Research Questions
What are the best predictors for IMDb rating score?
In this project I want to explore the relation between Rotten Tomatoes and IMDb rating systems. The question is of interest to me because Rotten Tomatoes and IMDb are two of the most popular movie review websites. However, the two platforms use different rating systems. I would like to see how well a model built using movies data from Rotten Tomatoes, would predict the rating score in IMDb rating system.
- Rotten Tomatoes rating variables : critics_score, critics_rating, audience_score, and audience_rating
- IMDb rating variable: imdb_rating
- Movie information variables : runtime, best_actress_win, best_actor_win, best_dir_win, best_pic_win, and top200_box, and title_type
About the Data:
The data set is comprised of 651 randomly sampled movies produced and released before 2016, collected from Rotten Tomatoes and IMDb.
Exploratory Data Analysis
#select the variables
mvs <- movies %>%
select(imdb_rating, critics_score,critics_rating, audience_score, audience_rating,
runtime, best_actress_win, best_actor_win, best_dir_win, best_pic_win,
top200_box, title_type) %>%
filter(!is.na(runtime))
#create new variable won_oscar, did the movie won any type of Oscar?
mvs <- mvs %>%
mutate(won_oscar = ifelse(best_actress_win == "yes" |
best_actor_win == "yes" |
best_pic_win == "yes" |
best_dir_win == "yes", "yes", "no" ))
mvs$won_oscar <- factor(mvs$won_oscar, levels = c("yes", "no"))
mvs$top200_box <- factor(mvs$top200_box, levels = c("yes", "no"))
#view data summary
summary(mvs)## imdb_rating critics_score critics_rating audience_score
## Min. :1.900 Min. : 1.00 Certified Fresh:135 Min. :11.00
## 1st Qu.:5.900 1st Qu.: 33.00 Fresh :208 1st Qu.:46.00
## Median :6.600 Median : 61.00 Rotten :307 Median :65.00
## Mean :6.492 Mean : 57.65 Mean :62.35
## 3rd Qu.:7.300 3rd Qu.: 83.00 3rd Qu.:80.00
## Max. :9.000 Max. :100.00 Max. :97.00
## audience_rating runtime best_actress_win best_actor_win best_dir_win
## Spilled:275 Min. : 39.0 no :578 no :557 no :607
## Upright:375 1st Qu.: 92.0 yes: 72 yes: 93 yes: 43
## Median :103.0
## Mean :105.8
## 3rd Qu.:115.8
## Max. :267.0
## best_pic_win top200_box title_type won_oscar
## no :643 yes: 15 Documentary : 54 yes:171
## yes: 7 no :635 Feature Film:591 no :479
## TV Movie : 5
##
##
## ggplot( mvs, aes(x = won_oscar , y = imdb_rating, fill = won_oscar)) +
geom_boxplot() +
labs(title = "IMDb Rating Distribustion & Wining an Oscar",
x = "Won Oscar",
y = "IMDb Rating",
fill = "Won Oscar?") +
theme(plot.title = element_text(hjust = 0.5),
legend.position = "none")
The above plot shows the distribution of IMDb ratings for movies that won and did not win Oscar. Both the distributions are left skewed. Oscar wining movies have less variation compared to non wining movies.
ggplot( mvs, aes(x = top200_box, y = imdb_rating, fill = top200_box)) +
geom_boxplot() +
labs(title = "IMDb Rating Distribustion & Top 200 Box Office",
x = "Top 200 Box Office?",
y = "IMDb Rating") +
theme(plot.title = element_text(hjust = 0.5),
legend.position = "none")
It seems that movies that made it to the top 200 Box office have higher median and nearly normal distribution of IMDb ratings. Meanwhile, movies that did not make it to the top 200 have more spread of ratings.
ggplot(mvs, aes( x = title_type, y = imdb_rating, fill = title_type)) +
geom_boxplot() +
labs(title = "IMDb Rating Distribustion & Type Of The Movie",
x = "Movie Type",
y = "IMDb Rating") +
theme(plot.title = element_text(hjust = 0.5),
legend.position = "none")
From the summary statistics done earlier, there are only 5 observations for TV movies. hence the shape of the distribution might not be accurate. Documentary distribution has the highest ratings and the least spread among other types of movies.
ggpairs(mvs, columns = c("critics_score", "audience_score", "imdb_rating", "runtime"),
progress = FALSE)
ggplot(mvs, aes(x = critics_score, y = audience_score)) +
geom_point() +
geom_smooth(method = "lm") +
labs(title = "Audience Score Vs Critics Score",
x = "Critics Score",
y = "Audience Score") +
theme(plot.title = element_text(hjust = 0.5))## `geom_smooth()` using formula 'y ~ x'
The above two plots shows strong correlation between audience score and critics score. In order to avoid collinearity, only one of the two variables will be used in the model. The choise will be based on whichever gives higher R-Squared.
Modeling
Backward elimination method will be used to select the best model (Parsimonious model). Since we are interested on prediction the R-squared will be used as the selection criterion.
