises, where we:
    • Calculate the regression coefficients, and express the regression equation in English.
    • Interpret the values of the regression coefficients.
    • Use the regression equation to make predictions.
    • Calculate the prediction error for our predictions.
    • Determine whether our predictions represent extrapolation.
  • In the Section 4.2 exercises, we work with the large data sets body_females and body_males, performing regression analysis using the techniques learned in the section.
  • Finally, in the Section 4.3 exercises, we again work with the large data sets body_females and body_males, and apply the further regression techniques learned in the section.

THE BIG PICTURE

Where we are coming from and where we are headed …

  • Chapter 3 showed us methods for summarizing data using descriptive statistics, but only one variable at a time.
  • In Chapter 4, we learn how to analyze the relationship between two quantitative variables using scatterplots, correlation, and regression.
  • In Chapter 5, we will learn about probability, which we will need to know about in order to perform statistical inference.