Intro Stats, Books a la Carte Edition (5th Edition)
5th Edition
ISBN: 9780134210285
Author: Richard D. De Veaux, Paul Velleman, David E. Bock
Publisher: PEARSON
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Chapter 20, Problem 23E
a.
To determine
Explain in context about the regression says.
b.
To determine
Check the assumptions and conditions for regression inference.
c.
To determine
The meaning of the output
d.
To determine
Find the value of the standard error of the slope of the regression line.
e.
To determine
Explain the meaning of the standard error in the context.
f.
To determine
Explain whether the analysis proves that global temperature changes are causing sea ice to melt.
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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.
5. Probability Distributions – Continuous Random Variables
A factory machine produces metal rods whose lengths (in cm) follow a continuous uniform distribution on the interval [98, 102].
Questions:
a) Define the probability density function (PDF) of the rod length.b) Calculate the probability that a randomly selected rod is shorter than 99 cm.c) Determine the expected value and variance of rod lengths.d) If a sample of 25 rods is selected, what is the probability that their average length is between 99.5 cm and 100.5 cm? Justify your answer using the appropriate distribution.
Chapter 20 Solutions
Intro Stats, Books a la Carte Edition (5th Edition)
Ch. 20.5 - Researchers in Food Science studied how big...Ch. 20.5 - Prob. 2JCCh. 20.5 - Prob. 3JCCh. 20.5 - Prob. 4JCCh. 20.5 - Prob. 5JCCh. 20.5 - Prob. 6JCCh. 20 - Graduate earnings Does attending college pay back...Ch. 20 - Shoot to score 2016 A college hockey coach...Ch. 20 - Prob. 3ECh. 20 - Shoot to score II Discuss the assumptions and...
Ch. 20 - Prob. 5ECh. 20 - Shoot to score, another one Using the regression...Ch. 20 - Prob. 7ECh. 20 - Shoot to score, hat trick Returning to the results...Ch. 20 - Prob. 9ECh. 20 - Shoot to score, number five What can the hockey...Ch. 20 - Prob. 11ECh. 20 - Prob. 12ECh. 20 - Prob. 13ECh. 20 - Prob. 14ECh. 20 - Prob. 15ECh. 20 - Shoot to score, double overtime Continuing from...Ch. 20 - Prob. 17ECh. 20 - Prob. 18ECh. 20 - Prob. 19ECh. 20 - Prob. 20ECh. 20 - Prob. 21ECh. 20 - Drug use 2013 The 2013 World Drug Report...Ch. 20 - Prob. 23ECh. 20 - Saratoga house prices How does the price of a...Ch. 20 - Prob. 25ECh. 20 - Prob. 26ECh. 20 - Prob. 27ECh. 20 - Prob. 28ECh. 20 - Prob. 29ECh. 20 - More cholesterol Look again at Exercise 28s...Ch. 20 - Prob. 31ECh. 20 - Cholesterol, finis Based on the regression output...Ch. 20 - Prob. 33ECh. 20 - Prob. 34ECh. 20 - Prob. 35ECh. 20 - Prob. 36ECh. 20 - Prob. 37ECh. 20 - Prob. 38ECh. 20 - Prob. 39ECh. 20 - Fuel economy A consumer organization has reported...Ch. 20 - Climate change 2016 Data collected from around the...Ch. 20 - Prob. 42ECh. 20 - Prob. 43ECh. 20 - Fuel economy, part III Consider again the data in...Ch. 20 - Climate change again Consider once again the CO2...Ch. 20 - Cereals A healthy cereal should be low in both...Ch. 20 - Brain size Does your IQ depend on the size of your...Ch. 20 - Prob. 48ECh. 20 - Prob. 49ECh. 20 - Prob. 50ECh. 20 - Ozone and population The Environmental Protection...Ch. 20 - Prob. 52ECh. 20 - Prob. 53ECh. 20 - More sales and profits Consider again the...Ch. 20 - Prob. 55ECh. 20 - Crawling Researchers at the University of Denver...Ch. 20 - Midterms The data set below shows midterm and...Ch. 20 - Prob. 58ECh. 20 - Prob. 59ECh. 20 - All the efficiency money can buy 2011 A sample of...Ch. 20 - Education and mortality The following software...Ch. 20 - Property assessments The following software output...Ch. 20 - Prob. 63ECh. 20 - Prob. 64E
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