Probability and Statistics for Engineers and Scientists
9th Edition
ISBN: 9780321629111
Author: Ronald E. Walpole, Raymond H. Myers, Sharon L. Myers, Keying Ye
Publisher: Prentice Hall
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Chapter 6.4, Problem 1E
a.
To determine
Show that
b.
To determine
Prove that
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(c) Because logistic regression predicts probabilities of outcomes, observations used to build a logistic regression model need not be independent.
A. false: all observations must be independent
B. true
C. false: only observations with the same outcome need to be independent
I ANSWERED: A. false: all observations must be independent.
(This was marked wrong but I have no idea why. Isn't this a basic assumption of logistic regression)
Business discuss
Spam filters are built on principles similar to those used in logistic regression. We fit a probability that each message is spam or not spam. We have several variables for each email. Here are a few: to_multiple=1 if there are multiple recipients, winner=1 if the word 'winner' appears in the subject line, format=1 if the email is poorly formatted, re_subj=1 if "re" appears in the subject line. A logistic model was fit to a dataset with the following output:
Estimate
SE
Z
Pr(>|Z|)
(Intercept)
-0.8161
0.086
-9.4895
0
to_multiple
-2.5651
0.3052
-8.4047
0
winner
1.5801
0.3156
5.0067
0
format
-0.1528
0.1136
-1.3451
0.1786
re_subj
-2.8401
0.363
-7.824
0
(a) Write down the model using the coefficients from the model fit.log_odds(spam) = -0.8161 + -2.5651 + to_multiple + 1.5801 winner + -0.1528 format + -2.8401 re_subj(b) Suppose we have an observation where to_multiple=0, winner=1, format=0, and re_subj=0. What is the predicted probability that this message is spam?…
Chapter 6 Solutions
Probability and Statistics for Engineers and Scientists
Ch. 6.4 - Given a continuous uniform distribution, show...Ch. 6.4 - Suppose X follows a continuous uniform...Ch. 6.4 - The daily amount of coffee, in liters, dispensed...Ch. 6.4 - A bus arrives every 10 minutes at a bus stop. It...Ch. 6.4 - Given a standard normal distribution, find the...Ch. 6.4 - Find the value of z if the area under a standard...Ch. 6.4 - Given a standard normal distribution, find the...Ch. 6.4 - Prob. 8ECh. 6.4 - Given the normally distributed variable X with...Ch. 6.4 - Prob. 10E
Ch. 6.4 - A soft-drink machine is regulated so that it...Ch. 6.4 - The loaves of rye bread distributed to local...Ch. 6.4 - Prob. 13ECh. 6.4 - The finished inside diameter of a piston ring is...Ch. 6.4 - Prob. 15ECh. 6.4 - In the November 1990 issue of Chemical Engineering...Ch. 6.4 - The average life of a certain type of small motor...Ch. 6.4 - Prob. 18ECh. 6.4 - Prob. 19ECh. 6.4 - Prob. 20ECh. 6.4 - The tensile strength of a certain metal component...Ch. 6.4 - If a set of observations is normally distributed,...Ch. 6.4 - Prob. 23ECh. 6.5 - A coin is tossed 400 times. Use the normal curve...Ch. 6.5 - A process for manufacturing an electronic...Ch. 6.5 - A process yields 10% defective items. If 100 items...Ch. 6.5 - The probability that a patient recovers from a...Ch. 6.5 - Researchers at George Washington University and...Ch. 6.5 - If 20% of the residents in a U.S. city prefer a...Ch. 6.5 - A drug manufacturer claims that a certain drug...Ch. 6.5 - One-sixth of the male freshmen entering a large...Ch. 6.5 - A pharmaceutical company knows that approximately...Ch. 6.5 - Statistics released by the National Highway...Ch. 6.5 - A pair of dice is rolled 180 times. What is the...Ch. 6.5 - A company produces component parts for an engine....Ch. 6.5 - Prob. 36ECh. 6.5 - The serum cholesterol level X in 14-year-old boys...Ch. 6.5 - Prob. 38ECh. 6.10 - Use the gamma function with to show that .
Ch. 6.10 - Prob. 40ECh. 6.10 - Prob. 41ECh. 6.10 - Prob. 42ECh. 6.10 - Prob. 43ECh. 6.10 - In a certain city, the daily consumption of...Ch. 6.10 - The length of time for one individual to be served...Ch. 6.10 - Prob. 46ECh. 6.10 - Suppose that the service life, in years, of a...Ch. 6.10 - Prob. 48ECh. 6.10 - Prob. 49ECh. 6.10 - Prob. 50ECh. 6.10 - Prob. 51ECh. 6.10 - Prob. 52ECh. 6.10 - In a biomedical research study, it was determined...Ch. 6.10 - Prob. 54ECh. 6.10 - Computer response time is an important application...Ch. 6.10 - Prob. 56ECh. 6.10 - Prob. 57ECh. 6.10 - The number of automobiles that arrive at a certain...Ch. 6.10 - Prob. 59ECh. 6.10 - Prob. 60ECh. 6.10 - Prob. 61RECh. 6.10 - Prob. 62RECh. 6.10 - Prob. 63RECh. 6.10 - Prob. 64RECh. 6.10 - Prob. 65RECh. 6.10 - Prob. 66RECh. 6.10 - Prob. 67RECh. 6.10 - Prob. 68RECh. 6.10 - The elongation of a steel bar under a particular...Ch. 6.10 - Prob. 70RECh. 6.10 - Prob. 71RECh. 6.10 - Prob. 72RECh. 6.10 - Prob. 73RECh. 6.10 - Prob. 74RECh. 6.10 - Prob. 75RECh. 6.10 - Prob. 76RECh. 6.10 - Prob. 77RECh. 6.10 - Prob. 78RECh. 6.10 - Prob. 79RECh. 6.10 - Prob. 80RECh. 6.10 - Prob. 81RECh. 6.10 - The length of life, in hours, of a drill bit in a...Ch. 6.10 - Prob. 83RECh. 6.10 - Prob. 84RECh. 6.10 - Prob. 85RECh. 6.10 - The length of time, in seconds, that a computer...
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