Machine learning project with the MovieLens dataset (Capstone of the HarvardX Data Science Professional Certificate)

This project is part of the last course of the HarvardX Data Science Professional Certificate. Before starting with the description of the dataset, I would like to briefly provide my feedback about the course. I attended the course while studying for my MBA and while working; it took me 3 years to pass all 9 courses and pursue this certificate. Overall, some courses were quite easy while others were tough; for example, Linear regression was particularly complicated because it implied basic knowledge of baseball, which I had not. An understanding of machine learning was required for the Capstone course, and I have also found very challenging the realization of an original analysis using the so common MovieLens dataset. Three things helped me in realizing this project. First thing I attended the Datacamp course “Machine Learning with caret in R”. Second thing I bought 2 Machine Learning books: “Machine learning for absolute beginners” by Theobald, and “Grokking machine learning” by Serrano. The third thing: study the tidymodels package at

table 7

RMarkdown file, script, and pdf are available on my GitHub profile:


The MovieLens dataset has been published for the first time on the MovieLens website in 1998. Since then, it has been downloaded several times by users because of its utility in various sectors, especially for educational purposes. This dataset can be used to explore movie rating systems or it can be adapted for assessing on the many popular rating systems other companies use these days. The analysis of this dataset opens further questions about the factors that influence users’
decisions and to future approaches (Harper & Konstan, 2015). Once ratings and movies are merged, the dataset shows the following variables: userId, movieId, rating, timestamp, title, genres; year is included in the title. My analysis has been performed using both Linux and Windows OS. The goal of this project is to create an original analysis providing movie predictions after using the dataset. As per “MovieLens Grading Rubric”, accuracy will be measured after providing an
RMSE \< 0.86490.

Methods/analysis including our modeling approach (we must provide at least 2 models).

Exploratory data analysis (EDA) is the “human” intervention to the dataset and it is fundamental to get users familiar with the data. It sometimes requires the removal of missing or incorrect data, or changes to make observations more workable (Theobald, 2017, p. 36). In my analysis, I start with the initial code provided by the course instructions in the “Create train and validation sets” section (attached in the Appendix). Here we install the packages required, we download a temporary file containing 2 datasets, we merge them, we create a train and test dataset paying attention that the validation dataset must be 10% of the original file. As we have seen, the Movielens dataset contains a lot of
observations and it takes time to load or process coding. For this reason and to attempt the many tests this analysis requires, I have printed the temporary file in csv (named edx.csv); the dataset I have used is available for download on GitHub.

if(!require(tidyverse)) install.packages("tidyverse", repos = "")
if(!require(visreg)) install.packages("visreg", repos = "")
if(!require(readr)) install.packages("readr", repos = "")
if(!require(caret)) install.packages("caret", repos = "")
if(!require(data.table)) install.packages("data.table", repos = "")
if(!require(readxl)) install.packages("readxl", repos = "")
if(!require(dplyr)) install.packages("dplyr", repos = "")
if(!require(ggplot2)) install.packages("ggplot2", repos = "")
if(!require(plotly)) install.packages("plotly", repos = "")
if(!require(lubridate)) install.packages("lubridate", repos = "")
if(!require(tidytext)) install.packages("tidytext", repos = "")
if(!require(textrecipes)) install.packages("textrecipes", repos = "")
if(!require(textfeatures)) install.packages("textfeatures", repos = "")
if(!require(LiblineaR)) install.packages("LiblineaR", repos = "")
if(!require(doParallel)) install.packages("doParallel", repos = "")
if(!require(vip)) install.packages("vip", repos = "")
if(!require(skimr)) install.packages("skimr", repos = "")

#Load the packages required (in Linux #use readxl instead of xlsx).

Preparation of the datasets

ratings <- read.csv("ratings.csv")

movies <- read_csv("movies.csv")

#check if the object is a data frame and coerce as a dataframe if necessary, then use mutate 
#to change existing variables
movies <- %>% mutate(movieId = as.numeric(movieId),
                                           title = as.character(title),
                                           genres = as.character(genres))

#join the datasets then create edx.csv file
edx <- left_join(ratings, movies, by = "movieId")
write.csv(edx, file = "edx.csv")
edx <- read.csv("edx.csv")
edx <- subset(edx, select = -c(X.1, X,...1 ))
edx <- na.omit(edx)

Load the file named edx.csv, give instructions to omit Na’s, and read
the first lines.

