(a) Write down the model using the coefficients from the model fit. log_odds(spam) = to_multiple + winner + format + 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?
(a) Write down the model using the coefficients from the model fit. log_odds(spam) = to_multiple + winner + format + 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?
Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:HOUGHTON MIFFLIN HARCOURT
Chapter9: Solving Quadratic Functions
Section: Chapter Questions
Problem 4CA
Related questions
Question
![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
Pr(>|Z])
(Intercept)
to_multiple
-0.8166
0.0883
-9.248
-2.6583
0.3023
-8.7936
winner
1.5705
0.3178
4.9418
format
-0.0799
0.1232
-0.6485
0.5166
re_subj
-2.807
0.3652
-7.6862
(a) Write down the model using the coefficients from the model fit.
log_odds(spam) =
to_multiple +
winner +
format +
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?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F54947304-f831-41a1-b5f6-b8a6e9faef54%2F72b2c755-529f-47b6-a21f-33a5a2e7c44a%2Fnezzbs_processed.png&w=3840&q=75)
Transcribed Image Text: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
Pr(>|Z])
(Intercept)
to_multiple
-0.8166
0.0883
-9.248
-2.6583
0.3023
-8.7936
winner
1.5705
0.3178
4.9418
format
-0.0799
0.1232
-0.6485
0.5166
re_subj
-2.807
0.3652
-7.6862
(a) Write down the model using the coefficients from the model fit.
log_odds(spam) =
to_multiple +
winner +
format +
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?
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