Spam filters are built on principles similar to those used in logistic regression. We fit a probability thateach 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 wasfit to a dataset with the following output:EstimateSEPr(>|Z])(Intercept)to_multiple-0.81660.0883-9.248-2.65830.3023-8.7936winner1.57050.31784.9418format-0.07990.1232-0.64850.5166re_subj-2.8070.3652-7.6862(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 thepredicted probability that this message is spam?

(a) From the information given, the estimate of intercept is -0.8166, estimate of to_multiple is…

(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?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

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?

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