Exercise 11.2

1.

(From Bhattacharyya and Johnson (1977), Statistical Concepts and Methods, New York: Wiley). Below are used-car prices (in thousands of dollars) for a foreign compact (1970's data) with their ages in years.

            Age     1      2    2     3     3     4     6      7     8     10
            Price  2.45  1.80  2.00  2.00  1.70  1.20  1.15   .69   .60   .47

(a)

Plot the data, Price versus Age. Comment on the car buyer's lament (depreciation).

(b)

Use the regression module to obtain the Wilcoxon fit of a linear model to the data.

(c)

Obtain a 95% confidence interval for slope and interpret it in terms of the problem.

(d)

Predict the price of an 11 year-old compact.

(e)

What are some other X variables that would help predict price?

(f)

If we had much older cars, would you expect to see a continual down hill trend? Why?

2.

(From Hettmansperger and McKean (1998), Robust Nonparametric Statistical Methods, London: Arnold). Below are the number of telephone calls (tens of millions) made in Belgium for the years 1950-1973:

            Year   50    51    52    53    54    55    56    57    58    59    60    61 
            Calls 0.44  0.47  0.47  0.59  0.66  0.73  0.81 0.88  1.06   1.20  1.35  1.49 

            Year  62   63    64    65    66    67    68    69    70    71    72    73 
            Calls 1.61 2.12 11.90 12.40 14.20 15.90 18.20 21.20 4.30  2.40  2.70  2.90

(a)

Plot the data and comment on the plot (There were a few years where a recording error was made. Find those years).

(b)

Use the regression module to obtain both the least squares and Wilcoxon fits of the data set.

(c)

Plot these fits. Which would you use for prediction for the number of calls in 1974.