The data set in Table 3.12 is based on 214 children with acute otitis media (otitis media with effusion, or OME) who participated in a randomized clinical trial [13], Each child had OME at the beginning of the study in either one (unilateral cases) or both (bilateral cases) ears and was randomly assigned to receive a 14-day course of one of two antibiotics, either cefaclor (CEF) or amoxicillin (AMO). The data here concern the 203 children whose middle-ear status was determined during a 14-day follow-up visit. The data in Table 3.12 are presented in data set EAR.DAT (at www .cengagebrain.com). While controlling for age, propose an analysis com- paring the effectiveness of the two antibiotics. Express your results in terms of RR.
The data set in Table 3.12 is based on 214 children with acute otitis media (otitis media with effusion, or OME) who participated in a randomized clinical trial [13], Each child had OME at the beginning of the study in either one (unilateral cases) or both (bilateral cases) ears and was randomly assigned to receive a 14-day course of one of two antibiotics, either cefaclor (CEF) or amoxicillin (AMO). The data here concern the 203 children whose middle-ear status was determined during a 14-day follow-up visit. The data in Table 3.12 are presented in data set EAR.DAT (at www .cengagebrain.com). While controlling for age, propose an analysis com- paring the effectiveness of the two antibiotics. Express your results in terms of RR.
The data set in Table 3.12 is based on 214 children with acute otitis media (otitis media with effusion, or OME) who participated in a randomized clinical trial [13], Each child had OME at the beginning of the study in either one (unilateral cases) or both (bilateral cases) ears and was randomly assigned to receive a 14-day course of one of two antibiotics, either cefaclor (CEF) or amoxicillin (AMO). The data here concern the 203 children whose middle-ear status was determined during a 14-day follow-up visit. The data in Table 3.12 are presented in data set EAR.DAT (at www .cengagebrain.com).
While controlling for age, propose an analysis com- paring the effectiveness of the two antibiotics. Express your results in terms of RR.
3. Bayesian Inference – Updating Beliefs
A medical test for a rare disease has the following characteristics:
Sensitivity (true positive rate): 99%
Specificity (true negative rate): 98%
The disease occurs in 0.5% of the population.
A patient receives a positive test result.
Questions:
a) Define the relevant events and use Bayes’ Theorem to compute the probability that the patient actually has the disease.b) Explain why the result might seem counterintuitive, despite the high sensitivity and specificity.c) Discuss how prior probabilities influence posterior beliefs in Bayesian inference.d) Suppose a second, independent test with the same accuracy is conducted and is also positive. Update the probability that the patient has the disease.
4. Linear Regression - Model Assumptions and Interpretation
A real estate analyst is studying how house prices (Y) are related to house size in square feet (X). A simple
linear regression model is proposed:
The analyst fits the model and obtains:
•
Ŷ50,000+150X
YBoB₁X + €
•
R² = 0.76
• Residuals show a fan-shaped pattern when plotted against fitted values.
Questions:
a) Interpret the slope coefficient in context.
b) Explain what the R² value tells us about the model's performance.
c) Based on the residual pattern, what regression assumption is likely violated? What might be the
consequence?
d) Suggest at least two remedies to improve the model, based on the residual analysis.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Introduction to experimental design and analysis of variance (ANOVA); Author: Dr. Bharatendra Rai;https://www.youtube.com/watch?v=vSFo1MwLoxU;License: Standard YouTube License, CC-BY