Problem 2. (10 points) The following table records the percentages of 15-year-old British boys and girls who were regular smokers, calculated from random samples taken over the years 1982-2003. | '1982' 1984 1986 1988 '1990 1992 1994 1996 |1998| 2000 2003| ISoys \\ 24 l 28 18 17 l 25 21 26 28 | 19 | 21 18 Girls 2 5 28 27 22 25 25 30 33 29 26 26 .AH 25 28 22 Ill 25 23 28 30 Ilil 23 22 Assuming a linear model: (a) (3 points) Test the hypothesis that the percentage of boys who smoked regularly did not change over time. (b) (3 points) Test the hypothesis that the percentage of girls who smoked regularly did not change over time. (c) (3 points) Test the hypothesis that the overall percentage of 15-year-olds who smoked did not change over time. (d) (1 point) Compare your answers from (a), (b), and (c). Given your answers to (a) and (b), is your answer to (c) surprising? Why or why not? Problem 3. (10 points) The dataset iris in R gives the measurements in centimeters of the variables sepal length and width and petal length and width, respectively, for 50 ewers from each of 3 species of iris. Load the dataset using the data(iris) command. (a) (4 points) Fit a multiple linear regression model to the data with sepal length as the response variable and sepal width, petal length and petal width as the predictor variables. Report the results using the summary command. (b) (3 points) Test the reduced model of H0 .6 sepalwidth =16 petallength = 0 with an F-test using the 5% signicance level. (0) (3 points) Test the reduced model of H0 {37 sepalwidth =5 petallength with an F-test using the 5% signicance level. Problem 4. (15 points) A national insurance organization wanted to study the consumption pattern of cigarettes in all 50 states and the District of Columbia. The variables chosen for the study are