**Mini-Assignment 10**

**Directions**

- Familiarize yourself with the codebook for the Email dataset below.
- Import/load the Email dataset.
- In this assignment we will focus on predicting whether an email is spam or not. Determine the number of emails that make up this data set and the proportion of the emails that were spam. (That is, you want to construct a univariate frequency table – something we did on Mini-Assignment 2). Answer Question 1 below.
- Determine what proportion of emails with an attachment are spam and what proportion of emails without an attachment are spam. (That is, you want to find the appropriate conditional percent – look for appropriate code under `bivariate’). Answer Question 2 below.
- Construct a chi-square test to determine whether there is an association between spam email and whether an email contained an attachment. Answer Question 3 below.
- Now, fit an appropriate regression model between spam and attachment. Answer Question 4 below.
- Find the odds ratios of model coefficients. Answer Question 5 below.
- Construct an appropriate model that can be used to determine whether the association between whether an email is spam and whether it has an attachment is significant after controlling for the number of characters . Answer Question 6 below.
- Find the odds ratios of model coefficients. Answer Question 7 below.
- Construct an appropriate model with our response variable (spam) and explanatory variables (attachment, number of characters, and whether there is exclamation point in the subject). Answer Question 8 below.

**Questions**

** Question 1**: How many emails make up this data set? What percent of the emails were spam?

** Question 2**: ____% of emails without an attachment were classified as spam, whereas _____ % of emails with an attachment were classified as spam.

** Question 3:** State the corresponding test statistic and p-value to test this association. What is your conclusion?

** Question 4:** What type of regression model is appropriate? Why?

** Question 5:** Interpret the odds ratio to compare emails with attachments to emails without attachments.

** Question 6:** Is there a significant association between whether an email is spam and whether the email has an attachment after controlling for number of characters of an email message has? What is the associated p-value and conclusion?

** Question 7**: What is the correct interpretation of the odds ratio corresponding to characters.

** Question 8**: Controlling for all other predictor variables, is whether a message is spam independently associated with whether there is an exclamation point in the subject? Why?

Submit your answers in moodle under Mini-Assignment 10.

**CODEBOOK: E-mail Data**

Today we will be working with a corpus of emails received by a single gmail account over the first three months of 2012. Just like any other email address this account received and sent regular emails as well as receiving a large amount of spam, unsolicited bulk email. We will be using what we have learned about logistic regression models to see if we can build a model that is able to predict whether or not a message is spam based on a variety of characteristics of the email (e.g. inclusion of words like winner, inherit, or password, the number of exclamation marks used, etc.) While the spam filters used by large coorportations like Google and Microsoft are quite a bit more complex the fundamental idea is the same – binary classification based on a set of predictors.

The description of the data is as follows:

*spam*Indicator for whether the email was spam.*tomultiple*Indicator for whether the email was addressed to more than one recipient.*from*Whether the message was listed as from anyone (this is usually set by default for regular outgoing email).*cc*Indicator for whether anyone was CCed*sent_email*Indicator for whether the sender had been sent an email in the last 30 days*image*Indicates whether any images were attached.*attach*Indicates whether any files were attached*dollar*Indicates whether a dollar sign or the word ‘dollar’ appeared in the email*winner*Indicates whether “winner” appeared in the email*inherent*Indicates whether “inherit” (or an extension, such as inheritance) appeared in the email.*password*Indicates whether “password” appeared in the email.*num_char*The number of characters in the email, in thousands.*line_breaks*The number of line breaks in the email (does not count text wrapping).*format*Indicates whether the email was written using HTML (e.g. may have included bolding or active links) or plaintext.*re_subj*Indicates whether the subject started with “Re:”, “RE:”, “re:”, or “rE”*exclaim_subj*Indicates whether there was an exclamation point in the subject.*urgent_subj*Indicates whether the word “urgent” was in the email subject.*exclaim_mess*The number of exclamation points in the email message.*number*Factor variable saying whether there was no number, a small number (under 1 million), or a big number.