Chapter 16

Regression

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Simple Linear Regression

  • Prediction versus Relation
  • Regression with z Scores
  • Determining the Regression Equation
  • The Standardized Regression Coefficient and Hypothesis Testing with Regression

Interpretation and Prediction

  • Regression and Error
  • Applying the Lessons of Correlation to Regression
  • Regression to the Mean
  • Proportionate Reduction in Error

Multiple Regression

  • Understanding the Equation
  • Stepwise Multiple Regression and Hierarchical Multiple Regression
  • Multiple Regression in Everyday Life

Next Steps: Structural Equation Modeling (SEM)

BEFORE YOU GO ON

  • You should understand the six steps of hypothesis testing (Chapter 7).
  • You should understand the concept of effect size (Chapter 8).
  • You should understand the concept of correlation (Chapter 15).
  • You should be able to explain the limitations of correlation (Chapter 15).

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Facebook and Social Capital The prediction tools introduced in this chapter helped researchers determine that increased use of Facebook predicts higher levels of social capital.
© hamideddine Bouali/Demotix/Demotix/Demotix/Corbis

In 2004, college student Mark Zuckerberg created the social networking site Facebook, which soon exploded in popularity across college campuses. By 2012, Facebook.com reported having almost 1 billion users, and it raised $16 billion in a public offering of its stock. As Facebook use ballooned, researchers at Michigan State University (MSU) (Ellison, Steinfeld, & Lampe, 2007) wanted to understand what college students were getting out of their Facebook relationships—that is, what they were gaining in social capital.

To find out, Ellison and colleagues’ study focused on the idea of “bridging” social capital; that is, they looked at the loose social connections we think of as acquaintances rather than friends. The researchers’ hypothesis was that greater use of Facebook would predict more of this type of social capital. Researchers measured this by asking students to rate several items, such as “I feel I am part of the MSU community” and “At MSU, I come into contact with new people all the time.”

Obviously, many influences determined how much social capital students get from Facebook, including the amount of time they spend on the site. Moreover, answers to the research question were complicated by gender, ethnicity, location of residence, and many other factors. In other words, to find out what students were getting out of their Facebook relationships, researchers had to account for the influence of many variables. The Michigan State University researchers controlled for all of these variables in their study and found that the more students used Facebook, the higher they tended to score on a measure of social capital.

The analytical methods we learn in this chapter build on correlation to help us to create prediction tools. We learn how to use one scale variable to predict outcome on a second scale variable. Then we discuss the limitations of this method—limitations that are similar to those we encountered with correlation. Finally, we expand this analytical method to allow us to use multiple scale variables to predict outcome on another scale variable.