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movielens.html
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<!DOCTYPE html>
<html>
<head>
<meta charset="utf-8" />
<meta name="generator" content="pandoc" />
<meta http-equiv="X-UA-Compatible" content="IE=EDGE" />
<meta name="author" content="Fahmi Harum" />
<title>Movielens</title>
<script>/*! jQuery v1.11.3 | (c) 2005, 2015 jQuery Foundation, Inc. | jquery.org/license */
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) 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<h1 class="title toc-ignore">Movielens</h1>
<h4 class="author">Fahmi Harum</h4>
<h4 class="date">5/24/2020</h4>
</div>
<div id="introduction" class="section level1">
<h1>1. Introduction</h1>
<p>Data has been essential for nowadays growth, data can be manipulated and elaborated by using statistical and analytics knowledge. Through this process data can be one of the most precious things in the world. This project has required me to create a movie recommendation system.</p>
<p>In details, the project specified the task to predict the rating a user will give a movie in a validation set based on a given set of users and movie ratings. A machine learning algorithm using the inputs in one subset will be developed to predict the movie ratings in the validation set. RMSE would be used to test the accuracy of the algorithm.</p>
<p>The data provided is Movielens 10M is further created and validated using EDX preprocessing syntaxes. The dataset can be acquired online in the ‘dslabs’ containing 9000055 tuples and 8 attributes in total.</p>
<p>This project will analyze all the data, gather insights from the analysis, create a prediction model and conclude a prediction results from the models.</p>
<div id="used-dataset" class="section level3">
<h3>Used Dataset</h3>
<ul>
<li>[MovieLens 10M dataset] <a href="https://grouplens.org/datasets/movielens/10m/" class="uri">https://grouplens.org/datasets/movielens/10m/</a></li>
<li>[MovieLens 10M dataset - zip file] <a href="http://files.grouplens.org/datasets/movielens/ml-10m.zip" class="uri">http://files.grouplens.org/datasets/movielens/ml-10m.zip</a></li>
</ul>
</div>
<div id="data-loading-validation" class="section level3">
<h3>Data Loading & validation</h3>
<pre class="r"><code>if(!require(tidyverse)) install.packages("tidyverse", repos = "http://cran.us.r-project.org")
if(!require(caret)) install.packages("caret", repos = "http://cran.us.r-project.org")
if(!require(data.table)) install.packages("data.table", repos = "http://cran.us.r-project.org")
dl <- tempfile()
download.file("http://files.grouplens.org/datasets/movielens/ml-10m.zip", 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")
movies <- as.data.frame(movies) %>% mutate(movieId = as.numeric(movieId),
title = as.character(title),
genres = as.character(genres))
movielens <- left_join(ratings, movies, by = "movieId")</code></pre>
</div>
<div id="used-libraries" class="section level3">
<h3>Used Libraries</h3>
<p>The following libraries were used in this report:</p>
<pre class="r"><code>library(ggplot2)
library(lubridate)
library(dplyr)
library(stringr)
library(tidyr)</code></pre>
</div>
<div id="aim-objectives" class="section level3">
<h3>Aim & Objectives</h3>
<p>The aim of this project is to develop a machine learning algorithm by making use of inputs acquired from the dataset stated above in Datasets that will be able to forecast movie ratings based on the validated datasets.</p>
<p>Some external libraries will be used in data exploration to acquire crucial insights and trends from the dataset and the factors affecting users’ voting. Four models will be created and assessed by comparing them through the RMSE results. An optimal model out of four models will be used for the prediction.</p>
</div>
</div>
<div id="methodology-analysis" class="section level1">
<h1>2. Methodology & Analysis</h1>
<div id="data-pre-processing-gaining-insightseda" class="section level2">
<h2>Data Pre-Processing & Gaining Insights(EDA)</h2>
<div id="rmse-evaluation" class="section level3">
<h3>RMSE evaluation</h3>
<p>Measurement of the accuracy of the model will be assessed by the Root Mean Square Error(RMSE). Compared with Mean Average Error(MAE), RMSE would be more suitable to this project because it penalizes larger errors stronger and hence suitable for cases that consider minor prediction errors are not the priority.</p>
<pre class="r"><code># function to calculate the RMSE values
RMSE <- function(true_ratings, predicted_ratings){
sqrt(mean((true_ratings - predicted_ratings)^2,na.rm = T))
}</code></pre>
</div>
<div id="training-testing-datasets" class="section level3">
<h3>Training & Testing Datasets</h3>
<p>Before proceeding further with this project, training and testing datasets will need to be acquired from the original dataset as a prerequisite to develop prediction models. The edx partitioned set will be used for training the algorithm and validation dataset will be used for testing. The ratio for the partitioning will be 10% for testing and 90% for training.</p>
<pre class="r"><code>#training and testing sets
# 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)` instead
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)
# Validation dataset can be further modified by removing rating column
validation_CM <- validation
validation <- validation %>% select(-rating)
rm(dl, ratings, movies, test_index, temp, movielens, removed)</code></pre>
<div id="modifying-the-year-genre" class="section level4">
<h4>Modifying the Year & Genre</h4>
<p>Dependencies in between the rating and release year can only be used by including the release year in a separated column, so we need to extract the year release from the title column. This is also done to the genre to extract to be attributes to that will be used for analysis</p>
<pre class="r"><code># lets modify the columns to suitable formats that can be further used for analysis
# Modify the year as a column in the edx & validation datasets
edx <- edx %>% mutate(year = as.numeric(str_sub(title,-5,-2)))
