Chapter 8.1, Problem 9E

In a study of the lung function of children, the volume of air exhaled under force in one second is called FEV₁. (FEV₁ stands for forced expiratory volume in one second.) Measurements were made on a group of children each year for two years. A linear model was fit to predict this year’s FEV₁ as a function of last year’s FEV₁ (in liters), the child’s gender (0 = Male, 1 = Female), the child’s height (in m), and the ambient atmospheric pressure (in mm). The following MINITAB output presents the results of fitting the model

     ${\text{FEV}}_1={\beta }_0+{\beta }_1\text{Last}{\text{FEV}}_1+{\beta }_2\text{Gender}+{\beta }_3\text{Height}+{\beta }_4\text{Pressure}+\epsilon$

1. a. Predict the FEV₁ for a boy who is 1.4 m tall, if the measurement was taken at a pressure of 730 mm and last year’s measurement was 2.113 L.
2. b. If two girls differ in height by 5 cm, by how much would you expect their FEV₁ measurements to differ, other things being equal?
3. c. The constant term β₀ is estimated to be negative. But FEV₁ must always be positive. Is something wrong? Explain.