Introduction to Statistical Quality Control
7th Edition
ISBN: 9781118146811
Author: Montgomery, Douglas C.
Publisher: John Wiley & Sons Inc
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Textbook Question
Chapter 4, Problem 52E
Analyze the residuals from the multiple regression model on the patient satisfaction data from Exercise 4.51. Comment on the adequacy of the regression model.
4.51. Reconsider the patient satisfaction data in Table 4E.11. Fit a multiple regression model using both patient age and severity as the regressors.
- (a) Test for significance of regression.
- (b) Test for the individual contribution of the two regressors. Are both regressor variables needed in the model?
- (c) Has adding severity to the model improved the quality of the model fit? Explain your answer.
TABLE 4E.11
Patient Satisfaction Data
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In this problem, we consider a Brownian motion (W+) t≥0. We consider a stock model (St)t>0
given (under the measure P) by
d.St 0.03 St dt + 0.2 St dwt,
with So 2. We assume that the interest rate is r = 0.06. The purpose of this problem is to
price an option on this stock (which we name cubic put). This option is European-type, with
maturity 3 months (i.e. T = 0.25 years), and payoff given by
F = (8-5)+
(a) Write the Stochastic Differential Equation satisfied by (St) under the risk-neutral measure
Q. (You don't need to prove it, simply give the answer.)
(b) Give the price of a regular European put on (St) with maturity 3 months and strike K = 2.
(c) Let X =
S. Find the Stochastic Differential Equation satisfied by the process (Xt)
under the measure Q.
(d) Find an explicit expression for X₁ = S3 under measure Q.
(e) Using the results above, find the price of the cubic put option mentioned above.
(f) Is the price in (e) the same as in question (b)? (Explain why.)
Chapter 4 Solutions
Introduction to Statistical Quality Control
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