About Dataset

The IMDB dataset contains information about movies, including their names, release dates, user ratings, genres, overviews, cast and crew members, original titles, production status, original languages, budgets, revenues, and countries of origin. This data can be used for various analyses, such as identifying trends in movie genres, exploring the relationship between budget and revenue, and predicting the success of future movies.

# Load the lubridate package
library(lubridate)

## 
## Attaching package: 'lubridate'

## The following objects are masked from 'package:base':
## 
##     date, intersect, setdiff, union

library(plyr)
library(plotly)

## Loading required package: ggplot2

## 
## Attaching package: 'plotly'

## The following object is masked from 'package:ggplot2':
## 
##     last_plot

## The following objects are masked from 'package:plyr':
## 
##     arrange, mutate, rename, summarise

## The following object is masked from 'package:stats':
## 
##     filter

## The following object is masked from 'package:graphics':
## 
##     layout

library(ggplot2)
library(dplyr)

## 
## Attaching package: 'dplyr'

## The following objects are masked from 'package:plyr':
## 
##     arrange, count, desc, failwith, id, mutate, rename, summarise,
##     summarize

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

library(readr)
library(car) # for VIF

## Loading required package: carData

## 
## Attaching package: 'car'

## The following object is masked from 'package:dplyr':
## 
##     recode

library(repr)

## Warning: package 'repr' was built under R version 4.3.2

library(tsibble)

## Warning: package 'tsibble' was built under R version 4.3.2

## 
## Attaching package: 'tsibble'

## The following object is masked from 'package:lubridate':
## 
##     interval

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, union

movieData <-read.csv('C:/Users/govin/OneDrive/Desktop/RStudio/Data/imdb_movies.csv')

movieData$date_x <- sapply(movieData$date_x, function(x) gsub("/", "-", x))
movieData[c('date_x')] <- lapply(movieData[c('date_x')], function(x) as.Date(x, format="%m-%d-%Y"))
movieData <- type_convert(movieData)

## 
## ── Column specification ────────────────────────────────────────────────────────
## cols(
##   names = col_character(),
##   genre = col_character(),
##   overview = col_character(),
##   crew = col_character(),
##   orig_title = col_character(),
##   status = col_character(),
##   orig_lang = col_character(),
##   country = col_character()
## )

Questions to ask from this Data

What is the trend of Movie budgets?

Do bigger budget movies get bigger revenues?

Which country spends most on movies?

Do movies with high imdb scores run well in theaters?

Revenue_country_wise <- aggregate(movieData$revenue, list(movieData$country), FUN=mean)
Revenue_country_wise <- Revenue_country_wise[order(Revenue_country_wise$x, decreasing = TRUE), ]
print(Revenue_country_wise)

##    Group.1         x
## 36      MU 728608266
## 22      GT 655664752
## 5       BO 638332463
## 44      PR 545316308
## 35      LV 542233172
## 12      CO 534571540
## 37      MX 469644985
## 1       AR 456560785
## 54      TW 451275064
## 30      IS 443980387
## 43      PL 440802594
## 32      JP 408106272
## 16      DO 400066522
## 52      TH 381085420
## 10      CL 376139634
## 24      HU 370750873
## 39      NL 369452979
## 6       BR 367192509
## 41      PE 361959154
## 14      DE 358353693
## 31      IT 357659815
## 46      PY 356935817
## 34      KR 350030132
## 17      ES 345563529
## 53      TR 337170686
## 49      SG 333077714
## 42      PH 331340101
## 23      HK 330804782
## 4       BE 328309975
## 13      CZ 316265039
## 25      ID 313651704
## 48      SE 312184372
## 19      FR 305631854
## 9       CH 297093649
## 11      CN 296076152
## 20      GB 295877850
## 28      IN 285128163
## 26      IE 270712673
## 56      US 270571053
## 27      IL 254504167
## 8       CA 253273459
## 15      DK 239348748
## 47      RU 220233805
## 40      NO 209286725
## 60      ZA 208272848
## 58      VN 206250037
## 29      IR 193600405
## 3       AU 192945447
## 57      UY 179105223
## 51      SU 177365780
## 7       BY 175269999
## 33      KH 175269999
## 50      SK 175269999
## 21      GR 154849503
## 55      UA 127479530
## 2       AT  72282768
## 18      FI  66214266
## 59      XC  23146523
## 38      MY  22443973
## 45      PT   1240262

We can see MU has highest avg revenue

Analysis of budget

movieData$decade <- year(movieData$date_x)%/%10 * 10
ggplot(movieData, aes(x = decade, y = budget_x)) + 
geom_point() +
geom_jitter() +
geom_smooth()

## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

Plotting helps us understand that movie budgets have been gradually increasing over the years.By regression we can expect this trend to continue.