Full Model
For the full model we consider all the variables explored earlier, excluding critics score to avoid collinearity. Moreover, the two variables audience_rating and critics_rating are added to the model.
frmla <- as.formula(imdb_rating ~ audience_score + runtime + title_type +
won_oscar + critics_rating + audience_rating + top200_box)
full.mdl <- lm(frmla, data = mvs )
summary(full.mdl)##
## Call:
## lm(formula = frmla, data = mvs)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.71909 -0.18752 0.04147 0.28859 1.17830
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.596917 0.233534 15.402 < 2e-16 ***
## audience_score 0.047818 0.002098 22.793 < 2e-16 ***
## runtime 0.006327 0.001102 5.743 1.44e-08 ***
## title_typeFeature Film -0.297373 0.076796 -3.872 0.000119 ***
## title_typeTV Movie -0.428371 0.234120 -1.830 0.067759 .
## won_oscarno -0.079322 0.047402 -1.673 0.094742 .
## critics_ratingFresh -0.068084 0.056873 -1.197 0.231704
## critics_ratingRotten -0.377054 0.063351 -5.952 4.37e-09 ***
## audience_ratingUpright -0.425180 0.078700 -5.403 9.28e-08 ***
## top200_boxno 0.021510 0.132559 0.162 0.871147
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4956 on 640 degrees of freedom
## Multiple R-squared: 0.7942, Adjusted R-squared: 0.7913
## F-statistic: 274.4 on 9 and 640 DF, p-value: < 2.2e-16Model Selection
After performing the backward elimination the following model is chosen based on Adjusted R-squared value. The final model eliminated the variable top200_box.
#final model
frmla <- as.formula(imdb_rating ~ audience_score + runtime + title_type +
won_oscar + critics_rating + audience_rating)
final.mdl <- lm(frmla, data = mvs )
summary(final.mdl)##
## Call:
## lm(formula = frmla, data = mvs)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.71894 -0.18747 0.04048 0.28851 1.17835
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.619590 0.186975 19.359 < 2e-16 ***
## audience_score 0.047818 0.002096 22.810 < 2e-16 ***
## runtime 0.006310 0.001096 5.759 1.31e-08 ***
## title_typeFeature Film -0.298054 0.076623 -3.890 0.000111 ***
## title_typeTV Movie -0.428820 0.233926 -1.833 0.067244 .
## won_oscarno -0.079379 0.047365 -1.676 0.094246 .
## critics_ratingFresh -0.066842 0.056313 -1.187 0.235678
## critics_ratingRotten -0.375838 0.062858 -5.979 3.73e-09 ***
## audience_ratingUpright -0.425374 0.078631 -5.410 8.92e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4952 on 641 degrees of freedom
## Multiple R-squared: 0.7942, Adjusted R-squared: 0.7916
## F-statistic: 309.2 on 8 and 641 DF, p-value: < 2.2e-16Audience_score Slope: all else held constant, for each 1% increase in audience score the model predicts the IMDb rating to be higher on average by 0.048 rating score.
- Title type Slope:
- All else held constant, the model predict that feature films ratings are on average 0.298 rating score lower than documentary movies.
- All else held constant, the model predict that TV movies ratings are on average 0.429 rating score lower than documentary movies.
- Won Oscar slope:
- All else held constant, the model predict that non Oscar wining movies ratings are on average 0.079 rating score lower than documentary movies.
- Critics rating Slope:
- All else held constant, the model predict that movies rated Fresh by critics are on average 0.067 rating score lower than Certified Fresh rated movies.
- All else held constant, the model predict that movies rated Rotten by critics are on average 0.376 rating score lower than Certified Fresh rated movies.
- Audience rating Slope:
- All else held constant, the model predict that movies rated Upright by Audience are on average 0.425 rating score lower than Certified Fresh rated movies.
Here we examine the conditions of multiple linear regression.
- Linear Relationship between audience score and IMDb rating
- Nearly normal residuals with mean 0
- Constant Variability of residuals
- Independent residuals
We notice that the lower tail have more negative residuals. Since the residuals are not randomly scattered around zero. This condition has not been met.
The distribution of residuals is centered around zero. However, there is a left skew in the distribution. Moreover, the probability plot shows huge deviation from the mean at the tail area. Hence, this condition is weakly satisfied.
The variability of the residuals decreases as the fitted values increases. Hence this condition is not satisfied.
It seems there is no time-series pattern. Hence, this conditions is met.
Prediction
Now we will see how does the model predict the IMDb rating for the movie “Arrival”
#create the movie data frame, IMDb rating : 7.9
film <- data.frame(runtime = 116,
title_type = "Feature Film",
won_oscar = "no",
audience_score = 82,
critics_rating = "Certified Fresh",
audience_rating = "Upright")
predict(final.mdl, film)## 1
## 7.469787
The model predicts an IMDb rating score of 7.5 for the provided movie information.
Prediction Interval
## fit lwr upr
## 1 7.469787 6.49277 8.446804
interpretation:
the model predicts, with 95% confidence, that a Feature movie with a Rotten Tomatoes audience score of 82, critics rating of “Certified Fresh”, audience rating of “Upright”, and no Oscar award is expected to have an IMDb rating score between 6.5 and 8.4.
Reference for the movie data:
https://www.rottentomatoes.com/m/arrival_2016
https://www.imdb.com/title/tt2543164/
Conclusion
Although the predicted value for the given movie was far from the true value. The model did not satisfy most of the condition. the model showed high inconsistency of residuals.This is probably due to the nature of relationship between the response variable and the explanatory numerical variable audience score.Although the two variables are highly correlated, it seems their relationship might not be linear.
Moreover, many of the used variables in the model are highly related to each other, for example, the audience rating is actually based the audience score. Therefore, the model might be overfitted.
Ideas for future research: Using a larger sample in the future would reveal the true nature of the relationship between the variables. Moreover, it might help the model to satisfy some of the conditions.