The following data shows the advertising expenses (expressed as a percentage of total expenses) and the net operating profit (expressed as a percentage of total sales) in a random sample of five furniture stores:
Advertising expenses Net operating profit
X Y
1.1 2.5
2.8 3.7
3.1 5.2
1.6 2.9
0.7 1.4
Fit a least-squares line to these data and construct a 99% confidence interval for mean net operating profit (expressed as a percentage of total sales) when the advertising expenses are 20.0% of total expenses.
States in each case whether you would expect a positive correlation, a negative correlation, or no correlation:
(a) the age of husbands and wives;
(b) the amount of rubber on tires and the number of miles that they have been driven;
(c) income and education;
(d) shirt size and sense of humor;
(e) the number of hours that bowlers practice and their scores;
(f) hair color and one's knowledge of foreign affairs.