Pacific Standard does a great job covering social science in the news. Here's a nice example of multiple regression analyses, in a study they headlined, "Turn off the TV, Save your brain?"
The basic story comes from a large study that found the amount of TV people watched in their young-adult years was linked to lower cognitive abilities in middle age.
a) So far, this is a simple bivariate correlation. Can you sketch a well-labelled scatterplot of this? Is the relationship positive or negative?
b) This bivariate correlation apparently has temporal precedence, because the TV variable was measured in young adulthood, before the cognitive abilities (in middle age). Can we make a causal claim now? If not, what third variables might be responsible for this relationship?
Here are some methodological details about the study. You'll see that the story shows the telltale signs of controlling for some of these possible third variables:
The study featured 3,247 people who were recruited from four American cities (Chicago, Minneapolis, Oakland, and Birmingham) in the late 1980s. All were between the ages of 18 and 30 at the study's outset. They were tracked for the next quarter century, with follow-up examinations every two to five years....once every five years, [the participants] indicated "the average number of hours per day (they) spent watching television in the past 12 months."Those who reported watching an average of more than three hours per day during more than two-thirds of their visits were categorized as having a "long-term pattern of high television viewing."
At year 25, the participants took three well-known cognitive tests: the Digit Symbol Substitution Test, which measures speed of mental processing; the Stroop Test, which measures processing speed and attention; and the Rey Auditory Verbal Learning Test, which assesses how well we remember information delivered orally.
Participants who showed a long-term pattern of high TV viewing (approximately 11 percent of the total) scored significantly lower, on average, on [the] cognitive tests...This held true after taking into consideration a range of factors, including age, race, education, alcohol use, and body mass index.
c) Based on the description above, you could sketch a multiple regression table depicting this study's results. What would be the criterion variable? What would be the predictor variables? What betas do you think would be significant? Which betas will be positive? Which will be negative?
d) The description above also tells you how some of the variables were operationalized. For example, how did they operationalize television viewing? How did they operationalize cognitive ability?
e) Even though this study sure feels like it could support a causal claim, it can't. (Remember, no correlational study can definitively support a causal claim.) That's because even though it has temporal precedence (TV was measured before cognitive ability), and controls for several third variables (including age, race, education, alcohol use, and BMI), they didn't control for all possible third variables. What are some additional third variables that were not controlled for in this study?