Relation between movies and their revenue

options(repr.plot.width = 10, repr.plot.height = 10)

ggplot(movieData, aes(x = budget_x, y = revenue, color = decade)) + 
geom_point() + 
geom_jitter() +
geom_smooth()

## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

## Warning: The following aesthetics were dropped during statistical transformation: colour
## ℹ This can happen when ggplot fails to infer the correct grouping structure in
##   the data.
## ℹ Did you forget to specify a `group` aesthetic or to convert a numerical
##   variable into a factor?

## With few outliers we can see a direct correlation between movies and their revenue.

Rise of foreign languages

options(repr.plot.width = 20, repr.plot.height = 100)

ggplot(movieData, aes(x = budget_x, y = country, color = decade)) + 
geom_point() + 
geom_jitter() +
geom_smooth()

## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

## Warning: Computation failed in `stat_smooth()`
## Caused by error in `gam.reparam()`:
## ! NA/NaN/Inf in foreign function call (arg 3)

Aside from predominantly hollywood entries, one other language seems to break the charts.Lets enquire.

options(repr.plot.width = 10, repr.plot.height = 10)

ggplot(filter(movieData, orig_lang == "Korean" | orig_lang == "English"), aes(x = budget_x, y = revenue, color = orig_lang)) + 
geom_point() + 
geom_jitter() +
geom_smooth()

## `geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'

options(repr.plot.width = 16, repr.plot.height = 16)

movieData$year <- year(movieData$date_x)

ggplot(filter(movieData, orig_lang == "Korean"), aes(x = year)) + 
geom_bar()

## Korean movies seem to be gaining in popularity

Back to the bigger picture:

Is there a relation between IMDB score and revenue?

options(repr.plot.width = 16, repr.plot.height = 16)

ggplot(movieData, aes(x = score, y = revenue, color = decade)) + 
geom_point() + 
geom_jitter()

#### There is good correlation between the movie’s IMDB rating and its collection at box office. It seems after a threshold, there is no direct correlation

Visual Summaries of distributions

# Creating a histogram
hist(movieData$revenue, 
     main = "Distribution of Revenue",  
     xlab = "Revenue",              # X-axis label
     ylab = "Frequency",          # Y-axis label
     col = "green",                # Bar color
     border = "black",            # Border color
     breaks = 20,
     freq = FALSE)                 # Number of bins or breaks

# Displaying density also
lines(density(movieData$revenue), col = "black", lwd = 2)

# Creating a histogram
hist(movieData$budget, 
     main = "Distribution of Budget",  
     xlab = "Budget",              # X-axis label
     ylab = "Frequency",          # Y-axis label
     col = "orange",                # Bar color
     border = "black",            # Border color
     breaks = 20,
     freq = FALSE)                 # Number of bins or breaks

# Displaying density also
lines(density(movieData$revenue), col = "black", lwd = 2)

# Creating a histogram
hist(movieData$score, 
     main = "Distribution of Score",  
     xlab = "Score",              # X-axis label
     ylab = "Frequency",          # Y-axis label
     col = "violet",                # Bar color
     border = "black",            # Border color
     breaks = 20,
     freq = FALSE)                 # Number of bins or breaks

# Displaying density also
lines(density(movieData$revenue), col = "black", lwd = 2)

Lets look at an even bigger picture and see how each variable correlates with each other

Correlation Heatmap for continuous variables

library(ggplot2)
library(reshape2)
numeric_data <- unlist(lapply(movieData, is.numeric))  
data_num <- movieData[ , numeric_data]                        #Subsetting numeric columns of data
movieData_corr <- cor(data_num)

heatmap_plot <- ggplot(data = melt(movieData_corr), aes(x = Var1, y = Var2, fill = value)) +
  geom_tile() +
  geom_text(aes(label = round(value, 2)), vjust = 1) +  
  labs(title = "Correlation Heatmap for continuous variables", x = "Features", y = "Features", fill = "Correlation")

# Print the heatmap
print(heatmap_plot)

This shows overrall correlation between variables. We can see the obvious correlations.

