Question - Predicting energy-drink consumption. Energy-drink advertising consistently emphasizes a physically active lifestyle and often features extreme sports and risk taking. Are these typical characteristics of an energy-drink consumer? A researcher decided to examine the links between energy-drink consumption, sport-related (jock) identity, and risk taking.3 She invited over 1500 undergraduate students enrolled in large introductory-level courses at a public university to participate. Each participant had to complete a 45-minute anonymous questionnaire. From this questionnaire jock identity and risk-taking scores were obtained where the higher the score, the stronger the trait. She ended up with 795 respondents. The following table summarizes the results of a multiple regression analysis using the frequency of energy-drink consumption in the past 30 days as the response variable:

A superscript of ∗∗ means that the individual coefficient t test had a P-value less than 0.01, and a superscript of ∗∗∗ means that the test had a P-value less than 0.001. All other P-values were greater than 0.05.

(a) The overall F statistic is reported to be 8.11. What are the degrees of freedom associated with this statistic?

(b) R is reported to be 0.28. What percent of the variation in energy-drink consumption is explained by the model? Is this a highly predictive model? Explain.

(c) Interpret each of the regression coefficients that are significant

(d) The researcher states, "Controlling for gender, age, race, ethnicity, parental educational achievement, and college GPA, each of the predictors (risk taking and jock identity) was positively associated with energy-drink consumption frequency." Explain what is meant by "controlling for" these variables and how this helps strengthen her assertion that jock identity and risk taking are positively associated with energy-drink consumption.