validation <- validation %>% mutate(year = as.numeric(str_sub(title,-5,-2)))
validation_CM <- validation_CM %>% mutate(year = as.numeric(str_sub(title,-5,-2)))
# Modify the genres variable in the edx & validation dataset (column separated)
split_edx <- edx %>% separate_rows(genres, sep = "\\|")
split_valid <- validation %>% separate_rows(genres, sep = "\\|")
split_valid_CM <- validation_CM %>% separate_rows(genres, sep = "\\|")</code></pre>
</div>
</div>
</div>
<div id="data-exploration-visualization" class="section level2">
<h2>Data Exploration & Visualization</h2>
<div id="summary-statisticsgeneral-data-information" class="section level3">
<h3>Summary Statistics/General Data Information</h3>
<p>The dataset is already cleaned and well organized. However, it will be further validated and preprocessed through the preprocessing process to do data cleaning and produce training and testing dataset. This project will breakdown the dataset into much precise form to gather valuable analysis and insights.</p>
<p>The datasets initially come with a tuple containing the name and the year of the movie. The year is extracted from the column to give a better analysis and ease the predictions process. And this process will need the newly extracted attribute to append with the validation dataset.</p>
<pre class="r"><code># The 1st rows of the edx & split_edx datasets are presented below:
head(edx) </code></pre>
<pre><code>## userId movieId rating timestamp title
## 1 1 122 5 838985046 Boomerang (1992)
## 2 1 185 5 838983525 Net, The (1995)
## 3 1 292 5 838983421 Outbreak (1995)
## 4 1 316 5 838983392 Stargate (1994)
## 5 1 329 5 838983392 Star Trek: Generations (1994)
## 6 1 355 5 838984474 Flintstones, The (1994)
## genres year
## 1 Comedy|Romance 1992
## 2 Action|Crime|Thriller 1995
## 3 Action|Drama|Sci-Fi|Thriller 1995
## 4 Action|Adventure|Sci-Fi 1994
## 5 Action|Adventure|Drama|Sci-Fi 1994
## 6 Children|Comedy|Fantasy 1994</code></pre>
<pre class="r"><code>head(split_edx)</code></pre>
<pre><code>## # A tibble: 6 x 7
## userId movieId rating timestamp title genres year
## <int> <dbl> <dbl> <int> <chr> <chr> <dbl>
## 1 1 122 5 838985046 Boomerang (1992) Comedy 1992
## 2 1 122 5 838985046 Boomerang (1992) Romance 1992
## 3 1 185 5 838983525 Net, The (1995) Action 1995
## 4 1 185 5 838983525 Net, The (1995) Crime 1995
## 5 1 185 5 838983525 Net, The (1995) Thriller 1995
## 6 1 292 5 838983421 Outbreak (1995) Action 1995</code></pre>
<pre class="r"><code># edx Summary Statistics
summary(edx)</code></pre>
<pre><code>## userId movieId rating timestamp
## Min. : 1 Min. : 1 Min. :0.500 Min. :7.897e+08
## 1st Qu.:18124 1st Qu.: 648 1st Qu.:3.000 1st Qu.:9.468e+08
## Median :35738 Median : 1834 Median :4.000 Median :1.035e+09
## Mean :35870 Mean : 4122 Mean :3.512 Mean :1.033e+09
## 3rd Qu.:53607 3rd Qu.: 3626 3rd Qu.:4.000 3rd Qu.:1.127e+09
## Max. :71567 Max. :65133 Max. :5.000 Max. :1.231e+09
## title genres year
## Length:9000055 Length:9000055 Min. :1915
## Class :character Class :character 1st Qu.:1987
## Mode :character Mode :character Median :1994
## Mean :1990
## 3rd Qu.:1998
## Max. :2008</code></pre>
<pre class="r"><code># Number of unique movies and users in the edx dataset
edx %>% summarize(n_users = n_distinct(userId), n_movies = n_distinct(movieId))</code></pre>
<pre><code>## n_users n_movies
## 1 69878 10677</code></pre>
<p>Then we extracted and separated the movies according to the genres in the split_edx, which a movie may have multiple genres. So, this split_edx will have recurring titles with unique genres classification. And it will be validated using the same method base in the EDX preprocessing scripts.</p>
<p>After genre splitting, we can acquire the total numbers of the movies and the numbers of the users of the dataset. Insights acquired are; a total of 69878 users has rated for 10677 movies listed in the datasets. Belows are some insights gathered from the analysis:</p>
<p>####Total Observation</p>
<pre class="r"><code>#Getting observation count
length(edx$rating) + length(validation$rating) </code></pre>
<pre><code>## [1] 9000055</code></pre>
<p>####Total Movie and User</p>
<pre class="r"><code>#getting user count and movie count
edx %>% summarize(n_users = n_distinct(userId), n_movies = n_distinct(movieId))</code></pre>
<pre><code>## n_users n_movies
## 1 69878 10677</code></pre>
<p>####Top 10 Movies Ranked</p>
<pre class="r"><code>edx %>% group_by(movieId, title) %>%
summarize(count = n()) %>%
arrange(desc(count))</code></pre>
<pre><code>## # A tibble: 10,677 x 3
## # Groups: movieId [10,677]
## movieId title count
## <dbl> <chr> <int>
## 1 296 Pulp Fiction (1994) 31362
## 2 356 Forrest Gump (1994) 31079
## 3 593 Silence of the Lambs, The (1991) 30382
## 4 480 Jurassic Park (1993) 29360
## 5 318 Shawshank Redemption, The (1994) 28015
## 6 110 Braveheart (1995) 26212
## 7 457 Fugitive, The (1993) 25998
## 8 589 Terminator 2: Judgment Day (1991) 25984
## 9 260 Star Wars: Episode IV - A New Hope (a.k.a. Star Wars) (1977) 25672
## 10 150 Apollo 13 (1995) 24284
## # ... with 10,667 more rows</code></pre>
<p>####Total Movie Ratings per Genre</p>
<pre class="r"><code>#getting rating counts per genre
split_edx%>%
group_by(genres) %>%
summarize(count = n()) %>%
arrange(desc(count))</code></pre>
<pre><code>## # A tibble: 20 x 2
## genres count
## <chr> <int>
## 1 Drama 3910127
## 2 Comedy 3540930
## 3 Action 2560545
## 4 Thriller 2325899
## 5 Adventure 1908892
## 6 Romance 1712100
## 7 Sci-Fi 1341183
## 8 Crime 1327715
## 9 Fantasy 925637
## 10 Children 737994
## 11 Horror 691485
## 12 Mystery 568332
## 13 War 511147
## 14 Animation 467168
## 15 Musical 433080
## 16 Western 189394
## 17 Film-Noir 118541
## 18 Documentary 93066
## 19 IMAX 8181
## 20 (no genres listed) 7</code></pre>
</div>
<div id="ratings-distribution" class="section level3">
<h3>Ratings Distribution</h3>
<p>The rating attribute in the validated dataset will be used to measure the models predictions. The rating holds value of 0.5 to 5.0 sequentially increasing by 0.5 which gives a better classification by doubling the range for better precisions. The movie has been splitted by the given ratings and has been classified uniquely to avoid redundant data.</p>
