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
FEV1 = β0 + β1 Last FEV1 + β2 Gender + β3 Height + β4 Pressure + ε

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.
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?
c. The constant term β0 is estimated to be negative. But FEV1 must always be positive. Is something wrong? Explain.

Transcribed Image Text:

The regression equation is FEV1-0.219 0.779 Last FEV 0.108 Gender +1.354 Height-0.00134 Pressure Predictor Constant Last FEV Gender Height Pressure Coef -0.21947 0.779 -0.10827 1.3536 0.0013431 SE Coef 0.4503 0.04909 0.0352 0.2880 0.0004722 -0.49 15.87 3.08 4.70 2.84 0.627 0.000 0.002 0.000 0.005 S 0.22039 R-Sq-93.5% R-Sq(adj) -93.3% Analysis of Variance Source Regression Residual Error Total DF 4 160 164 111.31 7.7716 119.08 MS 27.826 0.048572 572.89 0.000