The scope of this project is to predict rating, thus I immediately plot
rating to see how it looks like. There are more high ratings than low
ones, and “half ratings” are used less.

edx %>% 
  geom_histogram(bins = 15)
table 1

The following code comes from the capstone exercise and tells how many unique users the dataset contains (69878); this is relevant to understand if some users have voted for many movies. In this case, will this aspect be relevant to the model?

#unique users 

#some users made a lot of reviews, the "reviewer_weigth" variable illustrates them
reviewer_weigth <- edx %>% 
  select(userId, rating, title) %>% 
  group_by(userId) %>% 

table 2 user ids and their ratings

These boxplot and histogram represent the users who rated more movies. These results show that just a few users rated a really high number of movies (such as those who rated 6616 movies), and most users rated less than 250 movies.

#Boxplotof total ratings for each userID
        main ="Boxplot of IDs who rated more movies - totals ")

     col= "lightblue",
     main= "IDs who rated more movies - totals",
     xlab= "user IDs",
     ylab= "ratings_total",
     labels = TRUE)
table 3
table 4

After exploring users, I check ratings, and the top three most used ratings were 4 stars (2588430), then 3 stars (2121240), 5 stars (1390114).

edx_totratings <- edx %>% group_by(rating) %>%
  summarize(count = n()) %>% 

The bar chart represents in detail such results. My takeaway is that some users were benevolent so I wonder if these ratings were given to the same movies, or maybe the same genres? I create a histogram representing movies that received more rating assessments, and I identify the titles of such movies.

gedxratings <- edx_totratings %>% mutate(rating = factor(rating)) %>%
  ggplot(aes(rating, count)) +
  geom_col(fill = "lightblue", color = "black") +
  theme_dark() + 
  labs(x = "Ratings (range)", y = "Count",
       title = "Ratings Range Grouped",
       caption = "Figure 1 - edx dataset ratings")

movie_ratings <- edx %>% 
  count(movieId) %>% 
  ggplot(aes(n)) + 
  geom_histogram(bins=20, color = "black", fill = "lightblue") +
  scale_x_log10() + 
  ggtitle("# of Ratings each Movie") +
  xlab("Movie IDs") +
  ylab("# of Ratings")+

edx %>% group_by(movieId, title) %>%
  summarize(count = n()) %>% 
  top_n(10) %>%
table 5
table 6

Some movies received many more ratings than others, now I investigate genres. Drama (3910127) and comedy (3540930) are the most rated, but we need to further clean the genres variable since some of them are grouped.

genres = c("Drama", "Comedy", "Thriller", "Romance")
sapply(genres, function(g) {
  sum(str_detect(edx$genres, g))

   Drama   Comedy Thriller  Romance 
 4344198  3934068  2584435  1901883 

Since the year released is attached to the title variable, I extract the year and check if the most rated movies were released in some specific years, or maybe some genres were most popular in certain years. The new dataset edx2 contains the new variable named “year_released”.

edx2 <- edx %>% mutate(year_released = as.numeric(str_extract(str_extract(title, "[/(]\\d{4}[/)]$"), regex("\\d{4}"))),title = str_remove(title, "[/(]\\d{4}[/)]$"))

After extracting the year released, I split the number of movies for each year. Looks like most movies have been released during the 90s, so I plot this information to illustrate yearly movie trends. The graphic confirms there was a peak of movies released around the 90s. This is an
element I will consider when approaching the choice of the models I will use.

movies_per_year <- edx2 %>%
  select(movieId, year_released) %>% # I need movieId and year_released variables
  group_by(year_released) %>% # group_by to collect them by year
  summarise(count = n())  %>% # summarise/count to sum movies per year
  arrange(desc(count))# to see them in order from top released year

ggmovies_per_year <- movies_per_year %>%
  ggplot(aes(x = year_released, y = count)) +

1995	874436			
1994	746042			
1996	659425			
1999	543990			
1993	534899			
1997	477463			
1998	446739			
2000	425218			
2001	339508			
2002	302452
table 7

