(b)Estimate the regression parameters, the survival time for a patient
with a WBC of 20,000 (are estimates for di¤erent groups di¤erent?),
and draw the regression line on the same graph with the scatter dia-
gram.
(c) Test to see if the two factors are independent; state your hypotheses
and choice of test size.
(d) Calculate the coe‰cient of determination and provide your inter-
pretation.
(e) Is there evidence of an e¤ect modification? (Compare the two
coe‰cients of determination/correlation informally.)8.10 Refer to the data in Exercise 8.9, but in the context of a multiple regres-
sion problem with three independent variables: log WBC, the morpho-
logic characteristic (AG, represented by a binary indicator: 0 if AG neg-
ative and 1 if AG positive), and product log WBC by morphologic
characteristic (AG).
(a) Fit the multiple regression model to obtain estimates of individual
regression coe‰cients and their standard errors. Draw your conclu-
sion concerning the conditional contribution of each factor.
(b)Within the context of the multiple regression model in part (a), does
the morphologic characteristic (AG) alter the e¤ect of log WBC on
log survival time?
(c) Taken collectively, do the three independent variables contribute
significantly to the variation in log survival times?
(d) Calculate the coe‰cient of multiple determination and provide your
interpretation.
8.11 The purpose of this study was to examine the data for 44 physicians
working for an emergency at a major hospital so as to determine which
of a number of factors are related to the number of complaints received
during the preceding year. In addition to the number of complaints, data
available consist of the number of visits (which serves as thesizefor the
observation unit), the physician, and four other factors under investiga-
tion. Table E8.11 presents the complete data set. For each of the 44
physicians there are two continuous explanatory factors: the revenue
(dollars per hour) and the workload at the emergency service (hours),
and two binary variables: gender (female/male) and residency training in
emergency services (no/yes). Divide the number of complaints by the
number of visits and use this ratio (number of complaints per visit) as
the primaryoutcomeor dependent variableY. Individually for each of
the two continuous explanatory factors, revenue (dollars per hour) and
workload at the emergency service (hours):
(a) Draw a scatter diagram to show a possible association with the
number of complaints per visit, and check to see if a linear model is
justified.
EXERCISES 311