You are studying the effects of smoking by pregnant women on rates of asthma in their children. You collect data on the number of cigarettes smoked per day and whether or not the child developed asthma by the age of two. The data is below: Smoked 1-5 cigarettes per day --- 8.7% developed asthma Smoked 6-10 cigarettes per day --- 9.7% developed asthma Smoked 11-20 cigarettes per day --- 25.5% developed asthma Smoked 21-40 cigarettes per day --- 35.2% developed asthma Smoked 41-60 cigarettes per day --- 38.5% developed asthma. In order to study the relationship between the number of cigarettes smoked by pregnant women per day and the percentage of their children developed asthma by the age of two using statistical knowledge, we convert the above data into the following format and see if we can obtain an adequate fit using linear regression. Average number of cigarettes smoked per day
3
8
15.5
30.5
50.5
Percentage of children developed asthma
8.8%
9.8%
25.1%
35.2%
38.4%
What is the value of the correlation coefficient?
Assume that the best-fit line of the above data set is a good model for the study. For expectant mothers who smoke 46 cigarettes per day, what is the expected percentage of children who will develop asthma by the age of two.