Correct dates

edx2 <- mutate(edx2, year_rated = year(as_datetime(timestamp)))

release <- stringi::stri_extract(edx$title, regex = "(\\d{4})", comments = TRUE) %>% as.numeric()
edx_age <- edx2 %>% mutate(release_date = year_released) %>% select(-timestamp) #change the name of the variable to distinguish from the previous one and rename the new dataset

edx_age %>% 
  filter(release_date < 1900) %>% #filter release dates
  group_by(movieId, title, release_date) %>% #group the variables
  summarize(n = n())

edx_age[edx_age$movieId == "4311", "release_date"] <- 1998 #remove wrong dates after 2000
edx_age[edx_age$movieId == "5472", "release_date"] <- 1972
edx_age[edx_age$movieId == "6290", "release_date"] <- 2003
edx_age[edx_age$movieId == "6645", "release_date"] <- 1971
edx_age[edx_age$movieId == "8198", "release_date"] <- 1960
edx_age[edx_age$movieId == "8905", "release_date"] <- 1992
edx_age[edx_age$movieId == "53953", "release_date"] <- 2007

# fix out of range dates
edx_age %>% filter(release_date > 2020) %>% group_by(movieId, title, release_date) %>% summarize(n = n())

edx_age[edx_age$movieId == "27266", "release_date"] <- 2004 #remove remaining wrong dates 
edx_age[edx_age$movieId == "671", "release_date"] <- 1996
edx_age[edx_age$movieId == "2308", "release_date"] <- 1973
edx_age[edx_age$movieId == "4159", "release_date"] <- 2001
edx_age[edx_age$movieId == "5310", "release_date"] <- 1985
edx_age[edx_age$movieId == "8864", "release_date"] <- 2004
edx_age[edx_age$movieId == "1422", "release_date"] <- 1997

edx_age <- edx_age %>% 
  mutate(age_movie = 2022 - release_date, rating_age = year_rated - release_date) #update new age

Now that release dates are clean, I wonder: “do movies with the highest number/count of ratings have higher ratings?” I check the previous table I created with the top 10 movies and I use movieId to calculate their average ratings. I get 4.154789 for”Pulp Fiction” and 4.012822 for
“Forrest Gump”.

pulp_fiction <- edx2 %>% 
  select (movieId, rating, title, genres) %>% 
  filter (movieId == 296) %>% #here I filter Pulp Fiction
  summarise(avg = mean(rating)) %>%

forrest_gump <- edx2 %>% 
  select (movieId, rating, title, genres) %>% 
  filter (movieId == 356) %>% #here I filer Forrest Gump
  summarise(avg = mean(rating)) %>%

Thus, I use movieId to pull out average ratings of top 10 movies.

eamean_movie <- edx2 %>% 
  select (movieId, rating, title, genres) %>% 
  filter (movieId %in% c(296, 356, 593, 480, 318, 110, 457, 589, 260, 150)) %>% #these are the IDs of the top 10 movies receiving more ratings
  group_by(movieId) %>% 
  summarise(avg = mean(rating)) %>%
table 7

I want to compare the mean of all the movies in the dataset. Since the top 10 movies together have an average rating of 4.063742; the average rating of all the movies in the dataset is 3.512465. This is the most interesting aspect to me, and I will use these results to choose my algorithm model.

mean(edx$rating) #calculate the mean of all the movies in the dataset

In the next chart, I use the mean rating of all movies and the average age. This way I understand whether the movie’s age increases or decreases ratings. The scatterplot shows that the oldest movies have higher ratings compared to the most recent ones.

edx_avg_age <- edx_age %>% group_by(age_movie) %>% summarize(age_rating_avg = mean(rating)) #create average age of all movies and assign the new variable to edx_avg_age

edx_avg_age %>%
  ggplot(aes(age_rating_avg, age_movie)) +
  geom_point(aes(color=age_movie)) +
  ggtitle("Average Ratings compared to Average Age")+
table 8

Modeling approach 1 (we must provide at least 2 models).

According to Theobald, choosing the most relevant variables to use for a model is fundamental for obtaining the best results; following the same logic, wrong variables can decrease the model’s accuracy (2017, p. 36). According to (Serrano, 2021, p. 2) discovering patterns and correlations is the recommended approach for machine learning predictions. To choose where to start, Theobald suggests beginning with “simple supervised algorithms such as linear regression, logistic regression, decision trees, or K-means clustering” (2017, p. 52). Since the goal of this project is to predict an unknown variable (future ratings) I start with regression analysis using Caret package. Furthermore, the EDA has disclosed the possibility that some variables might have
similarities. For example, the chart illustrates the high number of positive ratings, average ratings among top movies that received more ratings, the average of the rest of the dataset, the concentration of movies during some years, and genres. After performing my regression
analysis using Caret and after the good RMSE result I attempt a cluster analysis. For the second model, I use the tidymodels package to identify those variables that likely have elements in common.

