Stats
5th Edition
ISBN: 9780135163825
Author: De Veaux, Richard D., Velleman, Paul F., BOCK, David E.
Publisher: Pearson,
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Chapter 8, Problem 44E
a.
To determine
Explain whether the linear model is appropriate for the post-1980 data.
b.
To determine
Interpret the meaning of slope in the equation about marriage ages.
c.
To determine
Explain the reason of not interpret the y-intercept.
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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 8 Solutions
Stats
Ch. 8.3 - Prob. 1JCCh. 8.3 - Prob. 2JCCh. 8.3 - Prob. 3JCCh. 8.7 - 4. You want to model the relationship between the...Ch. 8.7 - Prob. 5JCCh. 8.7 - Prob. 6JCCh. 8 - Prob. 1ECh. 8 - 2. Revenue and talent cost A concert production...Ch. 8 - Prob. 3ECh. 8 - 4. Revenue and ticket sales The concert production...
Ch. 8 - Prob. 5ECh. 8 - 6. Stopping times Using data from 20 compact cars,...Ch. 8 - Prob. 7ECh. 8 - Prob. 8ECh. 8 - Prob. 9ECh. 8 - Prob. 10ECh. 8 - Prob. 11ECh. 8 - Prob. 12ECh. 8 - Prob. 13ECh. 8 - Prob. 14ECh. 8 - Prob. 15ECh. 8 - Prob. 16ECh. 8 - Prob. 17ECh. 8 - 18. TVs and life expectancy Recall the example of...Ch. 8 - Prob. 19ECh. 8 - Prob. 20ECh. 8 - 21. Marriage age 2015 Is there evidence that the...Ch. 8 - 22. Smoking 2014 The Centers for Disease Control...Ch. 8 - Prob. 23ECh. 8 - Prob. 24ECh. 8 - Prob. 25ECh. 8 - 26. Bad model? A student who has created a linear...Ch. 8 - Prob. 27ECh. 8 - Prob. 28ECh. 8 - 29. Oakland passengers 2016 The scatterplot below...Ch. 8 - Tracking hurricanes 2016 In Chapter 6, we saw data...Ch. 8 - Prob. 31ECh. 8 - 32. More unusual points Each of the following...Ch. 8 - Prob. 33ECh. 8 - Prob. 34ECh. 8 - Prob. 35ECh. 8 - 36. What’s the effect? A researcher studying...Ch. 8 - Prob. 37ECh. 8 - Prob. 38ECh. 8 - Prob. 39ECh. 8 - 40. Speed How does the speed at which you drive...Ch. 8 - Prob. 41ECh. 8 - Prob. 42ECh. 8 - Prob. 43ECh. 8 - Prob. 44ECh. 8 - 45. Gestation For humans, pregnancy lasts about...Ch. 8 - Prob. 46ECh. 8 - Prob. 47ECh. 8 - Prob. 48ECh. 8 - Prob. 49ECh. 8 - Prob. 50ECh. 8 - Prob. 51ECh. 8 - Prob. 52ECh. 8 - Prob. 53ECh. 8 - Prob. 54ECh. 8 - Prob. 55ECh. 8 - Prob. 56ECh. 8 - Prob. 57ECh. 8 - 58. Crowdedness In a Chance magazine article...Ch. 8 - Prob. 59ECh. 8 - Prob. 60ECh. 8 - Prob. 61ECh. 8 - Prob. 62ECh. 8 - Prob. 63ECh. 8 - Prob. 64ECh. 8 - *65. Brakes The following table shows stopping...Ch. 8 - *66. Pendulum A student experimenting with a...Ch. 8 - *68. Planets Here is a table of the 9 sun-orbiting...Ch. 8 - Prob. 69ECh. 8 - Prob. 70ECh. 8 - Prob. 71ECh. 8 - Prob. 72ECh. 8 - Prob. 73ECh. 8 - Prob. 74ECh. 8 - Prob. 75ECh. 8 - Prob. 76ECh. 8 - Prob. 77ECh. 8 - Prob. 78ECh. 8 - Prob. 79ECh. 8 - 80. Tree growth A 1996 study examined the growth...
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