Essentials Of Business Analytics
1st Edition
ISBN: 9781285187273
Author: Camm, Jeff.
Publisher: Cengage Learning,
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Chapter 12, Problem 19P
A firm has three investment alternatives. Payoffs are in thousands of dollars.
- a. Using the
expected value approach, which decision is preferred? - b. For the lottery having a payoff of $100,000 with probability p and $0 with probability (1 – p), two decision makers expressed the following indifference probabilities. Find the most preferred decision for each decision maker using the expected utility approach.
- c. Why don’t decision makers A and B select the same decision alternative?
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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 12 Solutions
Essentials Of Business Analytics
Ch. 12 - Prob. 1PCh. 12 - Southland Corporation’s decision to produce a new...Ch. 12 - Amy Lloyd is interested in leasing a new Honda and...Ch. 12 - Investment advisors estimated the stock market...Ch. 12 - Hudson Corporation is considering three options...Ch. 12 - Prob. 6PCh. 12 - Myrtle Air Express decided to offer direct service...Ch. 12 - Video Tech is considering marketing one of two new...Ch. 12 - Seneca Hill Winery recently purchased land for the...Ch. 12 - Hemmingway, Inc. is considering a $5 million...
Ch. 12 - The following profit payoff table was presented in...Ch. 12 - Suppose that you are given a decision situation...Ch. 12 - A firm has three investment alternatives. Payoffs...Ch. 12 - Alexander Industries is considering purchasing an...Ch. 12 - In a certain state lottery, a lottery ticket costs...Ch. 12 - Three decision makers have assessed utilities for...Ch. 12 - In Problem 22, if P(s1) = 0.25, P(s2) = 0.50, and...Ch. 12 - Translate the following monetary payoffs into...Ch. 12 - Consider a decision maker who is comfortable with...
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