The data in this question come from From Sen and Srivastava (Exercise 2.12) [2] and can be used to model car ownership (measured in cars per person). The variables in the data set are:
AO cars per person
POP population in millions
DEN population density
GDP per capita income in U.S. dollars
PR petrol price in U.S. cents per litre
CON tonnes of petrol consumed per car per year
TR thousands of passenger kilometres per person by bus and train
This dataset carownership.dat is available
(a) Plot AO against any four of the other variables that you think might be strongly related to car ownership. Comment on the relationships you observe.
(b) Using all possible predictors select a model using forward regression.
(c) Using all possible predictors select a model using backward elimination.
(d) Exclude POP and DEN from the possible predictors to consider. Compute adjusted R^2, PRESS and Cm for all the remaining possible models (except the model with only the constant term). On the basis of this information, reduce the pool of models from 15 to a small subset for further consideration.Select a model, justifying your choice.
| Country |
AO |
POP |
DEN |
GDP |
PR |
CON |
TR |
| Austria |
0.27 |
7.5 |
89 |
7.7 |
49 |
1.1 |
2.6 |
| Belgium |
0.3 |
9.8 |
323 |
9.8 |
59 |
1 |
1.6 |
| Canada |
0.42 |
23.5 |
2 |
8.7 |
17 |
2.8 |
0.1 |
| Denmark |
0.28 |
5.1 |
119 |
11 |
56 |
1.2 |
1.9 |
| Finland |
0.24 |
4.8 |
16 |
7.1 |
49 |
1.2 |
2.2 |
| France |
0.33 |
53.3 |
97 |
8.8 |
61 |
1 |
1.5 |
| Germany |
0.35 |
61.3 |
247 |
10.4 |
49 |
1.1 |
1.7 |
| Greece |
0.08 |
9.4 |
71 |
3.4 |
56 |
1.7 |
0.7 |
| Iceland |
0.34 |
0.2 |
2 |
9.8 |
57 |
1.2 |
2 |
| Ireland |
0.2 |
3.2 |
46 |
3.8 |
40 |
1.5 |
0.3 |
| Italy |
0.3 |
56.7 |
188 |
4.6 |
61 |
0.6 |
1.8 |
| Japan |
0.18 |
114.9 |
309 |
8.5 |
49 |
1.2 |
3.5 |
| Luxembourg |
0.43 |
0.4 |
138 |
9.8 |
44 |
1.6 |
0.8 |
| Netherlands |
0.3 |
13.9 |
412 |
9.4 |
56 |
1 |
1.5 |
| New Zealand |
0.4 |
3.1 |
12 |
5.9 |
34 |
1.3 |
0.2 |
| Norway |
0.28 |
4.1 |
13 |
9.8 |
61 |
1 |
1.7 |
| Portugal |
0.1 |
9.8 |
107 |
1.8 |
68 |
0.7 |
0.9 |
| Spain |
0.18 |
36.8 |
73 |
4 |
44 |
0.8 |
1.3 |
| Sweden |
0.34 |
8.3 |
18 |
10.6 |
42 |
1.3 |
1.7 |
| Switzerland |
0.32 |
6.3 |
153 |
13.3 |
56 |
1.3 |
2 |
| Turkey |
0.014 |
42.7 |
55 |
1.2 |
36 |
3.3 |
0.1 |
| U.K. |
0.27 |
55.8 |
229 |
5.5 |
35 |
1.2 |
1.6 |
| U.S.A. |
0.53 |
218.2 |
23 |
9.7 |
17 |
2.7 |
0.3 |
| Yugoslavia |
0.09 |
22 |
86 |
2.1 |
40 |
1.1 |
2.1 |