RMSE The goal of this project is to assess our model using RMSE, and the result must be lower than 0.86490. RMSE is widely used in regression analysis statistics to measure the relationship between predictor and response variables; it tells how good our model is (Bobbit, 2020).

The formula is:

To prepare data for my model I use the whole dataset named edx and I select some numeric variables. Since I was impressed by the number of ratings those first 10 movies had, I decide to start with them and I select three variables: movieId, rating, and userId; I assign them the name “edx_reduced”.

edx_reduced <- edx %>% select(movieId, rating, userId) %>% #select the numeric variables I want to investigate
  group_by(movieId, userId) %>% 
  summarise(rating = mean(rating)) %>% #assign rating variable to the mean rating of the movies selected
  top_n(10) #pick the top 10 movies

print(edx_reduced, n=10)

The formula for linear regression is mod \<- lm(y ~ x, my_data)

The formula to make predictions is pred \<- predict(mod, my_data)

The formula to calculate RMSE is sqrt(mean(error \^ 2))

I will fit my linear model, make my prediction, and calculate errors
using the formula errors = predicted – actual(Mayer & Kuhn, n.d.)

model <- lm(rating ~ ., edx_reduced) #this is the formula

Now I use the same dataset to compute “Out-of-sample” RMSE for linear regression. This is important because it tells me how my model performs on new data. I randomly order my data and then split the dataset using train/test functions; this process is often compared to “shuffling decks
of playing cards” before playing. The train and split functions are also very important to avoid over-optimistic predictions (overfitting) after using the same dataset (Mayer & Kuhn, n.d.). “The model is accurate when the error rate for the training and test dataset is low” (Theobald, 2017
p. 48).

set.seed(42) #set a random seed

rows <- sample(nrow(edx_reduced)) #the sample function shuffles row indices in the edx_reduced dataset I have previously created

edx_age_reduced <- edx_reduced[rows, ] # randomly reorder data

There are many ways to train/test and split data (also called “split validation”). Theobald (2017, p. 46) recommends 70/30 or 80/2, but we should also consider the size of the dataset, so there is not a fixed rule. The instructions of the Capstone exercise required that “Validation set to be 10% of the whole data”, so I will use 90/10.

split <- round(nrow(edx_reduced) * 0.90) # use the split function to tell the percentage to split

train <- edx_reduced[1:split, ] # Create train

test <- edx_reduced[(split + 1):nrow(edx_reduced), ] # Create test

To predict on test set I have split edx_reduced using the split function to train and test, then I use the lm() function for model fitting only on the training dataset (instead of the whole dataset).

In R, the predict() function predicts the model on new data – the test dataset – because this has not been used for training the model. This way I obtain the error for the out-of-sample model; then, I use the error for RMSE’s formula (sqrt(mean(error\^2))).

model <- lm(rating ~ ., train) # regression formula to train model

p <- predict(model, test) # assign prediction to "p" and predict using test

error <- p - test[["rating"]] #apply formula errors = predicted - actual, thus errors between the predicted rating and the actual rating

sqrt(mean(error^2)) #RMSE formula, the next result is our RMSE

According to this RMSE the model is accurate.

Model Number 2 Kmeans k-Means is an unsupervised clustering model that groups similar data points. The method splits data into k groups and it is helpful to discover new patterns or similarities, or disclose information about the number of clusters identified (Theobald, 2017, p.
72). I am using it following the logic of the previous analysis related to the top 10 movies, those receiving the most ratings. The next model runs using the tidymodels package (Silge & Kuhn, 2022). This code takes some time to run; in order to see how it works I recommend running just a
part of the dataset.

