In a study of the lung function of children, the volume of

Chapter 8, Problem 7E

(choose chapter or problem)

In a study of the lung function of children, the volume of air exhaled under force in one second is called \(\mathrm{FEV}_{1}\). (\(\mathrm{FEV}_{1}\) 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 \(\mathrm{FEV}_{1}\) as a function of last year’s \(\mathrm{FEV}_{1}\) (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

     \(\mathrm{FEV}_{1}=\beta_{0}+\beta_{1} \text { Last } \mathrm{FEV}_{1}+\beta_{2} \text { Gender }+\beta_{3} \text { Height }+\beta_{4} \text { Pressure }+\varepsilon\)

a. Predict the \(\mathrm{FEV}_{1}\) 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.

b. If two girls differ in height by 5 cm, by how much would you expect their \(\mathrm{FEV}_{1}\) measurements to differ, other things being equal?

c. The constant term \(\mathrm{FEV}_{1}\) is estimated to be negative. But \(\mathrm{FEV}_{1}\) must always be positive. Is something wrong? Explain.

Equation Transcription:

Text Transcription:

FEV_1

FEV_1

FEV_1

FEV_1

FEV_1=beta_0+beta_1 Last FEV_1+beta_2 Gender+beta_3 Height+beta_4 Pressure+varepsilon

FEV_1

FEV_1

beta_0

FEV_1

FEV_1

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