Pearson eText for Basic Business Statistics -- Instant Access (Pearson+)
14th Edition
ISBN: 9780137400119
Author: MARK BERENSON, David Levine
Publisher: PEARSON+
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Chapter 18, Problem 3CRP
To determine
Determine which factors influence attendance and analyze the data of the Philadelphia Phillies.
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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.
Chapter 18 Solutions
Pearson eText for Basic Business Statistics -- Instant Access (Pearson+)
Ch. 18 - In many manufacturing processes, the term...Ch. 18 - Many factors determine the attendance at Major...Ch. 18 - Prob. 3CRPCh. 18 - Prob. 4CRPCh. 18 - Prob. 5CRPCh. 18 - The file Euro Tourism 2 contains a sample of 28...Ch. 18 - The file Philly contains a sample of 25...Ch. 18 - Prob. 8CRPCh. 18 - The file UsedCars contains attributes of cars that...Ch. 18 - A study was conducted to determine whether any...
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