A large sample of students was surveyed at a particular university. Among other things, they were asked to report their weight and their age.
a. Explain why we can expect the relationship between weight and age to be positive.
b. Which makes the most sense to play the role of explanatory variable: weight or age; or are both equally good? Explain.
c. Suppose (just temporarily) that weight and age were not related, but that there were substantially more females than males who have unusually high age values. Would this lead to a negative or positive relationship between age and weight, if regression of weight on age were performed for males and females together?
d. Use software to separate out the weights and ages of males from females. Regress weight on age for each gender group and report the value of the correlation r and the P-value for males and for females.
e. Both gender groups contain high outliers for age and weight. Explain why the distribution of standardized sample slope should still be fairly close to a standard normal (z) distribution.
f. Do your regression results suggest that, in general, older students weigh more? Explain.
g. For males, use the sample slope b1 and the standard error of the slope to construct an approximate 95% confidence interval for population slope b1, and fill in the blanks: If one male is a year older than another, we predict him to be heavier by ______ to ______ pounds (round to the nearest tenth).
h. For females, use the sample slope b1 and standard error of the slope to construct an approximate 95% confidence interval for population slope b1, and fill in the blanks: If one female is a year older than another, we predict her to be heavier by ______ to ______ pounds (round to the nearest tenth).
i. Give at least one reason why one of your interval estimates for slope is wider than the other.