In a study of 1006 men in four occupations, a multiple regression was carried out to show how lung function was related to age, smoking and occupation. The four occupations represented in the study were physician, reghter, farm worker, and chemical worker. The variables in the regression were:

Y air capacity (ml) that the worker can expire in one second X1 age in years X2 number of cigarettes smoked per day X3 1 if chemical worker, 0 otherwise X4 1 if farm worker, 0 otherwise X5 1 if reghter, 0 otherwise

The model Y = 0 + 1X1 + 2X2 + 3X3 + 4X4 + 5X5 + e was t to the data with the following result:

Y = 450039X1 9X2 350X3 380X4 180X5

It was found that MSE = 9 and

(X0X)1 =

9 8 7 6 7 7 8 3 5 6 6 1 1 1 7 4 5 6 1 6 9 9 8 3 7 5 5 5 8 8 7 3 4 1 5 4

(a) What is the mean air capacity of a 20 year old farmworker who smokes (2) 10 cigarettes per day?

(b) What is the estimated dierence in air capacity between two farmers of the same age, one of whom smokes 10 cigarettes per day, and the other of (2) whom does not smoke?

2

(c) Construct a 95% condence interval for 5. [Note: In R you can get the(3) upper 2.5'th percentile of the t distribution with m degrees of freedom, as qt(.975,m). You can also nd this value in tables, although tables will NOT be provided with the midterm.]

(d) Use the Bonferroni procedure to construct simultaneous 95% condence intervals for 5 and 0 (5) .

(e) Construct a 95% condence interval for the mean of Y , for a 30 year old (4) chemical worker who does not smoke.

3

(f) Construct a 95% prediction interval for the mean of Y , for a 30 year old (3) chemical worker who does not smoke.

(g) Construct a 95% condence interval for 0 + 5 (5) .