Suppose height is regressed on age for a sample of children.
a. What kind of relationship, if any, do we expect to see between the two variables for the sample and for the population from which the sample was obtained?
b. Which of these confidence intervals for slope b1 would convince us that the relationship is positive for the larger population of children: (2.0, 2.5), (-1.0, 4.0), or (-2.5, -2.0)?
c. Which one of these would help to convince us that, in general, height increases with age: b0 small, b1 small, b0large, or b1 large?
d. Suppose we performed the regression on just a few children. Would we be more likely to obtain weak evidence of a strong relationship or strong evidence of a weak relationship?