Understandable Statistics: Concepts and Methods
12th Edition
ISBN: 9781337119917
Author: Charles Henry Brase, Corrinne Pellillo Brase
Publisher: Cengage Learning
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Chapter 9.2, Problem 2P
To determine
Mention the marginal change in
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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 9 Solutions
Understandable Statistics: Concepts and Methods
Ch. 9.1 - Statistical Literacy When drawing a scatter...Ch. 9.1 - Prob. 2PCh. 9.1 - Prob. 3PCh. 9.1 - Prob. 4PCh. 9.1 - Prob. 5PCh. 9.1 - Prob. 6PCh. 9.1 - Prob. 7PCh. 9.1 - Prob. 8PCh. 9.1 - Prob. 9PCh. 9.1 - Critical Thinking: Lurking Variables Over the past...
Ch. 9.1 - Prob. 11PCh. 9.1 - Prob. 12PCh. 9.1 - Prob. 13PCh. 9.1 - Health Insurance: Administrative Cost The...Ch. 9.1 - Prob. 15PCh. 9.1 - Geology: Earthquakes Is the magnitude of an...Ch. 9.1 - Prob. 17PCh. 9.1 - Prob. 18PCh. 9.1 - Prob. 19PCh. 9.1 - Prob. 20PCh. 9.1 - Prob. 21PCh. 9.1 - Prob. 22PCh. 9.1 - Prob. 23PCh. 9.1 - Prob. 24PCh. 9.2 - Statistical Literacy In the least-squares line...Ch. 9.2 - Prob. 2PCh. 9.2 - Critical Thinking When we use a least-squares line...Ch. 9.2 - Prob. 4PCh. 9.2 - Prob. 5PCh. 9.2 - Critical Thinking: Interpreting Computer Printouts...Ch. 9.2 - Prob. 7PCh. 9.2 - For Problems 718, please do the following. (a)...Ch. 9.2 - Prob. 9PCh. 9.2 - For Problems 718, please do the following. (a)...Ch. 9.2 - Prob. 11PCh. 9.2 - Prob. 12PCh. 9.2 - For Problems 718, please do the following. (a)...Ch. 9.2 - Prob. 14PCh. 9.2 - Prob. 15PCh. 9.2 - For Problems 718, please do the following. (a)...Ch. 9.2 - Prob. 17PCh. 9.2 - Prob. 18PCh. 9.2 - Prob. 19PCh. 9.2 - Residual Plot: Miles per Gallon Consider the data...Ch. 9.2 - Prob. 21PCh. 9.2 - Prob. 22PCh. 9.2 - Prob. 23PCh. 9.2 - Prob. 24PCh. 9.2 - Prob. 25PCh. 9.3 - Prob. 1PCh. 9.3 - Prob. 2PCh. 9.3 - Prob. 3PCh. 9.3 - Prob. 4PCh. 9.3 - Prob. 5PCh. 9.3 - Prob. 6PCh. 9.3 - Prob. 7PCh. 9.3 - In Problems 712, parts (a) and (b) relate to...Ch. 9.3 - Prob. 9PCh. 9.3 - Prob. 10PCh. 9.3 - In Problems 712, parts (a) and (b) relate to...Ch. 9.3 - Prob. 12PCh. 9.3 - Prob. 13PCh. 9.3 - Prob. 14PCh. 9.3 - Prob. 15PCh. 9.3 - Expand Your Knowledge: Time Series and Serial...Ch. 9.3 - Prob. 17PCh. 9.4 - Statistical Literacy Given the linear regression...Ch. 9.4 - Prob. 2PCh. 9.4 - For Problems 3-6, use appropriate multiple...Ch. 9.4 - For Problems 3-6, use appropriate multiple...Ch. 9.4 - Prob. 5PCh. 9.4 - Prob. 6PCh. 9 - Prob. 1CRPCh. 9 - Prob. 2CRPCh. 9 - Prob. 3CRPCh. 9 - Prob. 4CRPCh. 9 - Prob. 5CRPCh. 9 - Prob. 6CRPCh. 9 - Prob. 7CRPCh. 9 - Prob. 8CRPCh. 9 - Prob. 9CRPCh. 9 - Prob. 10CRPCh. 9 - Prob. 1DHCh. 9 - Prob. 1LCCh. 9 - Prob. 1UTCh. 9 - Prob. 2UTCh. 9 - Prob. 3UTCh. 9 - Prob. 4UTCh. 9 - Prob. 5UTCh. 9 - Prob. 6UTCh. 9 - Prob. 7UTCh. 9 - In Problems 16, please use the following steps (i)...Ch. 9 - Prob. 2CURPCh. 9 - Prob. 3CURPCh. 9 - Prob. 4CURPCh. 9 - Prob. 5CURPCh. 9 - Prob. 6CURPCh. 9 - Prob. 8CURPCh. 9 - Linear Regression: Blood Glucose Let x be a random...
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