# country Vs revenue column
ggplot(movieData, aes(x = country, y = revenue)) +
  geom_boxplot() +
  labs(x = "Country", y = "Revenue") +
  ggtitle("Box Plot of Country vs. Revenue") +
  theme(axis.text.x = element_text(angle = 90, hjust = 1)) +
  coord_flip() +
  theme(plot.margin = margin(1, 4, 1, 1, "cm"))

This box plot can tell us the high and lows of revenues, its range and certain outliers.

movieData <- movieData %>%
  mutate(profit = revenue - budget_x)

ggplot(data = movieData, mapping = aes(x = budget_x, y = revenue)) + 
  geom_point() +
  geom_smooth(method="lm") +
  labs(title="Budget vs Revenue",
       x="Budget",
       y="Revenue")

## `geom_smooth()` using formula = 'y ~ x'

These scatter plots show a positive relationship between the budget allocated for movies and their revenue. As the budget increases, the revenue tends to increase as well. This trend is suggested by the upward direction of the linear regression line.

cor(movieData$budget_x, movieData$revenue)

## [1] 0.6738296

ggplot(data = movieData, mapping = aes(x = budget_x, y = profit)) + 
  geom_point() +
  geom_smooth(method="lm") +
  labs(title="Budget vs Profit",
       x="Budget",
       y="Profit")

## `geom_smooth()` using formula = 'y ~ x'

Lets try and compute the confidence intervals for Movie Ratings and Revenues

revenue_mean <- mean(movieData$revenue)
revenue_mean

## [1] 253140093

revenue_sd <- sd(movieData$revenue)
revenue_sd

## [1] 277788049

margin_error <- qnorm(0.975) * (revenue_sd / sqrt(nrow(movieData)))
margin_error

## [1] 5396727

lower <- revenue_mean - margin_error 
upper <- revenue_mean + margin_error

paste0("95% CI: [",lower, ", ", upper,"]")

## [1] "95% CI: [247743366.72094, 258536820.11667]"

# Calculate confidence intervals for movie ratings and revenues
rating_CI <- t.test(movieData$score)$conf.int
revenue_CI <- t.test(movieData$revenue)$conf.int

rating_CI

## [1] 63.23403 63.76007
## attr(,"conf.level")
## [1] 0.95

revenue_CI

## [1] 247742725 258537462
## attr(,"conf.level")
## [1] 0.95

For Revenue:

Manual (CI): the 95% CI for movie revenue is approximately [$247,743,366.72, $258,536,820.12]. This interval suggests that we are 95% confident that the true mean revenue of movies falls between these two values.

T-test Calculation: When using t-test function, the 95% CI for revenue is [$247,742,725, $258,537,462]. This CI aligns closely with the manually calculated CI, reinforcing the confidence in the estimated range for the true mean revenue of movies.

For Movie Ratings:

T-test Calculation: The 95% CI for movie ratings is [$63.23403, $63.76007].

Inference: The 95% CI for movie ratings is relatively narrow, indicating a smaller range in which the true mean rating of movies likely lies. The interval suggests that we are 95% confident that the actual mean movie rating falls between approximately 63.23 and 63.76.

options(repr.plot.width=12, repr.plot.height=6)
library(car) # for VIF


movieData <-read.csv('C:/Users/govin/OneDrive/Desktop/RStudio/Data/imdb_movieData.csv')

movieData$date_x <- sapply(movieData$date_x, function(x) gsub("/", "-", x))
movieData[c('date_x')] <- lapply(movieData[c('date_x')], function(x) as.Date(x, format="%m-%d-%Y"))
movieData <- type_convert(movieData)

## 
## ── Column specification ────────────────────────────────────────────────────────
## cols(
##   names = col_character(),
##   genre = col_character(),
##   overview = col_character(),
##   crew = col_character(),
##   orig_title = col_character(),
##   status = col_character(),
##   orig_lang = col_character(),
##   country = col_character()
## )

movieData$date_x <- as.Date(movieData$date_x, format = "%Y-%m-%d")

Exploring Time-based Trends in Movie Releases

Let us move on and apply time series to gather insight from the long period of entries.

We choose the response variable as: Score

# Aggregating data by date and calculating the average score
movie_aggregated <- movieData %>%
  group_by(date_x) %>%
  summarize(average_score = mean(score, na.rm = TRUE))

# Creating a tsibble object
movie_tsibble <- movie_aggregated %>% 
  as_tsibble(index = date_x)

# Plotting data over time
movie_plot <- ggplot(movie_tsibble, aes(x = date_x, y = average_score)) +
  geom_line(color = "#1f77b4", size = 1) +
  geom_point(color = "#ff7f0e", size = 1, alpha = 0.3) + # Reduced alpha for points
  theme_minimal(base_size = 15) + # Larger text in minimal theme
  labs(title = "Average Movie Ratings Over Time",
       subtitle = "Time Series of IMDb Average Movie Ratings",
       x = "Date",
       y = "Average Rating",
       caption = "Data Source: IMDb") +
  theme(
    plot.title = element_text(size = 16, face = "bold"),
    plot.subtitle = element_text(size = 14),
    axis.title = element_text(size = 14, face = "bold"),
    axis.text = element_text(size = 12),
    plot.caption = element_text(size = 10)
  ) +
  scale_x_date(date_breaks = "10 years", date_labels = "%Y") + # Sparser x-axis labels
  scale_y_continuous(breaks = seq(0, 100, by = 10))

## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

# Adjusting plot size and aspect ratio
ggsave("movie_plot.png", movie_plot, width = 12, height = 8, units = "in") # Increase the size

print(movie_plot)

There is a high density of data points in recent years, suggesting an increase in the number of movies being rated.

