In a study of lung function of children, the volume of air exhaled under force i

Question

In a study of lung function of children, the volume of air exhaled under force in one second is called FEV_1. Measurements were made on a group of children each year for two years. A linear model was fit to predict this year's FEV_1 as a function of last year's FEV_1 (in liters), the child's gender (0 = M, 1 = F), the child's height (in m) and the ambient atmospheric pressure (in mm). The following model was obtained: FEV_1 = -0.219 + 0.779*LAST FEV_1 - 0.108*Gender + 1.354*Height - 0.00134*Pressure a) Use the multiple regression model above to predict this year's 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) Find the residual for the child specified in part a if this year's measurement was 2.213 L. c) If two girls differ in height by 05 m, by how much would you expect their FEV_1 measurements to differ, all other things being equal? d) The constant term beta_0 is estimated to be negative. But, FEV_1 must always be positive. Is something wrong? Explain.

Explanation / Answer

a) FEV = -0.219 + 0.779 * LAST_FEV - 0.108 *Gender + 1.354 *Height - 0.00134*Pressure

=  -0.219 + 0.779 * 2.113 - 0.108 *0 + 1.354 *1.4 - 0.00134*730

= 2.344427

b) residual = y^ -y = 2.344427 - 2.213 =0.131427

c) required answer = 0.05 * 1.354 = 0.0677

d)

No ,there is nothing wrong , there are other terms in regression , when we put the values

FEV will be positive

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