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 16, Problem 37PS
a.
To determine
Perform a residual analysis.
b.
To determine
Compute
c.
To determine
Compute the MAD.
d.
To determine
Discuss which forecasting model should be selected.
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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 16 Solutions
Pearson eText for Basic Business Statistics -- Instant Access (Pearson+)
Ch. 16 - If you are using exponential smoothing for...Ch. 16 - Consider a nine-year moving average used to smooth...Ch. 16 - You are using exponential smoothing on an annual...Ch. 16 - Prob. 4PSCh. 16 - Prob. 5PSCh. 16 - How have stocks performed in the past? The...Ch. 16 - Prob. 7PSCh. 16 - Prob. 8PSCh. 16 - Prob. 9PSCh. 16 - Prob. 10PS
Ch. 16 - The linear trend forecasting equation for an...Ch. 16 - There has been much publicity about bounces paid...Ch. 16 - Prob. 13PSCh. 16 - Prob. 14PSCh. 16 - Prob. 15PSCh. 16 - The data shown in the following table and stored...Ch. 16 - Prob. 17PSCh. 16 - Prob. 18PSCh. 16 - Prob. 19PSCh. 16 - Prob. 20PSCh. 16 - Prob. 21PSCh. 16 - Prob. 22PSCh. 16 - You are given an annual time series with 40...Ch. 16 - Prob. 24PSCh. 16 - Prob. 25PSCh. 16 - Prob. 26PSCh. 16 - Prob. 27PSCh. 16 - Prob. 28PSCh. 16 - Prob. 29PSCh. 16 - Using the average baseball salary from 200 through...Ch. 16 - Using the yearly amount of solar power generated...Ch. 16 - The following residuals are from a linear trend...Ch. 16 - Prob. 33PSCh. 16 - Prob. 34PSCh. 16 - Prob. 35PSCh. 16 - Prob. 36PSCh. 16 - Prob. 37PSCh. 16 - Prob. 38PSCh. 16 - Prob. 39PSCh. 16 - Prob. 40PSCh. 16 - In forecasting daily time-series data, how many...Ch. 16 - In forecasting a quarterly time series over the...Ch. 16 - Prob. 43PSCh. 16 - Prob. 44PSCh. 16 - Are gasoline prices higher during the height of...Ch. 16 - Prob. 46PSCh. 16 - Prob. 47PSCh. 16 - The file Silver-Q contains the price in London for...Ch. 16 - Prob. 49PSCh. 16 - What is a time series?Ch. 16 - What are the different components of a time-series...Ch. 16 - What is the difference between moving average and...Ch. 16 - Prob. 53PSCh. 16 - How does the least-squares linear trend...Ch. 16 - How does autoregressive modelling differ from the...Ch. 16 - What are the different approaches to choosing an...Ch. 16 - What is the major difference between using SYX and...Ch. 16 - How does forecasting for monthly or quarterly data...Ch. 16 - Prob. 60PSCh. 16 - The monthly commercial and residential prices for...Ch. 16 - The data stored in McDonalds represent the gross...Ch. 16 - Teachers’ Retirement System of the City of New...Ch. 16 - Prob. 64PS
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