<pre class="r"><code>#converting to vectors
vec_ratings <- as.vector(edx$rating)
unique(vec_ratings) </code></pre>
<pre><code>## [1] 5.0 3.0 2.0 4.0 4.5 3.5 1.0 1.5 2.5 0.5</code></pre>
<pre class="r"><code>#plotting rating histogram
vec_ratings <- vec_ratings[vec_ratings != 0]
vec_ratings <- factor(vec_ratings)
qplot(vec_ratings) +
ggtitle("Ratings' Distribution")</code></pre>
<p><img 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" width="672" /> Rating distribution has been acquired and in general, it can see that users tend to vote between 3.0 and 4.0 rate. To make a better predictions model, it is needed to explore the different features in the data set.</p>
<p>##Features Elaboration From the insights gathered in the processed data and EDA, it has been found that; some movies are rated more often than others, users has personal preferences to particular movies which will have varies review on the movies, popularity of the movie genre may depends on the preferred trends of the year and the perspective of a movies may evolve over the time. This project will focus on these features to support the model building :</p>
</div>
<div id="movie-bias" class="section level3">
<h3>Movie Bias</h3>
<pre class="r"><code>#plotting # movies & # rated to explore user bias
edx %>%
count(movieId) %>%
ggplot(aes(n)) +
geom_histogram(bins = 30, color = "black") +
scale_x_log10() +
ggtitle("Movies VS # Ratings")+
labs(y=" # of MOvies", x = "# of ratings")</code></pre>
<p><img 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" width="672" /> From the graph, it can be seen that movies have variation of rating given which can be inferred that less rated movies should be given lower importance in movie prediction.</p>
</div>
<div id="user-bias" class="section level3">
<h3>User Bias</h3>
<pre class="r"><code>#plotting # user & # movie rated to explore user bias
edx %>% count(userId) %>%
ggplot(aes(n)) +
geom_histogram(bins = 30, color = "black") +
scale_x_log10() +
ggtitle("Users VS # Movie Rated")+
labs(y=" # of Users", x = "# ratings")</code></pre>
<p><img 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VYGgQYmc3gqLwGBVgaBBiZzeCovAYFWBoEGJnN4Ki8BgVYGgQYmc3gqLwGBVgaBBiZzeCovAYFWBoEGJnN4Ki8BgVYGgQYmc3gqLwGBVgaBBiZzeCovAYFWBoEGJnN4Ki8BgVYGgQYmc3gqLwGBVgaBBiZzeCovAYFWBoEGJnN4Ki8BgVYGgQYmc3gqLwGBVgaBBiZzeCovAYFWBoEGJnN4Ki8BgVYGgQYmc3gqLwGBVgaBBiZzeCovAYFWBoEGJnN4Ki8BgVYGgQYmc3gqLwGB+jGwgUDDkjk8lZeAQP1AoLSxDiovAYH6YXQjAg1L5vBUXgIC9QOB0sY6qLwEBOoHAqWNdVB5CQjUDwRKG+ug8hIQqB8IlDbWQeUlIFA/EChtrIPKS0CgfiBQ2lgHlZeAQP1AoLSxDiovAYH6gUBpYx1UXgIC9QOB0sY6qLwEBOoHAqWNdVB5CQjUDwRKG+ug8hIQqB8IlDbWQeUlIFA/EChtrIPKS0CgfiBQ2lgHlZfgIdBHv782HP67v2kffDx+8PYX5z1AoAg0HpnDU3kJDgJ98O5wwl83D36YPnjpy8c/QKAINCCZw1N5CYcL9NH14ctfjB793+GLvxo/ujF85YvRg+vDV7577AMEikADkjk8lZdwuEC/b3cqvx2+OhrdvzZ58MO7jU13P0CgCDQimcNTeQkHC3S8A/qLxaOJRSdf33ncAwSKQCOSOTyVl3CwQH94d/ldzRutTb9vdLn7AQJFoBHJHJ7KSzhYoPevvfLdv/yn4fDlfxg1u6PtAXrz3d0Ppr/5k5a9p4yKp0DVzwUA9qeTQD+enoV/B4EiUIAfM/s37vfNBUzfjR79vjkLv6TJl77c/WB1C0X2qwts9Fw4hOdAUgeVl+Ah0OlZoRvDV/fbA0WgCDQYmcNTeQkHC/T+NZMzESgCjU/m8FRegoNA20PyyT84C49AE5M5PJWXcLBA57uW3zefMZpd5dle+rnrAQJFoBHJHJ7KSzhYoJP3Pqdf3+GTSAg0bSc0ZA5P5SUcLtD715pbLE3PwrcfjG8/8b77AQJFoBHJHJ7KSzhcoKPvr00uA31x8h7ng+V7Lu1+gEARaEAyh6fyEhwEOnrQ3OjzP38xezC25NvfnfcAgSLQeGQOT+UleAj0QIo8qwIbPRcEShvroPISEKgfCJQ21kHlJSBQP+oKdGCj/NNegTZWQeUlIFA/EChtrIPKS0CgftQWqNOGXKGNVVB5CQjUDwRKG+ug8hIQqB8IlDbWQeUlIFA/EChtrIPKS0CgfngK1AIC9SZzeCovAYH6gUBpYx1UXgIC9cNToG4bqlwD2lgFlZeAQP1AoLSxDiovAYH6gUBpYx1UXgIC9QOB0sY6qLwEBOoHAqWNdVB5CQjUDwRKG+ug8hIQqB8IlDbWQeUlIFA/EChtrIPKS0CgfiBQ2lgHlZeAQP1AoLSxDiovAYH6EVKgle+6TBuroPISEKgfCJQ21kHlJSBQP0IK1DTIrwa0sQoqLwGB+oFAaWMdVF4CAvUDgdLGOqi8BATqBwKljXVQeQkI1A8EShvroPISEKgfCJQ21kHlJSBQPxAobayDyktAoH4gUNpYB5WXgED9QKC0sQ4qLwGB+oFAaWMdVF4CAvUDgdLGOqi8BATqBwKljXVQeQkI1A8EShvroPISEKgfCJQ21kHlJSBQPxAobayDyktAoH4gUNpYB5WXgED9QKC0sQ4qLwGB+oFAaWMdVF4CAvUDgdLGOqi8BATqBwKljXVQeQkI1A8EShvroPISEKgfCJQ21kHlJSBQPxAobayDyktAoH4gUNpYB5WXgED9QKC0sQ4qLwGB+oFAaWMdVF4CAvUDgdLGOqi8BATqBwKljXVQeQkI1A8EShvroPISEKgfCJQ21kHlJSBQPxAobayDyktAoH4gUNpYB5WXgED9QKC0sQ4qLwGB+oFAaWMdVF4CAvUDgdLGOqi8BATqBwKljXVQeQkI1A8EShvroPISEKgfCJQ21kHlJSBQPxAobayDyktAoH4gUNpYB5WXgED9QKC0sQ4qLwGB+oFAaWMdVF4CAvUDgdLGOqi8BATqBwKljXVQeQkI1A8EShvroPISEKgfCJQ21kHlJSBQP3ot0IEN2lgFlZeAQP1AoAhUB5WXgED96LlATVuijVVQeQkI1A8EikB1UHkJCNQPBIpAdVB5CQjUDwSKQHVQeQkI1A8EikB1UHkJCNQPBIpAdVB5CQjUDwSKQHVQeQkI1A8EikB1UHkJCNQPBIpAdVB5CQjUDwSKQHVQeQkI1A8EikB1UHkJCNQPBIpAdVB5CQjUDwSKQHVQeQkI1A8EikB1UHkJCNQPBIpAdVB5CQjUDwSKQHVQeQkI1A8EikB1UHkJCNQPBIpAdVB5CQjUDwSKQHVQeQkI1A8EikB1UHkJCNQPBIpAdVB5CQjUDwSKQHVQeQkI1A8EikB1UHkJCNQPBIpAdVB5CQjUDwSKQHVQeQkI1A8EikB1UHkJCNQPBIpAdVB5CQjUDwSKQHVQeQkBBNob8grU78kVLzJAYNgDPYC8AvV7cuwHqaDyEhCoHwgUgeqg8hIQqB8IFIHqoPISEKgfCBSB6qDyEhCoHwgUgeqg8hIQqB8IFIHqoPISEKgfCBSB6qDyEhCoHwgUgeqg8hIQqB8IFIHqoPISEKgfCBSB6qDyEhCoHwgUgeqg8hIQqB8IFIHqoPISEKgfCBSB6qDyEhCoHwgUgeqg8hIQqB95BWrCtCXaWAWVl4BA/UCgCFQHlZeAQP3IK1C/QbSxCiovAYH6gUARqA4qLwGB+oFAEagOKi8BgfqBQBGoDiovAYH6gUARqA4qLwGB+oFAEagOKi8BgfqBQBGoDiovAYH6gUARqA4qLwGB+oFAEagOKi8BgfqBQBGoDiovAYH6gUARqA4qLwGB+oFAEagOKi8BgfqBQBGoDiovAYH6gUARqA4qLwGB+oFAEagOKi8BgfqBQBGoDiovAYH6gUARqA4qLwGB+oFAEagOKi8BgfqBQBGoDiovAYH6gUARqA4qLwGB+oFAEagOKi8BgfqBQBGoDiovAYGa8PzLv06DEKg/mcNTeQkI1AQCRaDBofISEKiJgLYKGAmBCqHyEhCoiYC2ChgJgQqh8hIQqImAtgoYCYEKofISEKiJgLYKGAmBCqHyEhCoiYC2ChgJgQqh8hIQqImAtgoYCYEKofISEKiJgLYKGAmBCqHyEhCoiYC2ChjpL2xXyzq/No6kbePbCFQEAjUR0FYBIyFQIQhUAgI1EdBWASMZczu/No6kbePbCFQEAjURUkQ1Z0Og0UGgEhCoiZAiqjkbAo0OApWAQE2EFFHN2RBodBCoBARqIqSIas6GQKODQCUgUBMhRVRzNgQaHQQqAYGaCCmimrMh0OggUAkI1ERIEdWcDYFGB4FKQKAmQoqo5mwINDoIVAICNRFSRDVnQ6DRQaASEKiJkCKqORsCjQ4ClYBATYQUUc3ZEGh0EKgEBGoipIhqzoZAo4NAJSBQEyFFVHM2BBodBCoBgZoIKaKasyHQ6CBQCQjUREgR1ZwNgUYHgUpAoCZCiqjmbAg0OghUAgI1EVJENWdDoNFBoBIQqImQIqo5GwKNDgKVgEBNhBRRzdkQaHQQqAQEaiKkiGrOhkCjg0AlIFATIUVUczYEGh0EKgGBmggpopqzIdDoIFAJCNRESBHVnA2BRgeBSkCgJkKKqOZsCDQ6CFQCAjURUkQ1Z0Og0UGgEhCoiZAiqjkbAo0OApWAQE2EFFHN2RBodBCoBARqIqSIas6GQKODQCUgUBMhRVRzNgQaHQQqAYGaCCmimrMh0OggUAkI1ERIEdWcDYFGB4FKQKAmQoqo5mwINDoIVAICNRFSRDVnQ6DRQaASEKiJkCKqORsCjQ4ClYBATYQUUc3ZEGh0EKgEBGoipIhqzoZAo4NAJSBQEyFFVHM2BBodBCoBgZoIKaKasyHQ6CBQCQjUREgR1ZwNgUYHgUpAoCZCiqjmbAg0OghUAgI1EVJENWdDoNFBoBIQqImQIqo5GwKNDgKVgEBNhBRRzdkQaHQQqAQEaiKkiGrOhkCjg0AlIFATIUVUczYEGh0EKgGBmggpopqzIdDoIFAJCNRESBHVnA2BRgeBSkCgJkKKqOZsCDQ6CFQCAjURUkQ1Z0Og0UGgErwEev/aK99N/vHo42vD4dtfjM55gEAPHRQwEgIVgkAl7CfQsz/85rdbf/Do+nAq0B/eHTa89OXjHyDQgwcFjIRAhSBQCVaB3v3bW6PRw9cGg8HFj7b8+NthK9Abw1e+GD1odbr7AQI9eFDASAhUCAKVYBToyeCJz0ej40FD86817l9rBXr/2mQP84d3X/zV4x4g0MMHBYyEQIUgUAk2gZ5OtHnnaPDUrbtXBi+s/3h8AP/fpu+Bfjt8dfKdb4fvPO4BAj18UMBICFQIApVgE+jx2JyNRi981Py3+fcKN4avtieRbgx/MfnO940udz9AoIcPChgJgQpBoBJMAj17rzFnq9GHV9aP4b8fH75PBfroenuA3jzc/WD6az9p2e7sWIQUUc3ZPHOrX0yAUmxf3FNnPrwyuDTaItDJ25oIFIEiUPix8ziB3jkaXB1tEeiN5l3NDYG+9OXuB6tbL7Jf7bzBkCKqORuH8NHhEF6CSaDTQ/iTyVugG++Bfjs5/95hDxSBHjQoYCQEKgSBSjAJdHQ8uNScfm/MuX4W/v61iRkRKAJFoEoQqASbQE8nF4COj+DP3h9M90PnfDucMz425yx8tUEBIyFQIQhUgk2g48P3MZcmJ5IuXF35yapAZ1d5tpd+7nqAQA8fFDASAhWCQCUYBTq6+8HPPhx/efiXz/1u68/bI3M+iVRtUMBICFQIApVgFeh5tAJ9dH348vwT77sfINDDBwWMhECFIFAJNoEe79jv3BDo6MHyPZd2P0CgBw8KGAmBCkGgEkwCfXhlcHXrDzYFOnrw8diSb7d7mbsfINBDBwWMZMxtwvkFtJG2jW8jUBFGgW65A5MbRZ6V8wZDiqjmbAg0OghUgkmg7WfhEWglx/RcoKYNOb+ANtK28W0EKsIk0NHJ4Knz3gRFoDFFFG4QAi0DApVgE+i9Xw8GTz77RsvP1m9nh0D3UYPToICREKgQBCrBJNCHV1bennJ+Q7TIs3LeYF4RhRuEQMuAQCUgUBN5RRRuEAItAwKVYBJoWYo8K+cN5hVRuEEItAwIVAICNZFXROEGIdAyIFAJ+wj07BsE6qAGp0EBIyFQIQhUglmgX7/evPn58C/f9D0Fj0C7DgoYCYEKQaASjAI9+2R69ujhlcFF7w8lFXlWzhvMK6JwgxBoGRCoBKNAjweDi//h6InPz/77YPOvGiPQvdTgNChgJAQqBIFKsAn0dDB4q/1E/FdH595YBIHWGBQwEgIVgkAl2AR63PwdpPaWIieTP26MQDurwWlQwEgIVAgClWAS6PRmIq1A7xxxIf1BanAaFDASAhWCQCWYBDpVZytQ93vbFXlWzhvMK6JwgxBoGRCoBARqIq+Iwg1CoGVAoBJMAj17rzlx1Jrz1Ps0fJFn5bzBvCIKNwiBlgGBSjAJdHriaCrQsUw5iXSQGpwGBYyEQIUgUAk2gd45Gjx/ayLQu68NvO9OX+RZOW8wr4jCDUKgZUCgEmwCHe+CDgaXjy48+/T46wu+/kSg3QYFjIRAhSBQCUaBjv75aHY3UG9/ItBugwJGQqBCEKgEq0BH9z69PLbnk+f+gXgEWmlQwEgIVAgClWAWaDmKPCvnDeYVUbhBCLQMCFQCAjWRV0ThBiHQMiBQCfsJ9OwPv/ktAj1QDU6DAkZCoEIQqASrQO/+7a3R6OFrg8HgovNVTAi026CAkRCoEAQqwSjQk8mf4jwu8Uc5EWi3QQEjIVAhCFSCTaCnE23eORo8devuFe8LmYo8K+cN5hVRuEEItAwIVIJNoMeTz7+fTj6ExGfhD1SD06CAkRCoEAQqwSTQ6f1AW41yN6YD1eA0KGAkBCoEgUowCXR2O7vJbUQQ6IFqcBoUMBICFYJAJewh0DvTv4aEQA9Ug9OggJEQqBAEKsEk0Okh/Mn0Pky8B3qgGpwGBYyEQIUgUAkmgY6OB5ea0++NOTkLf6ganAYFjIRAhSBQCTaBnk5vxHR1dPb+gPuBHqgGp0EBIyFQIQhUgk2gk/uBTu9KP7jg/GfhEWi3QQEjIVAhCFSCUaCjux/87MPxl4d/6X8/uyLPynmDeUUUbhACLQMClWAVaEGKPCvnDeYVUbhBCLQMCFQCAjWRV0ThBiHQMiBQCQjURF4RhRuEQMuAQCWcI9CzD95Y4ue/+QyBHqwGp0EBIyFQIQhUwjkCfXhlsMbzvlfRI9CugwJGQqBCEKiEvQU6uOh8O1AE2m1QwEgIVAgClXCOQFc5u/n+0eRyUAR6gBqcBgWMhECFIFAJewl0NLmjyMD5Svoiz8p5g3lFFG4QAi0DApWwr0CbzyQ574IWeVbOG8wronCDEGgZEKiEvQU6+bseCPQANTgNCnkH/FsAACAASURBVBgJgQpBoBL2FujDK95/Va7Is3LeYF4RhRtk3JAJ51c5bxvfRqAiEKiJvCIKNwiBlgGBSkCgJvKKKNwgz9mcX+W8bXwbgYrYW6C8B1pFDdFmi5nb+VXO28a3EaiIvQXKWfgqaog2W8zczq9y3ja+jUBF7CtQrgOto4Zos8XM7fwq523j2whUxH4Cvffp2J/OR/AItNuggJEQqBAEKuEcgW75LLzzKSQE2nFQwEgIVAgClbC3QJ/jbkw11BBttpi5nV/lvG18G4GKOEegq/cDfePvuR9oJTVEmy1mbudXOW8b30agIs4RaA2KPCvnDfZcRDUHIdAyIFAJCNREz0VUcxACLQMClYBATfRcRDUHIdAyIFAJCNREz0VUcxACLQMClYBATfRcRDUHIdAyIFAJCNREz0VUcxACLQMClYBATfRcRDUHIdAyIFAJCNREz0VUcxACLQMClYBATfRcRDUHIdAyIFAJ5wj07L0LH42/3PsGgdZVQ7TZYuZ2fpXztvFtBCriHIE+vNLcO2T6XwRaUQ3RZouZ2/lVztvGtxGoiHMF2uyBItCei6jmIARaBgQq4RyBnr03eOq3f7x55YnP/rjA+Xi+yLNy3mDPRVRzEAItAwKVcI5Am7/gUfqOoEWelfMGey6imoMQaBkQqITzBHr2CQK9jUCD5nZ+lfO28W0EKuI8gY4V+sff/OPRhV/+ZsFv+aucxdUQbbaYuZ1f5bxtfBuBijhfoCNOIiHQoLmdX+W8bXwbgYowCfTsg5+5/yEPBHrgoICREKgQBCrBJNCyFHlWzhvsuYhqDkKgZUCgEswCvffp5cHgwuU3/T+TVORZOW+w5yKqOQiBlgGBSrAKdHE50wsItIIaos0WM7fzq5y3jW8jUBFGgTb+fPLZN376dAGDFnlWzhvsuYhqDkKgZUCgEmwCvXM0eOp3k3/dfW8wub0IAi2rhmizxczt/CrnbePbCFSETaDHg6dmp+HP3htcQqDF1RBttpi5nV/lvG18G4GKMAm0vandlDtHT3EhfXE1RJstZm7nVzlvG99GoCJMAl25kN79qvoiz8p5gz0XUc1BCLQMCFQCAjXRcxHVHIRAy4BAJZgEevbe4Or8wemAQ/jyaog2W8zczq9y3ja+jUBFmATKSaSei6jmIARaBgQqwSbQO0eDi59N/nXzNS5jqqGGaLPFzO38Kudt49sIVIRNoNMPIl2+fLnER5GKPCvnDfZcRDUHIdAyIFAJRoGOvjpqP8l54S1nfyLQboMCRkKgQhCoBKtAR2df/3S8B/rsh/73tSvyrJw32HMR1RyEQMuAQCWYBVqOIs/KeYM9F1HNQQi0DAhUAgI10XMR1RyEQMuAQCUgUBM9F1HNQQi0DAhUAgI10XMR1RyEQMuAQCUgUBM9F1HNQQi0DAhUAgI10XMR1RyEQMuAQCUgUBM9F1HNQQi0DAhUQgCBZqDnIqo5yHM29bIAWIU90O30XEQ1B7EHWgb2QCVYBPrw9cvPfL70FYGWV0O02WLmdn6V87bxbQQq4hyBnv3hm+YWyoPJPZRnXxFoeTVEmy1mbhP7rBvnZVMTBCrhHIGOnTm4/MYRAu23iGoOQqBlQKASzhHo2fvtXZgu/vyzWwi0nhqizZY49z7rxnnZ1ASBSjhHoA03Pz2a/98cgVbq+mizJc69z7pxXjY1QaASDAKdHLr/8u9eb+8H+uwvv0Ggxbs+2myJc++zbpyXTU0QqASrQNv3QEvshhZ5Vs4bRER5c++zbpyXTU0QqIQ9BfrE5/f+8QPna5mKPCvnDSKivLn3WTfOy6YmCFTCOQJ9+MH4gJ3LmBBo4tz7rBvnZVMTBCrhPIE2R+1PDxAoIkqbe59147xsaoJAJZwj0LOvf/r09I3Pyz//7Z8QaLWujzZb4tz7rBvnZVMTBCrhHIFO+H+Ly5gu/G/+qFyVro82W+Lc+6wb52VTEwQqwSLQ5tD9n25++vpRex3T//KVaJFn5bxBRJQ39z7rxnnZ1ASBSrAKtH0P9MJlLmOq0vXRZkuce59147xsaoJAJewp0PHXe3/4W/ZAi3d9tNkS595n3Tgvm5ogUAn7C9SdIs/KeYOIKG/ufdaN87KpCQKVYBFoYYo8K+cNIqK8ufdZN87LpiYIVAICNYGI8ubeZ904L5uaIFAJCNQEIsqbe59147xsaoJAJSBQE4gob+591o3zsqkJApWAQE0gory591k3zsumJghUAgI1gYjy5t5n3Tgvm5ogUAkI1AQiypt7n3XjvGxqgkAlIFATiChv7n3WjfOyqQkClYBATSCivLn3WTfOy6YmCFQCAjWBiPLm3mfdOC+bmiBQCQjUBCLKm3ufdeO8bGqCQCUgUBOIKG/ufdaN87KpCQKVgEBNIKK8ufdZN87LpiYIVAICNYGI8ubeZ904L5uaIFAJCNQEIsqbe59147xsaoJAJSBQE4gob+591o3zsqkJApWAQE0gory591k3zsumJghUAgI1gYjy5t5n3Tgvm5ogUAkI1AQiypt7n3XjvGxqgkAlIFATiChv7n3WjfOyqQkClYBATSCivLn3WTfOy6YmCFQCAjWBiPLm3mfdOC+bmiBQCQjUBCLKm3ufdeO8bGqCQCUgUBOIKG/ufdaN87KpCQKVgEBNIKK8ufdZN87LpiYIVAICNYGI8ubeZ904L5uaIFAJCNQEIsqbe59147xsaoJAJSBQE4gob+591o3zsqkJApWAQE0gory591k3zsumJghUAgI1gYjy5t5n3Tgvm5ogUAkI1AQiypt7n3XjvGxqgkAlIFATiChv7n3WjfOyqQkClYBATSCivLn3WTfOy6YmCFQCAjWBiPLmNtGuG+dlUxMEKgGBmkBEeXMj0ASkDY9ATSCinudu143zsqkJApWAQE0E7PqAkRLnbteN87KpCQKVgEBNBOz6gJES527XjfOyqQkClYBATQTs+oCREudu143zsqkJApWAQE0E7PqAkRLnbteN87KpCQKVgEBNBOz6gJES527XjfOyqQkClYBATQTs+oCREudu143zsqkJApWAQE0E7PqAkRLnbteN87KpCQKVgEBNBOz6gJES527XjfOyqQkClYBATQTs+oCREudu143zsqkJApWAQE0E7PqAkRLnbteN87KpCQKVgEBNBOz6gJES527XjfOyqQkClYBATQTs+oCREudu143zsqkJApWAQE0E7PqAkRLnbteN87KpCQKVgEBNBOz6gJES527XjfOyqQkClYBATQTs+oCREudu143zsqkJApWAQE0E7PqAkRLnbteN87KpCQKVgEBNBOz6gJES527XjfOyqQkClYBATQTs+oCREudu143zsqkJApWAQE0E7PqAkRLnbteN87KpCQKVgEBNBOz6gJES527XjfOyqQkClYBATQTs+oCREudu143zsqkJApWAQE0E7PqAkRLnbteN87KpCQKVgEBNBOz6gJES527XjfOyqQkClYBATQTs+oCREudu143zsqkJApWAQE0E7PqAkRLnbteN87KpCQKVgEBNBOz6gJES527XjfOyqQkClYBATQTs+oCREudu143zsqkJApWAQE0E7PqAkRLnbteN87KpCQKVgEBNBOz6gJES527XjfOyqQkClYBATQTs+oCREudu143zsqkJApWAQE0E7PqAkRLnbteN87KpCQKVgEBNBOz6gJES527XjfOyqQkClYBATQTs+oCREudu143zsqkJApWAQE0E7PqAkRLnbteN87KpCQKVgEBNBOz6gJES527XjfOyqQkClYBATQTs+oCREudu143zsqkJApWAQE0E7PqAkRLnbteN87KpCQKVgEBNBOz6gJES527XjfOyqQkClYBATQTs+oCREudu143zsqkJApWAQE0E7PqAkRLnbteN87KpCQKVgEBNBOz6gJES527XjfOyqQkClYBATQTs+oCREudu143zsqkJApWAQE0E7PqAkRLnbteN87KpCQKVgEBNBOz6gJES527XjfOyqQkClYBATQTs+oCREudu143zsqkJApWAQE0E7PqAkRLnbteN87KpCQKVgEBNBOz6gJES527XjfOyqQkCleAh0H/9r8Phi29/MX3w6ONrw+H5DxDooYMCRkqcu103zsumJghUgoNAfz+c8OKvmgc/vDt58NKXj3+AQA8eFDBS4tztunFeNjVBoBIOF+j3wxf/ZjR6cH2qxhvDV75oHrzy3WMfINCDBwWMlDi3Bec15QwClXCwQB9dH/6i+TrewRx/vX9totEf3m32R3c/QKCHDwoYKXFuBKolbfiDBfrDu+1B+Y3hO6PRt8NXJw++ffwDBHr4oICRep7beU05g0AlHCzQOROB3pjujo6P61993AMEeviggJF6ntt5TTmDQCW4CXRybP7oenuAfv/aK9/tfjD9jZ+0dJ6yIiEbuuZs5B4oLvGDZHRfJJNDdARab1DASD3PrV6EEJ/Oi+T7yWVMS5p86cvdD1Z/tch+tfMGQzZ0zdnIzSF8SdKGdxLo99debN7i3GsPFIEeNChgpJ7ndl5TziBQCT4C/ba9jB6B1hsUMFLPczuvKWcQqAQXgf5+OLu4k7Pw1QYFjNTz3M5ryhkEKsFBoI9uDF+eva05u8qzvfRz1wMEeviggJF6ntt5TTmDQCU4CPTG0qcz+SRStUEBI/U8t/OacgaBSjhcoN8uf7r90fXhy/NPvO9+gEAPHxQwUs9zO68pZxCohIMF2t5kqaF5c/PB8j2Xdj9AoAcPChip57md15QzCFTCwQL9frgi0NGDj8f/ervdy9z9AIEeOihgpJ7ndl5TziBQCQcL9HCKPCvnDYZs6JqzkRuBliRteARqImRD15yN3Ai0JGnDI1ATIRu65mzkRqAlSRsegZoI2dA1ZyM3Ai1J2vAI1ETIhq45G7kRaEnShkegJkI2dM3ZyI1AS5I2PAI1EbKha85GbgRakrThEaiJkA1dczZyI9CSpA2PQE2EbOias5EbgZYkbXgEaiJkQ9ecjdwItCRpwyNQEyEbuuZs5EagJUkbHoGaCNnQNWcjNwItSdrwCNREyIauORu5EWhJ0oZHoCZCNnTN2ciNQEuSNjwCNRGyoWvORm4EWpK04RGoiZANXXM2ciPQkqQNj0BNhGzomrORG4GWJG14BGoiZEPXnI3cCLQkacMjUBMhG7rmbORGoCVJGx6BmgjZ0DVnIzcCLUna8AjURMiGrjkbuRFoSdKGR6AmQjZ0zdnIjUBLkjY8AjURsqFrzkZuBFqStOERqImQDV1zNnIj0JKkDY9ATYRs6JqzkRuBliRteARqImRD15yN3Ai0JGnDI1ATIRu65mzkRqAlSRsegZoI2dA1ZyM3Ai1J2vAI1ETIhq45G7kRaEnShkegJkI2dM3ZyI1AS5I2PAI1EbKha85GbgRakrThEaiJkA1dczZyI9CSpA2PQE2EbOias5EbgZYkbXgEaiJkQ9ecjdwItCRpwyNQEyEbuuZs5EagJUkbHoGaCNnQNWcj98CG88Kzg0AlIFATIRu65mzkRqAlSRsegZoI2dA1ZyO3cUPOC88OApWAQE3kbehwgwJGQqBy0oZHoCbyNnS4QQEjIVA5acMjUBN5GzrcoICREKictOERqIm8DR1uUMBICFRO2vAI1ETehg43KGAkBConbXgEaiJvQ4cbFDASApWTNjwCNZG3ocMNChgJgcpJGx6Bmsjb0OEGBYyEQOWkDY9ATeRt6HCDAkZCoHLShkegJvI2dLhBASMhUDlpwyNQE3kbOtyggJEQqJy04RGoibwNHW5QwEgIVE7a8AjURN6GDjcoYCQEKidteARqIm9DhxsUMBIClZM2PAI1kbehww0KGAmBykkbHoGayNvQ4QYFjIRA5aQNj0BN5G3ocIMCRkKgctKGR6Am8jZ0uEEBIyFQOWnDI1ATeRs63KCAkRConLThEaiJvA0dblDASAhUTtrwCNRE3oYONyhgJAQqJ214BGoib0OHGxQwEgKVkzY8AjWRt6HDDQoYCYHKSRsegZrI29DhBgWMhEDlpA2PQE3kbehwgwJGQqBy0oZHoCbyNnS4QQEjIVA5acMjUBN5GzrcoICREKictOERqIm8DR1uUMBICFRO2vAI1ETehg43KGAkBConbXgEaiJvQ4cbFDASApWTNjwCNZG3ocMNChgJgcpJGx6Bmsjb0OEGBYyEQOWkDY9ATeRt6HCDAkZCoHLShkegJvI2dLhBASMhUDlpwyNQE3kbOtyggJEQqJy04RGoibwNHW5QwEgIVE7a8AjURN6GDjcoYCQEKidteARqIm9DhxsUMBIClZM2PAI1kbehww0KGAmBykkbHoGayNvQ4QYFjIRA5aQNj0BN5G3ocIMCRvLMbcJ5dU5AoBIQqIm8DR1uUMBICFRO2vAI1ETehg43KGCk6rmdV+cEBCoBgZroeUPXHBQwEgKVkzY8AjXR84auOShgJAQqJ214BGqi5w1dc1DASAhUTtrwCNREzxu65qCAkRConLThEaiJnjd0zUEBIyFQOWnDI1ATPW/omoMCRkKgctKGR6Amet7QNQcFjIRA5aQNj0BN9Lyhaw4KGAmBykkbHoGa6HlD1xwUMBIClZM2PAI10fOGrjkoYCQEKidteARqoucNXXNQwEgIVE7a8AjURM8buuaggJEQqJy04RGoiZ43dM1BASMhUDlpwyNQEz1v6JqDAkZCoHLShkegJnre0DUHBYyEQOWkDY9ATfS8oWsOChgJgcpJGx6Bmuh5Q9ccFDASApWTNnwAgWag5w1dc1DASNVzq5czlII90O30vKFrDgoYiT1QOWnDI1ATPW/omoMCRkKgctKGR6Amet7QNQcFjIRA5aQNj0BN9Lyhaw4KGAmBykkbHoGa6HlD1xwUMBIClZM2PAI10fOGrjkoYCQEKidteARqoucNXXNQwEgIVE7a8AjURM8buuaggJEQqJy04RGoiZ43dM1BASMhUDlpwyNQEz1v6JqDAkZCoHLShkegJnre0DUHBYyEQOWkDY9ATfS8oWsOChgJgcpJGx6Bmuh5Q9ccFDASApWTNjwCNdHzhq45KGAkBConbXgEaqLnDV1zUMBICFRO2vAI1ETPG7rmoICREKictOERqImeN3TNQQEjVc9tQr3mq5I2PAI10fOGrjkoYCQEKidteARqoucNXXNQwEgxc6vXfFXShkegJmhociPQgqQNj0BN0NDkRqAFSRsegZqgocmNQAuSNjwCNUFDkxuBFiRteARqgoYmNwItSNrwCNQEDU1uBFqQtOERqAkamtwItCBpwyNQEzQ0uRFoQdKGR6AmaGhyI9CCpA2PQE3Q0ORGoAVJGx6BmqChyY1AC5I2PAI1QUOTG4EWJG14BGqChiY3Ai1I2vAI1AQNTW4EWpC04RGoCRqa3Ai0IGnDI1ATNDS5EWhB0oZHoCZoaHIj0IKkDY9ATdDQ5EagBUkbHoGaoKHJjUALkjY8AjVBQ5MbgRYkbXgEaoKGJjcCLUja8AjUBA1NbgRakLThEagJGprcCLQgacMjUBM0NLkRaEHShkegJmhociPQgqQNj0BN0NDkRqAFSRsegZqgocldO5KJgmu+KmnDI1ATNDS5EWhB0oZHoCZoaHLHi/QXCFQOAjURsHsCRiI3Au1I2vAI1ETA7gkYidwItCNpwyNQEwG7J2AkciPQjqQNj0BNBOyegJHIjUA7kjY8AjURsHsCRiI3Au1I2vAI1ETA7gkYidwItCNpwyNQEwG7J2AkciPQjqQNj0BNBOyegJHIjUA7kjY8AjURsHsCRiI3Au1I2vAI1ETA7gkYidwItCNpwyNQEwG7J2AkciPQjqQNj0BNBOyegJHIjUA7kjY8AjURsHsCRiI3Au1I2vAI1ETA7gkYidwItCNpwyNQEwG7J2AkciPQjqQNj0BNBOyegJHIjUA7kjY8AjURsHsCRiJ39UH73bU+LggUgdLQ5EagHUGgCJSGJnfAQQi0KAjURMjGqDkbuQNGQqB6EKiJkI1RczZyB4yEQPUgUOPfj6255nve0DVnIzcCLQoCRaDk7nfuAg3mDgJNLNCay5mGDhip57kLNJg7CBSB0tDkDjgIgRYFgQZc8z1v6JqzkRuBFgWBBlzzPW/omrORG4EWBYEGXPM9b+ias5EbgRYFgQZc8z1v6JqzkRuBFgWBBlzzPW/omrORG4EWBYEGXPM9b+ias5EbgRYFgQZc8z1v6JqzkRuBFgWBBlzzPW/omrORG4EWBYEGXPM9b+ias5EbgRYFgQZc8z1v6JqzkRuBFgWBBlzzPW/omrORG4EWBYEGXPM9b+ias5EbgRYFgQZc8z1v6Jqzkdt4u8YCXbgPCBSB0tDkDjgIgRYFgQZc8z1v6Jqzkdu4oQJduA8IFIHGbIxwgwJGIjcC7QoCDbjmaeiAgwJGQqB6EGjANU9DBxwUMBIC1YNAA655GjrgoICREKgeBBpwzdPQAQcFjIRA9SDQgGuehg44KGAkBKoHgQZc8zR0wEEBIyFQPQg04JqnoQMOChgJgepBoAHXPA0dcFDASJ65xR9XQqAINGZjhBsUMBK5EWhXEGjANU9DBxwUMFL13AVaddax5TZdFgQacM3T0AEHBYxUPXe53VQEej6PPr42HL79BQL1GRQwErkDDkKgRakn0B/eHTa89CUCdRkUMBK5Aw6qHqlbx3b6rQDUE+iN4StfjB5cH77yHQL1GBQwErkDDkKgRakm0PvXJvueP7z74q8QqMeggJHIHXAQAi1KNYF+O3y1/foOAvUYFDASuQMOqh6p0xulCPQ8bgx/Mfn6fSvSQwVqfKEsVF5gToMCRiJ3wEExBRqQ2AJ9dL09dL9/bfYm6E9aum1QXW4A6BMunkOgAPBjxMVzNQS6fiFTt13nc/arC2y0GpnDU3kVVF6CQKDr1zEVeVYFNlqNzOGpvAoqLwGBxiNzeCqvgspLqCVQ97Pw5zyrAhutRubwVF4FlZdQTaCz6z/DXQcaj8zhqbwKKi+hmkDDfhIpHpnDU3kVVF5CNYE+uj58OeRn4eOROTyVV0HlJVQT6OhB0LsxxSNzeCqvgspLqCfQ0YOPx/58e33/E4FukDk8lVdB5SVUFOguijyrAhutRubwVF4FlZeAQOOROTyVV0HlJSDQeGQOT+VVUHkJCDQemcNTeRVUXgICjUfm8FReBZWXgEDjkTk8lVdB5SUg0HhkDk/lVVB5CQg0HpnDU3kVVF4CAo1H5vBUXgWVl4BA45E5PJVXQeUlINB4ZA5P5VVQeQkINB6Zw1N5FVReAgKNR+bwVF4FlZeAQOOROTyVV0HlJSDQeGQOT+VVUHkJCDQemcNTeRVUXgICjUfm8FReBZWXgEDjkTk8lVdB5SUg0HhkDk/lVVB5CQg0HpnDU3kVVF4CAo1H5vBUXgWVl4BA45E5PJVXQeUlINB4ZA5P5VVQeQkINB6Zw1N5FVReAgKNR+bwVF4FlZeAQOOROTyVV0HlJQQQaAF+8hN1gh8rVF4FlY8AAoWDoPIqqHwEECgcBJVXQeUjgEDhIKi8CiofAQQKB0HlVVD5CCBQOAgqr4LKRwCBwkFQeRVUPgIIFA6Cyqug8hHoiUABAOqDQAEAOoJAAQA6gkABADqCQAEAOoJAAQA6gkABADqCQAEAOpJeoD+8+2r7r0cfXxsO3/5CmuZHwY6SU/+CWGrOCyAgvUBvDNuV9cO7w4aXvtTm+RGwveTUvySGmvMCKEgu0Ec3hrOVdWP4yhejB9eHr3wnTdR7dpWc+pfDVHNeAAW5Bfqv/2U4W1n3r03+1/vDuy/+Spup5+wqOfUvh6nmvAASUgv02+Hwr/+lXVnfzr++o4zUd3aWnPoXw1ZzXgAJuQX68j+Mvm/XzY3hLyZfZ4+hCDtLTv2LYas5L4CE1AJtaNfLo+vtkcv9a7wHVJhtJaf+ZTm35rwAGhAo7AsCrQ8CDUoPBcp1HIXZVnLqX5Zza84LoKGHAuV/wIVhD7Q+7IEGBYHCviDQ+iDQoPRFoJyErAdn4evDWfig9Eags8vfuAyuOFtLTv2Lcn7NeQEk9EagfBCjGltLTv2Lcn7NeQEk9Eagj64PX+ajwFXYWnLqX5Tza84LIKE3Ah094GY0ldhecupfEkPNeQEU9Eegowcfj5fP2/zvtzg7Sk79C2KpOS+AgPQCBQBQgUABADqCQAEAOoJAAQA6gkABADqCQAEAOoJAAQA6gkABADqCQAEAOoJAAQA6gkABADqCQAEAOoJAAQA6gkAhMieDS+P/nr03uLrXrx0PnrpVJhDAMggUInM8MefDK098bhv/1b+9Nf01BAo1QKAQmLP3Lnw0/nLnyOjDmTgRKNQBgUJg2l3P08mBvAHECXVBoBCY06kQjwcv2MYjUKgLAoWYPLwyWMG0D4pAoS4IFGKyW6DNOfmvXxsMnmzeHr35/tH4h5ffbLx5Mh35wkyk4028cPbp0+ORb860+vXrg8GF52+dDKZnpe5OfvuZD+s/PegHCBRi8liBvtF8Z+zAs09mP774+VaB/tlrix9PfnPCE+9PBfrV8m8D7A8ChbjcOZp47mT1+L3R4IWPRnc/nCjz+bEp777WCnb1LHzj4At/dWt0973B9E3U48nwiXWbDd85Gjz1u/H2fm18gwBgHQQKcTmdaXHlMvpGoNNvjA15afaP9mzTukCvtr/RPB4Lc3oy6mQq0NmB/Hi49TpTgBUQKMTlZCK89mLQOWMdtr47HbQ/mX1rQ6DtOaXjVWGOfzB9vLphgH1BoBCX7Z9Davcn10ZuF2h7aD5R5/j3Lq0MPx0f4T/3WdmnAP0GgUJYHl6Z7CGervlySYQN927+5oOnBzsE2l4/OhHo4uFsX3R6CurJN78p/lSgpyBQiMljz8LPH3z19OznXQQ6uappchaeC5mgEwgUYmIR6PSypMtv/P03uw7h1wQ628jJUeOrUgAAAYpJREFU4qzRzQ8mDt7vbk8AUxAoxMQi0PYqptHu90CXBbrxHuh8g78e8Akm6AQChai0dwFtLwZd+f6l2T9a77Wn1R8v0PWz8DuFCmAFgUJUdt2KaYtATyzvgW65DnRxFRR7oNAFBApRae8CerJ+K6aNQ/ibzec1Jy5slHj2zS6BtuPnn0Qa//zCW80Hmd7jPVDoBgKFqGz/HNKyQB+2n3QfPPfrqQJP23dLdwj07Lg96f4/p4/vHM3eYTXeLg9gFQQKUZneBbS9GHSJpfcuJ/daai6Gn51h/2qsxEu3dgl0425MZ59ebi4EfZ4LQaEbCBR+hHDfUPABgcKPhvm59rXPMgF0BYHCj4aT2bmi+el4gMNAoPCjYezNC2+N9z+/OuKyT/ABgcKPh9PZWfeLv1NHgX6AQOFHxL1Pnp78DSTOIIEPCBQAoCMIFACgIwgUAKAjCBQAoCMIFACgIwgUAKAjCBQAoCMIFACgIwgUAKAjCBQAoCMIFACgIwgUAKAjCBQAoCMIFACgI/8fYlEXodcBOJsAAAAASUVORK5CYII=" width="672" /> From the histogram, it can be concluded that not all users are equally active in giving ratings which result in bias from the users to the prediction results.</p>
</div>
<div id="genres-popularity-per-year" class="section level3">
<h3>Genres Popularity per Year</h3>
<p>Genres vs year: 4 genres are chosen for readability: animation, sci-fi, war and western movies.</p>
<pre class="r"><code>genres_popularity %>%
filter(year > 1930) %>%
filter(genres %in% c("War", "Sci-Fi", "Animation", "Western")) %>%
ggplot(aes(x = year, y = number)) +
geom_line(aes(color=genres)) +
scale_fill_brewer(palette = "Paired")+
labs(y=" # genres", x = "years")+
ggtitle("Genres per years") </code></pre>
<p><img 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" width="672" /></p>
<p>From the chart, some popular genres have been plotted to see the trends over the period of time. It can be seen that the most favored genres from 1970 to 2010 are the western genre movies. And the chart of all of the genres is below; the most preferred genre is the drama genre.</p>
<pre class="r"><code>genres_popularity %>%
filter(year > 1930) %>%
ggplot(aes(x = year, y = number)) +
geom_line(aes(color=genres)) +
scale_fill_brewer(palette = "Paired")+
labs(y=" # genres", x = "years")+
ggtitle("Genres per years") </code></pre>
<p><img 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" width="672" /></p>
</div>
<div id="the-effects-of-release-year-genre-on-ratings" class="section level3">
<h3>The Effects of Release Year & Genre on Ratings</h3>
</div>
<div id="rating-vs-release-year" class="section level3">
<h3>Rating vs Release Year</h3>
<p>A clear trend is shown in the below figure: the most recent years have in average lower rating than earlier years.</p>
<pre class="r"><code>#plotting rating vs release year for the movies to see user rating trends.
edx %>% group_by(year) %>%
summarize(rating = mean(rating)) %>%
ggplot(aes(year, rating)) +
geom_point() +
geom_smooth()+
ggtitle("Ratings per Year Release")+
labs(y="Ratings Given",x="Years Movie Release")</code></pre>
<pre><code>## `geom_smooth()` using method = 'loess' and formula 'y ~ x'</code></pre>
<p><img 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" width="672" /></p>
<p>The graph above depicts the trend of user ratings per year released, it can be inferred that in recent years, the lower ratings are given than the late 1930 years. It can be understood that movies at that time were of low quality as there are so many constraints at that moment.</p>
<pre class="r"><code>#plotting rating vs release year for the movies to see user rating trends.
split_edx %>% group_by(genres) %>%
summarize(n = n(), avg = mean(rating), se = sd(rating)/sqrt(n())) %>%
mutate(genres = reorder(genres, avg)) %>%
ggplot(aes(x = genres, y = avg, ymin = avg - 2*se, ymax = avg + 2*se)) +
geom_point() +
geom_errorbar() +
theme(axis.text.x = element_text(angle = 90, hjust = 1))+
ggtitle("Ratings per Genre")+
labs(y="Ratings Given",x="Genre")</code></pre>
<p><img 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" width="672" /></p>
<p>This depicts the rating given according to the genre. It can be seen on the histogram that the highest median is Film-Noir genre and the genre lowest median is Horror.</p>
</div>
</div>
<div id="model-development-preparation" class="section level2">
<h2>Model Development : Preparation</h2>
<pre class="r"><code>#Initiate RMSE results to compare various models
rmse_results <- data_frame()</code></pre>
<pre><code>## Warning: `data_frame()` is deprecated as of tibble 1.1.0.
## Please use `tibble()` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_warnings()` to see where this warning was generated.</code></pre>
<div id="mean-ratings" class="section level3">
<h3>Mean Ratings</h3>
<p>The initial step is to compute the dataset’s mean rating.</p>
<pre class="r"><code>mu <- mean(edx$rating)
mu</code></pre>
<pre><code>## [1] 3.512465</code></pre>
</div>
<div id="movie-effect" class="section level3">
