Some studies have suggested that a nightly glass of wine may not only take the edge off a day but also improve health. Is wine good for your health? A study of nearly 1.3 million middle-aged British women examined wine consumption and the risk of breast cancer. The researchers were interested in how risk changed as wine consumption increased. Risk is based on breast cancer rates in drinkers relative to breast cancer rates in nondrinkers in the study, with higher values indicating greater risk. In particular, a value greater than 1 indicates a greater breast cancer rate than that of nondrinkers. Wine intake is the mean wine intake, in grams per day, of all women in the study who drank approximately the same amount of wine per week. Here are the data (for drinkers only) Wine Intake X 2.5 8.5 15.5 26.5 (grams per day) Realtive Risk y 1.00 1.08 1.15 1.22
(a) Make a scatterplot of these data. Based on the scatterplot, do you expect the correlation to be positive or negative? Near ±1 or not?
(b) Find the correlation r between wine intake and relative risk. Do the data show that women who consume more wine tend to have higher relative risks of breast cancer