#Do not run if you have the other dataset loaded from EDA, but if you want to run this faster, then select fewer rows, for example 10000 such as below
edx <- read.csv("edx.csv", nrows = 10000)

#reload edx_reduced with fewer observations
edx_reduced <- edx %>% select(movieId, rating, userId) %>% #select the variables we have previously identified
  group_by(movieId, userId) %>%
  summarise(rating = mean(rating)) %>%

In Tidymodels, recipes are used to prepare data we will use (feature engineering). The extraction method named Principal Component Analysis (PCA) is an unsupervised method and it combines new features with the predictors we originally used. PCA’s new features are not correlated
with each other and they perform better when variables are normalized. The next code implies that we have already performed EDA as we did at the beginning of this analysis (Silge & Kuhn, 2022, chapter 8).

edx_rec <- recipe(~ ., data = edx_reduced) %>% 
  step_normalize(all_predictors()) %>% #normalize variables 
  step_pca(all_predictors(), num_comp = 2, id = "pca")

# Print out recipe

I call prep() to estimate the statistics required by PCA and I apply them to a new variable named “features_2d_edx” I call bake(new_data = NULL) to get fitted PC transformation of “features_2d_edx”

edx_estimates <- prep(edx_rec) #the function prep() estimates the necessary statistics and applies them to the new variable "edx_estimates"

features_2d_edx <- edx_estimates %>% # the function bake(new_data = NULL) returns preprocessed data
  bake(new_data = NULL)

features_2d_edx %>% # Print baked data 
  slice_head(n = 5)

Components containing more information (i.e. variance); “pca_estimates” returns each component’s variance (RPubs, 2021).

edx_estimates %>% 
  tidy(id = "pca", type = "variance") %>% #variance for each component in original variables
  filter(str_detect(terms, "percent"))

# Plot PC variance 
edx_estimates %>% 
  tidy(id = "pca", type = "variance") %>% 
  filter(terms == "percent variance") %>% 
  ggplot(mapping = aes(x = component, y = value)) +
  geom_col(fill = "white", alpha = 0.7) +
  ylab("% of total variance")

#Plot of PC scores
features_2d_edx %>% 
  ggplot(mapping = aes(x = PC1, y = PC2)) +
  geom_point(size = 0.5, color = "white")
table 9

kmeans() built-in function runs after using numeric values having the
same scale

edx_features<- recipe(~ ., data = edx_reduced) %>% 
  step_normalize(all_predictors()) %>% #normalize data 
  prep() %>% 
  bake(new_data = NULL)

# Print to see data
edx_features %>% 
  slice_head(n = 5)

Create a model, at this point I still do not know the ideal number of clusters

# Create 10 models with 1 to 10 clusters
kclusts <- tibble(k = 1:10) %>% 
    model = map(k, ~ kmeans(x = edx_features, centers = .x, nstart = 20)), #use map to replace for loops
    glanced = map(model, glance)) %>% 
  unnest(cols = c(glanced))

# See kclusts

Plot to obtain an elbow curve showing the ideal number of clusters using the Total within-cluster sum of squares (WCSS) method (tot.withinss)`. The result shows a change at the 4th point, meaning that the optimal clusters are 4 (I tried and this result is similar if you run the whole edx_reduced dataset or 100000 observations).

kclusts %>% 
  ggplot(mapping = aes(x = k, y = tot.withinss)) +
  geom_line(size = 1.2, alpha = 0.5, color = "white") +
  geom_point(size = 2, color = "white")
table 10

Now I use K-Means with k = 4 clusters as per the previous elbow plot

final_kmeans <- kmeans(edx_features, centers = 4, nstart = 100, iter.max = 1000)

results <- augment(final_kmeans, edx_features) %>% #prediction is added 
  bind_cols(features_2d_edx)  # bind columns pca_data - features_2d_edx

results %>% 
  slice_head(n = 5) #see results

#Visualize clusters using plotly package to so hover and see data together with clusters
cluster_plot <- results %>% 
  ggplot(mapping = aes(x = PC1, y = PC2)) +
  geom_point(aes(shape = .cluster), size = 2, color = "white")


#If you zoom you can see the 4 distinct clusters represented by the different shapes. #These are the group of movies that are similar. One group t the top and three more
#similar ones at the bottom.
table 11

Results and comments about the model

The regression analysis performed using the caret package, a selection of the variables movieId, rating, and userId returns an RMSE in line with our objective. This result is also consistent with EDA and shows that some movies received more ratings and higher ratings than others.
Just for curiosity, I have performed the same linear regression using tidymodels package and I have obtained similar results. One interesting aspect is that tidymodels has the vip() function, which illustrates which variables are the most important ones and movieId turned out to be the most relevant (the chart is attached in the appendix 2 section). One interesting thing to note is that this exercise required a 90/10 split and results were quite different using other splits (e.g. 80/20). Additionally, after using different seeds and shuffles RMSE’s result sensibly changes, but always reaches the goal when I use the top_n(10) movies approach.

