12.12) The following table shows the assessed values and the selling prices of eight houses constituting a random sample of all the houses sold recently in each metropolitan area:

Assessed value (in $1,000)                                          Selling price (in $1,000)

40.3                                                                                     63.4

72.0                                                                                   118.3

32.5                                                                                    55.2

44.8                                                                                     74.0

27.9                                                                                    48.8

51.6                                                                                    81.1

80.4                                                                                   123.2

58.0                                                                                     92.5

Fit a least-squares line that will enable us to predict the selling prices of a house in terms of its assessed value, and test the null hypothesis β = 1.30 against the alternative hypothesis β > 1.30 at the level of significance 0.05.

12.18) 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.

12.38) 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.