Does one’s cola consumption predict one’s bone mineral density? Using regression analyses, nutrition researchers found that older women who drank more cola (but not more of other carbonated drinks) tended to have lower bone mineral density, a risk factor for osteoporosis (Tucker, Morita, Qiao, Hannan, Cupples, & Kiel, 2006). Cola intake, therefore, does seem to predict bone mineral density. 

a. Explain why we cannot conclude that cola intake causes a decrease in bone mineral density. 

b. The researchers included a number of possible third variables in their regression analyses. Among the included variables were physical activity score, smoking, alcohol use, and calcium intake. They included the possible third variables first, and then added the bone density measure. Why would they have used multiple regression in this case? Explain. 

c. How might physical activity play a role as a third variable? Discuss its possible relation to both bone density and cola consumption. 

d. How might calcium intake play a role as a third variable? Discuss its possible relation to both bone density and cola consumption.