3.5. FITTING LINEAR MODELS TO DATA Problems Exercise 23 As part of an experiment

Question

3.5. FITTING LINEAR MODELS TO DATA Problems Exercise 23 As part of an experiment, 0.85 mg of a drug is injected into a 205 person. One day later, 0.65 mg is still present in the bloodstream. a. Set up a linear model for this situation. Identify your variables and as sumptions clearly. (We will learn later in Chapter 4 how to set up exponential b. If the model is correct, how much will be present after 2 days? How much c. Evaluate your model. What is its largest possible domain of applicability? models, which are a better fit for drug elimination.) will be present after 3 days?

Explanation / Answer

Exercise 23

Here at t = 0 the drug injected into a person = 0.85 mg

after one day, t= 1 the drug injected a person = 0.65 mg

so if drug injected is variable y^

y^ = 0.85 - (0.85 -0.65)t = 0.85 - 0.2t

(b) If model is correct

then at t =2 ; y^ (2)= 0.85 - 0.2 * 2 = 0.45 mg

at t = 3; y^ (3) = -.85 - 0.2 * 3 = 0.25 mg

(c) THe model is not suitable here as because in next some days the whole amount of drug would be reduced to 0 mg. That's not feasible. for t = (0.85/0.2) = 4.25 days the drug traces will be zero. So, the model is not a good fit for the data.

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