<h3>Movie Effect</h3>
<p>In model development, the most basic step to start with is the mean, for this dataset the mean rating is 3.5(3.512465). Considering the movie bias, the histogram of the ratings distribution can be seen skewed because one of factors of the effect of the bias can be take into account by finding the penalty term: B_I = mean(rating-mean(rating))</p>
<pre class="r"><code>#taking into account the movie effect cause by the bias
movie_avgs_norm <- edx %>%
group_by(movieId) %>%
summarize(b_i = mean(rating - mu))
#plotting graph for movie effexts
movie_avgs_norm %>% qplot(b_i, geom ="histogram", bins = 20, data = ., color = I("black"))+
ggtitle("Movie Effect")+
labs(y="# Movie", x="Effect(rating-mean)")</code></pre>
<p><img 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" width="672" /></p>
<p>###User Effect</p>
<p>Another feature discovered from the EDA is the user bias, different users rate movies differently according to your perspective. Picky users may rate a good movie movie badly or vice versa because they do not care for the assessment of the movie. The bias can be empirically calculated through the penalty term of: B_U = mean(rating - mu - B_I)</p>
<pre class="r"><code>#taking user effects into account
user_avgs_norm <- edx %>%
left_join(movie_avgs_norm, by='movieId') %>%
group_by(userId) %>%
summarize(b_u = mean(rating - mu - b_i))
#plotting graph for user effects
user_avgs_norm %>% qplot(b_u, geom ="histogram", bins = 30, data = ., color = I("black"))+
ggtitle("User Effect")+
labs(y="# Users", x="User Effect(B-U)")</code></pre>
<p><img 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" width="672" /></p>
</div>
</div>
<div id="model-development-creation" class="section level2">
<h2>Model Development: Creation</h2>
<p>The quality of the model will be assessed by the RMSE (the lower the better).</p>
<div id="baseline-model" class="section level3">
<h3>Baseline Model</h3>
<p>For model building process, RMSE will be used to measure the accuracy or quality of a model. It is expected that models with lower RMSE have better quality. First, a base model is developed to act as the foundation of models that are to be developed. Base model does a simple method by ignoring all features and takes mean into consideration as a prediction value.</p>
<pre class="r"><code>#model creation part
#creating base model
#rmse(rating,mu)- taking mean as prediction
baseline_rmse <- RMSE(validation_CM$rating,mu)
## Test results based on simple prediction
baseline_rmse</code></pre>
<pre><code>## [1] 1.061202</code></pre>
<pre class="r"><code>## Check results
rmse_results <- data_frame(method = "Using mean only", RMSE = baseline_rmse)
rmse_results</code></pre>
<pre><code>## # A tibble: 1 x 2
## method RMSE
## <chr> <dbl>
## 1 Using mean only 1.06</code></pre>
</div>
<div id="movie-effect-model" class="section level3">
<h3>Movie Effect Model</h3>
<p>The next model will take into account the movie bias, Movie Effect model is an improved version of the baseline model which will make use of the b_i penalty described in the preparation stage. This model eliminated the bias from the movie. By using a simple math formula for predicting, adding mean with the penalty term.</p>
<pre class="r"><code># Movie effects only
predicted_ratings_movie_norm <- validation %>%
left_join(movie_avgs_norm, by='movieId') %>%
mutate(pred = mu + b_i)
model_movie_rmse <- RMSE(validation_CM$rating,predicted_ratings_movie_norm$pred)
rmse_results <- bind_rows(rmse_results,
data_frame(method="Movie Effect Model",
RMSE = model_movie_rmse ))
rmse_results %>% knitr::kable()</code></pre>
<table>
<thead>
<tr class="header">
<th align="left">method</th>
<th align="right">RMSE</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="left">Using mean only</td>
<td align="right">1.0612018</td>
</tr>
<tr class="even">
<td align="left">Movie Effect Model</td>
<td align="right">0.9439087</td>
</tr>
</tbody>
</table>
<pre class="r"><code>rmse_results</code></pre>
<pre><code>## # A tibble: 2 x 2
## method RMSE
## <chr> <dbl>
## 1 Using mean only 1.06
## 2 Movie Effect Model 0.944</code></pre>
</div>
<div id="movie-and-user-effect-model" class="section level3">
<h3>Movie and User Effect Model</h3>
<p>In this model, b_u and b_i are taken into consideration to eliminate the biases from both parties: user and model.</p>
<pre class="r"><code># Use test set,join movie averages & user averages
# Prediction equals the mean with user effect b_u & movie effect b_i
predicted_ratings_user_norm <- validation %>%
left_join(movie_avgs_norm, by='movieId') %>%
left_join(user_avgs_norm, by='userId') %>%
mutate(pred = mu + b_i + b_u)
# test and save rmse results
model_mnu_rmse <- RMSE(validation_CM$rating,predicted_ratings_user_norm$pred)
rmse_results <- bind_rows(rmse_results,
data_frame(method="Movie and User Effect Model",
RMSE = model_mnu_rmse ))
rmse_results %>% knitr::kable()</code></pre>
<table>
<thead>
<tr class="header">
<th align="left">method</th>
<th align="right">RMSE</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="left">Using mean only</td>
<td align="right">1.0612018</td>
</tr>
<tr class="even">
<td align="left">Movie Effect Model</td>
<td align="right">0.9439087</td>
</tr>
<tr class="odd">
<td align="left">Movie and User Effect Model</td>
<td align="right">0.8653488</td>
</tr>
</tbody>
</table>
<pre class="r"><code>rmse_results</code></pre>
<pre><code>## # A tibble: 3 x 2
## method RMSE
## <chr> <dbl>
## 1 Using mean only 1.06
## 2 Movie Effect Model 0.944
## 3 Movie and User Effect Model 0.865</code></pre>
</div>
<div id="regularized-movie-and-user-effect-model" class="section level3">
<h3>Regularized Movie and User Effect Model</h3>
<p>Using the concept of regularization, this model takes into account low ratings’ number effects from users and movies. In the previous section, it showed that the ratings given are not consistent by the users, which will strongly affect the prediction, so regularization helps to reduce the overfitting effect.</p>
<pre class="r"><code># Use cross-validation to choose lmabda.
