Reason 1 could be possible, but isn't likely, that mil drinking alone is a cause of stroke. Reason 2 is not likely, since it would say that a low risk of stroke causes people to drink milk. People usually do not even know whether or not they are at risk for strokes. Reason 3 could be possible, that milk drinking is one of many factors that reduces the risk of a stroke. Reason 4 is quite likely, that confounding variables exist. One example is general good diet and good health which leads to reduced stroke risk. Reason 5 is likely, that both reduced stroke risk and increased milk consumption result from a common cause, such as interest in taking care of one's health. Related to reasons 4 and 5, the article notes that the same individuals who consumed the most milk were also the leanest and most physically active. Reason 6, that both variables are changing over time, is not relevant. Reason 7, that the association is just coincidence is possible. Any single study could find a relationship just by chance.
Problem 4.
b) If X-rays were deleted, the correlations would decrease to 0.13, because outliers that fall in line with the rest of the data tend to increase correlation. If pesticides were deleted (but not X-rays) correlation would increase to 0.68, because outliers that do not fit the pattern of the rest of the data tend to decrease correlation.
c) That would decrease the correlation because it would be an extreme outlier, not in line with the data. It also makes sense that it should decrease the correlation because it is an example of a case in which students and experts are not in agreement at all, and thus weakens the relationship.
Problem 6.
They are designed to rule out Reason 4 "confounding variables may exist"
Problem 7.
a) The lines are almost parallel, and the regression line falls entirely below the actual=ideal line. This indicates that when averaged over males and females, the data imply that people's ideal and actual weight are very similar, with ideal weight always being slightly less than actual weight.
b) Men - 157.5 pounds, women - 133.9 pounds, combined - 143 pounds.
c) With the combined equation we would concluded that individuals weighing 150 pounds, on average, like to weigh about 7 pounds less. From the separate equations, we see that on average women would like to weigh much less, and men would prefer to weigh more, not less than their actual weight of 150.
d) "The missing link, a third variable" is the problem. Combining men and women produces misleading results.
Problem 8.
There would automatically be a relationship between the actual numbers, because large cities would have higher numbers for both than for small cities. The more meaningful question is whether or not the per capita figures for beer sales and highway deaths are related.
Problem 11.
First, they may have a biological explanation, like the fact that alcohol and tobacco are irritants on those parts of the body. Second, they may have found that the relationship holds under varying conditions, such as in different cultures, for different types of alcohol, in different age groups, and so on. Third, they may have ruled out potential confounding factors, like diet, by measuring them and determining whether or not they also have an impact.