Running a simple linear regression using the entire dataset to see if there’s an overall trend:

# Linear regression using score as the response variable and date_x as the predictor
linear_model_full <- lm(score ~ date_x, data = movieData)

# Summary of the full model to check for trends and strength
summary(linear_model_full)

## 
## Call:
## lm(formula = score ~ date_x, data = movieData)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -67.716  -4.525   1.763   7.850  38.411 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  6.840e+01  3.590e-01   190.5   <2e-16 ***
## date_x      -3.491e-04  2.375e-05   -14.7   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 13.4 on 10176 degrees of freedom
## Multiple R-squared:  0.02079,    Adjusted R-squared:  0.02069 
## F-statistic:   216 on 1 and 10176 DF,  p-value: < 2.2e-16

Suspecting different trends in different time periods, we would subset the data. Lets test if movie ratings trends are different before and after the year 2000.

# Subset data before the year 2000
movieData_pre2000 <- filter(movieData, date_x < as.Date("2000-01-01"))

# Subset data from the year 2000 onwards
movieData_post2000 <- filter(movieData, date_x >= as.Date("2000-01-01"))

# Linear regression for the first subset
linear_model_pre2000 <- lm(score ~ date_x, data = movieData_pre2000)
summary(linear_model_pre2000)

## 
## Call:
## lm(formula = score ~ date_x, data = movieData_pre2000)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -67.183  -4.628   1.485   6.821  33.940 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  6.807e+01  3.307e-01  205.85   <2e-16 ***
## date_x      -4.529e-04  4.391e-05  -10.31   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 10.77 on 2258 degrees of freedom
## Multiple R-squared:  0.045,  Adjusted R-squared:  0.04457 
## F-statistic: 106.4 on 1 and 2258 DF,  p-value: < 2.2e-16

# Linear regression for the second subset
linear_model_post2000 <- lm(score ~ date_x, data = movieData_post2000)
summary(linear_model_post2000)

## 
## Call:
## lm(formula = score ~ date_x, data = movieData_post2000)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -65.079  -4.619   1.852   8.108  39.232 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  7.454e+01  1.099e+00   67.84   <2e-16 ***
## date_x      -7.057e-04  6.595e-05  -10.70   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 14.02 on 7916 degrees of freedom
## Multiple R-squared:  0.01426,    Adjusted R-squared:  0.01414 
## F-statistic: 114.5 on 1 and 7916 DF,  p-value: < 2.2e-16

Linear regression on the entire dataset suggests a slight negative relationship between movie release year and ratings (R-squared: 2.08%).

Pre-2000, ratings show a stronger negative trend (R-squared: 4.5%)

While post-2000 exhibits a weaker one (R-squared: 1.43%). Statistically significant.

These trends indicate decreasing ratings over time.

The low R-squared values in all models suggest that linear regression might not be the best model to capture the relationship between time and movie ratings.

The p-values indicate that there is a statistically significant relationship between time and movie ratings in all models, but the strength of the relationship is weak.

Using smoothing to detect season

library(forecast)

## Warning: package 'forecast' was built under R version 4.3.2

## Registered S3 method overwritten by 'quantmod':
##   method            from
##   as.zoo.data.frame zoo

# Apply smoothing (e.g., 5-period moving average) to the 'score' column
movieData_smoothed <- movieData %>%
  mutate(smoothed_score = zoo::rollmean(score, k = 5, fill = NA))

# Create a plot to compare the smoothed data with the original data
ggplot() +
  geom_line(data = movieData, aes(x = date_x, y = score), color = "blue", alpha = 0.5, size = 1) +
  geom_line(data = movieData_smoothed, aes(x = date_x, y = smoothed_score), color = "red", size = 1) +
  labs(title = "Original vs. Smoothed Movie Scores",
       x = "Date",
       y = "Score") +
  theme_minimal()

Seasonality Detection and ACF/PACF

library(forecast)

movieData_ts <- ts(movieData$score, frequency = 12)
movieData_decomp <- stl(movieData_ts, s.window = "periodic")

plot(movieData_decomp)

acf(movieData_decomp$time.series[, "seasonal"])

pacf(movieData_decomp$time.series[, "seasonal"])

summary(movieData_decomp$time.series[, "seasonal"])

