Question

Problem 3: A linear regression by using famous data set found in Freedman et al. (1991) in Table 1: ‘Statistics’ refers to the percapita consumption of cigarettes in various countries in 1930 and the death rates (number of deaths per million people) from lung cancer for 1950.

Table 1: Death rate data in in Freedman
Obs	Country	Cigarette	Deaths per million
1	Australia	480	180
2	Canada	500	150
3	Denmark	380	170
4	Finland	1100	350
5	GreatBritain	1100	460
6	Iceland	230	60
7	Netherlands	490	240
8	Norway	250	90
9	Sweden	300	110
10	Switzerland	510	250
11	USA	1300	200

1. Order the data by cigarette using into 5 groups by (2, 2, 2, 2, 3), calculate the standard deviation, and make the graph of standard deviation against cigarettes.
2. Check the graph in 1, what kind of transformation should be used to stabilize the variance?

Answer 1

The data

Table 1: Death rate data in in Freedman
Obs	Country	Cigarette	Deaths per million
1	Australia	480	180
2	Canada	500	150
3	Denmark	380	170
4	Finland	1100	350
5	GreatBritain	1100	460
6	Iceland	230	60
7	Netherlands	490	240
8	Norway	250	90
9	Sweden	300	110
10	Switzerland	510	250
11	USA	1300	200

we can draw the scatter plot for the data

Since the scatter plot of cigarette and the standard deviation of the 5 groups in Figure 2: almost perfect linear relationship through origin.

Model 5 is used to stablize the variance .