HW1_assignment

Homework 1 Assignment Amazon Reviews The dataset consists of 13 319 reviews for selected products on Amazon from Jan-Oct 2012. Reviews include product information, ratings, and a plain text review. We will look for words associated with good/bad ratings. The data consists of three tables: ##Review subset.csv is a table containing, for each review, its • ProductId: Amazon ASIN product code • UserId: ID of the reviewer • Score: numeric 1-5 (the number of stars) • Time: date of the review • Summary: review summary in words • Nrev: number of reviews by the user • Length: number of words in the review • Prod Category: Amazon product category • Prod Group: Amazon product group Word freq.csv is a simple triplet matrix of word counts from the review text including • Review ID: the row index of Review subset.csv • Word ID: the row index of words.csv • Times Word: how many times the word occurred in the review Words.csv contains 1125 alphabetically ordered words that occur in the reviews. 1

Data exploration The code below loads the data. library(knitr) # library for nice R markdown output # READ REVIEWS data <- read.table( "Review_subset.csv" , header= TRUE) dim(data) [1] 13319 9 # 13319 reviews # ProductID: Amazon ASIN product code # UserID: id of the reviewer # Score: numeric from 1 to 5 # Time: date of the review # Summary: text review # nrev: number of reviews by this user # Length: length of the review (number of words) # READ WORDS words <- read.table( "words.csv" ) words <- words[, 1 ] length(words) [1] 1125 #1125 unique words # READ text-word pairings file doc_word <- read.table( "word_freq.csv" ) names(doc_word) <- c( "Review ID" , "Word ID" , "Times Word" ) # Review ID: row of the file Review_subset # Word ID: index of the word # Times Word: number of times this word occurred in the text Marginal Regression Screening We would like to pre-screen words that associate with ratings. To this end, we run a series of (independent) marginal regressions of review Score on word presence in review text for each of 1125 words. In the starter script below, you will find a code to run these marginal regressions (both in parallel and sequentially). The code gives you a set of p-values for a marginal effect of each word. That is, we fit stars i = α + β j I [ x ji > 0] + ji for each word term j with count x ji in review i , and return the p-value associated with a test of β j = 0 . We’ll use these 1125 independent regressions to screen words. # We ll do 1125 univariate regressions of # star rating on word presence, one for each word. # Each regression will return a p-value, and we can 2

# mrgpvals <- c(mrgpvals,margreg(P[,j])) # } # make sure we have names names(mrgpvals) <- colnames(P) # The p-values are stored in mrgpvals Homework Questions: (1) Plot the p-values from the marginal screening and comment on their distribution. (10 point) (2) Let’s do standard statistical testing. How many tests are significant at the alpha level 0.05 and 0.01? (10 point) (3) What is the p-value cutoff for 1% FDR? Plot and describe the rejection region. (10 point) (4) How many discoveries do you find at q=0.01 and how many do you expect to be false? (10 point) (5) What are the 10 most significant words? Do these results make sense to you? What are the advantages and disadvantages of our FDR anaysis? (10 point) 4