Refer to the Journal of Human Stress study of firefighters, Exercise 12.5. It is thought that a complete second-order model, shown here, will be adequate to describe the relationship between emotional distress and years of experience for two groups of firefighters—those exposed to a chemical fire and those unexposed.

E(y) = β₀ + β₁x₁ + β₂ x₁² + β₃x₂ + β₄x₁x₂ + β₅x₁²x₂

where

a. What hypothesis would you test to determine whether the rate of increase of emotional distress with experience is different for the two groups of firefighters?

b. What hypothesis would you test to determine whether there are differences in mean emotional distress levels that are attributable to exposure group?

c. The second-order model was fit to data collected for a sample of 200 firefighters, resulting in . The reduced model, E(y) = β₀ + β₁x₁ + β₂ x₁², is fit to the same data, resulting in SSE = 795.23. Is there sufficient evidence to support the claim that the mean emotional distress levels differ for the two groups of firefighters? Use α = .05.

Data from Exercise 12.5

The Journal of Human  Stress (Summer 1987) reported on a study of “psychological  response of firefighters to a chemical fire.” The researchers  used multiple regression to predict emotional  distress as a function of the following independent variables.  Identify each independent variable as quantitative or  qualitative. For qualitative variables, suggest several levels  that might be observed. For quantitative variables, give a range of values (levels) for which the variable might be observed.

Transcribed Image Text:

y = Emotional distress x = Experience (years) [1 if exposed to chemical fire X2 = 1o if not