lambdas <- seq(0, 10, 0.25)
# For each lambda,find b_i & b_u, followed by rating prediction & testing
# note:the below code could take some time
rmses <- sapply(lambdas, function(l){
mu <- mean(edx$rating)
b_i <- edx %>%
group_by(movieId) %>%
summarize(b_i = sum(rating - mu)/(n()+l))
b_u <- edx %>%
left_join(b_i, by="movieId") %>%
group_by(userId) %>%
summarize(b_u = sum(rating - b_i - mu)/(n()+l))
predicted_ratings <- validation %>%
left_join(b_i, by = "movieId") %>%
left_join(b_u, by = "userId") %>%
mutate(pred = mu + b_i + b_u) %>%
.$pred
return(RMSE(validation_CM$rating,predicted_ratings))
})
# Plot rmses vs lambdas to select the optimal lambda
qplot(lambdas, rmses) </code></pre>
<p><img src="data:image/png;base64,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" width="672" /></p>
<pre class="r"><code>lambda <- lambdas[which.min(rmses)]
lambda</code></pre>
<pre><code>## [1] 5.25</code></pre>
<pre class="r"><code># Compute regularized estimates of b_i using lambda
movie_avgs_reg <- edx %>%
group_by(movieId) %>%
summarize(b_i = sum(rating - mu)/(n()+lambda), n_i = n())
# Compute regularized estimates of b_u using lambda
user_avgs_reg <- edx %>%
left_join(movie_avgs_reg, by='movieId') %>%
group_by(userId) %>%
summarize(b_u = sum(rating - mu - b_i)/(n()+lambda), n_u = n())
# Predict ratin gs
predicted_ratings_reg <- validation %>%
left_join(movie_avgs_reg, by='movieId') %>%
left_join(user_avgs_reg, by='userId') %>%
mutate(pred = mu + b_i + b_u) %>%
.$pred
# Test and save results
model_regmnu_rmse <- RMSE(validation_CM$rating,predicted_ratings_reg)
rmse_results <- bind_rows(rmse_results,
data_frame(method="Regularized Movie and User Effect Model",
RMSE = model_regmnu_rmse ))
rmse_results %>% knitr::kable()</code></pre>
<table>
<thead>
<tr class="header">
<th align="left">method</th>
<th align="right">RMSE</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="left">Using mean only</td>
<td align="right">1.0612018</td>
</tr>
<tr class="even">
<td align="left">Movie Effect Model</td>
<td align="right">0.9439087</td>
</tr>
<tr class="odd">
<td align="left">Movie and User Effect Model</td>
<td align="right">0.8653488</td>
</tr>
<tr class="even">
<td align="left">Regularized Movie and User Effect Model</td>
<td align="right">0.8648170</td>
</tr>
</tbody>
</table>
<pre class="r"><code>rmse_results</code></pre>
<pre><code>## # A tibble: 4 x 2
## method RMSE
## <chr> <dbl>
## 1 Using mean only 1.06
## 2 Movie Effect Model 0.944
## 3 Movie and User Effect Model 0.865
## 4 Regularized Movie and User Effect Model 0.865</code></pre>
</div>
<div id="regularized-movie-user-year-and-genre-effects-model" class="section level3">
<h3>Regularized Movie, User, Year and Genre Effects Model</h3>
<p>This model improved all the previous models and utilizes the genre and rating effects too</p>
<pre class="r"><code># b_y and b_g represent the year & genre effects, respectively
lambdas <- seq(0, 20, 1)
# Note: the below code could take some time
rmses <- sapply(lambdas, function(l){
mu <- mean(edx$rating)
b_i <- split_edx %>%
group_by(movieId) %>%
summarize(b_i = sum(rating - mu)/(n()+l))
b_u <- split_edx %>%
left_join(b_i, by="movieId") %>%
group_by(userId) %>%
summarize(b_u = sum(rating - b_i - mu)/(n()+l))
b_y <- split_edx %>%
left_join(b_i, by='movieId') %>%
left_join(b_u, by='userId') %>%
group_by(year) %>%
summarize(b_y = sum(rating - mu - b_i - b_u)/(n()+lambda), n_y = n())
b_g <- split_edx %>%
left_join(b_i, by='movieId') %>%
left_join(b_u, by='userId') %>%
left_join(b_y, by = 'year') %>%
group_by(genres) %>%
summarize(b_g = sum(rating - mu - b_i - b_u - b_y)/(n()+lambda), n_g = n())
predicted_ratings <- split_valid %>%
left_join(b_i, by='movieId') %>%
left_join(b_u, by='userId') %>%
left_join(b_y, by = 'year') %>%
left_join(b_g, by = 'genres') %>%
mutate(pred = mu + b_i + b_u + b_y + b_g) %>%
.$pred
return(RMSE(split_valid_CM$rating,predicted_ratings))
})
# Compute new predictions using the optimal lambda
# Test and save results
lamplot2 <- qplot(lambdas, rmses)
lambda_2 <- lambdas[which.min(rmses)]
lambda_2</code></pre>
<pre><code>## [1] 14</code></pre>
<pre class="r"><code>movie_reg_avgs_2 <- split_edx %>%
group_by(movieId) %>%
summarize(b_i = sum(rating - mu)/(n()+lambda_2), n_i = n())
user_reg_avgs_2 <- split_edx %>%
left_join(movie_reg_avgs_2, by='movieId') %>%
group_by(userId) %>%
summarize(b_u = sum(rating - mu - b_i)/(n()+lambda_2), n_u = n())
year_reg_avgs <- split_edx %>%
left_join(movie_reg_avgs_2, by='movieId') %>%
left_join(user_reg_avgs_2, by='userId') %>%
group_by(year) %>%
summarize(b_y = sum(rating - mu - b_i - b_u)/(n()+lambda_2), n_y = n())
genre_reg_avgs <- split_edx %>%
left_join(movie_reg_avgs_2, by='movieId') %>%
left_join(user_reg_avgs_2, by='userId') %>%
left_join(year_reg_avgs, by = 'year') %>%
group_by(genres) %>%
summarize(b_g = sum(rating - mu - b_i - b_u - b_y)/(n()+lambda_2), n_g = n())
predicted_ratings <- split_valid %>%
left_join(movie_reg_avgs_2, by='movieId') %>%
left_join(user_reg_avgs_2, by='userId') %>%
left_join(year_reg_avgs, by = 'year') %>%
left_join(genre_reg_avgs, by = 'genres') %>%
mutate(pred = mu + b_i + b_u + b_y + b_g) %>%
.$pred
model_regmnug_rmse <- RMSE(split_valid_CM$rating,predicted_ratings)
rmse_results <- bind_rows(rmse_results,
data_frame(method="Reg Movie, User, Year, and Genre Effect Model",
RMSE = model_regmnug_rmse ))
rmse_results %>% knitr::kable()</code></pre>
<table>
<thead>
<tr class="header">
<th align="left">method</th>
<th align="right">RMSE</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="left">Using mean only</td>