K-means is an unsupervised method that can be used to identify clusters, thus used to identify patterns, groups, clusters, and similar characteristics; however, it does not provide an outcome such as a dependent variable as we might expect from other models. In fact, the output of a prediction made using regression analysis is numeric, while classification models return qualitative values that can be both ordered or not (Silge & Kuhn, 2022).

K-means provided interesting information about existing clusters. Another aspect of this approach is that I have used the Tidymodels package which offers an easy way to execute machine learning predictions using workflows. That means, once the model has been created, we can easily switch and try another one without re-writing the code from scratch.

Conclusion, limitations, and future work

This project has confirmed the importance of EDA and data cleaning to understand the way variables work and the relationships between them. The results obtained using the Movielens datasets could be used to explore further correlations, for example, the most rated movies were
released in the 90s, and this aspect can be related to other elements such as social, economic, and technological. For example, what is the psychology behind ratings? And since the most rated movies have higher ratings, do people mostly rate only what they like? And does the order
or the time when the first rating is made affect other users’ behavior? Another example is that according to YouTube experts, users are “all or nothing”, which means they like it or they do not. For this reason, the company together with Netflix and other firms has substituted ratings
with “thumbs up and thumbs down” (Khanna, 2017).

It would also be interesting to investigate the overall budget invested for movie production and advertising, and how users’ interests have been
influenced in recent years by social media. The Numbers website (2019) states that movie budgets are not easy to find, but they have published the ranking of the most expensive movie budgets, and these were all released between 2007 and 2019. However, in terms of budget, the comparison between recent movies and the ones we used in the dataset should consider other elements, for example, technological advancement. For instance, Lewis (1987) explained that movie popularity increased at the end of the 80s thanks to video cassettes. This statement is consistent with the results of our project and the peaks in released movies around the 90s., but technologies changed a lot since then. New services such as Netflix have disrupted the movie landscape and these companies have a lot of data about their customers, so they can create customized
proposals for their users after analyzing their behaviors. In future work, I expect to find more useful variables, for example, the channels where the movies were released (cinema or video streaming).

Appendix 1
Initial code provided
Create edx set, validation set (final hold-out test set)
Note: this process could take a couple of minutes
if(!require(tidyverse)) install.packages(“tidyverse”, repos = ““) if(!require(caret)) install.packages(“caret”, repos = ““) if(!require(data.table)) install.packages(“data.table”, repos = ““)
library(tidyverse) library(caret) library(data.table)
MovieLens 10M dataset:
dl \<- tempfile() download.file(““, dl)
ratings \<- fread(text = gsub(“::”, “\t”, readLines(unzip(dl,”ml-10M100K/ratings.dat”))), col.names = c(“userId”, “movieId”, “rating”, “timestamp”))
movies \<- str_split_fixed(readLines(unzip(dl, “ml-10M100K/movies.dat”)), “\::”, 3) colnames(movies) \<- c(“movieId”, “title”, “genres”)
if using R 3.6 or earlier:
movies \<- %\>% mutate(movieId = as.numeric(levels(movieId))[movieId], title = as.character(title), genres = as.character(genres)) # if using R 4.0 or later: movies \<- %\>% mutate(movieId = as.numeric(movieId), title = as.character(title), genres = as.character(genres))
movielens \<- left_join(ratings, movies, by = “movieId”)
Validation set will be 10% of MovieLens data
set.seed(1, sample.kind=”Rounding”) # if using R 3.5 or earlier, use set.seed(1) test_index \<- createDataPartition(y = movielens\$rating, times = 1, p = 0.1, list = FALSE) edx \<- movielens[-test_index,] temp \<- movielens[test_index,]
Make sure userId and movieId in validation set are also in edx set
validation \<- temp %\>% semi_join(edx, by = “movieId”) %>% semi_join(edx, by = “userId”)
Add rows removed from validation set back into edx set
removed \<- anti_join(temp, validation) edx \<- rbind(edx, removed)
rm(dl, ratings, movies, test_index, temp, movielens, removed)
Appendix 2
2 Graphic showing variable importance (obtained after running the same analysis and regression model using Tydimodels)

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