##       Min.    1st Qu.     Median       Mean    3rd Qu.       Max. 
## -0.7272926 -0.2569826 -0.0488401 -0.0000006  0.2510333  0.8118548

# Create a time series object
movie_ts <- ts(movieData$score, frequency = 12)

# Decompose the time series to detect seasonality
decomp <- decompose(movie_ts)

# Plot the ACF and PACF
par(mfrow = c(2, 1))
acf(decomp$seasonal, main = "ACF of Seasonal Component")
pacf(decomp$seasonal, main = "PACF of Seasonal Component")

Auto-Correlation Function (ACF) helps unearth temporal patterns in movie releases, offers insights into evolving audience preferences over time.

Neyman-Pearson Hypothesis Test for Movie Genres’ Ratings

# Perform Neyman-Pearson hypothesis test for ratings among different genres
# Assuming we want to compare Drama and Comedy genres
drama_ratings <- movieData$score[movieData$genre == "Drama"]
comedy_ratings <- movieData$score[movieData$genre == "Comedy"]

# Perform the test
np_test <- t.test(drama_ratings, comedy_ratings)
np_test

## 
##  Welch Two Sample t-test
## 
## data:  drama_ratings and comedy_ratings
## t = 3.8613, df = 911.36, p-value = 0.0001208
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  2.014544 6.179190
## sample estimates:
## mean of x mean of y 
##  63.62770  59.53083

The p-value obtained (p = 0.0001208)<<0.05. Therefore, we reject the null hypothesis.

This indicates strong statistical evidence to suggest that there is a significant difference between the average ratings of movies in Drama and Comedy genres.

Based on the confidence interval (2.014544, 6.179190), we can infer that the mean rating for Drama movies is estimated to be approximately 2.01 to 6.18 points higher than that for Comedy movies. This difference in means is statistically significant at a 95% confidence level.

In summary, there is strong evidence to support that Drama movies, on average, have higher ratings compared to Comedy movies in this dataset.

Lets perform the Fisher’s style test to evaluate the relationship between movie budgets and revenues

fisher_test <- cor.test(movieData$budget_x, movieData$revenue, method = "pearson")
fisher_test

## 
##  Pearson's product-moment correlation
## 
## data:  movieData$budget_x and movieData$revenue
## t = 91.994, df = 10176, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.6630821 0.6842993
## sample estimates:
##       cor 
## 0.6738296

The obtained p-value (p < 2.2e-16) << 0.05. Hence, we reject the null hypothesis.

This suggests compelling statistical evidence to support that there is a significant non-zero correlation between movie budgets and revenues.

The correlation coefficient (0.6738296) indicates a strong positive linear relationship between movie budgets and revenues.

This implies that as the budget of a movie increases, there’s a tendency for its revenue to increase as well.

We can assume better organization and effort when involving bigger budgets.

Now lets do an ANOVA for Analyzing Variations in User Ratings among Genres or Languages

# ANOVA to analyze variations in user ratings among genres or languages
anova_ratings <- aov(score ~ genre + orig_lang, data = movieData)
summary(anova_ratings)

##               Df  Sum Sq Mean Sq F value Pr(>F)    
## genre       2302  462691   201.0   1.356 <2e-16 ***
## orig_lang     51   64667  1268.0   8.556 <2e-16 ***
## Residuals   7739 1146844   148.2                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 85 observations deleted due to missingness

ANOVA: User rating vs Genre

The p-value obtained for genres is highly significant (<2e-16), indicating that there are significant variations in user ratings among different movie genres.However, the F-value (1.356) is relatively low, suggesting a weaker relationship between genres and user ratings.

Highly variant but low correlation

ANOVA: User rating vs Language

The p-value for original languages is also highly significant (<2e-16), demonstrating significant variations in user ratings among different languages in which movies are released.

The higher F-value (8.556) indicates a relatively stronger relationship between original languages and user ratings compared to genres.

This suggests that the language in which a movie is originally released might have a more pronounced impact on user ratings compared to its genre.

Inferences after thorough analysis.

Exploratory analysis of IMDB Data

2023-12-05

About Dataset

Questions to ask from this Data

What is the trend of Movie budgets?

Do bigger budget movies get bigger revenues?

Which country spends most on movies?

Which language is most trending?

Do movies with high imdb scores run well in theaters?

We can see MU has highest avg revenue

Analysis of budget

Plotting helps us understand that movie budgets have been gradually increasing over the years.By regression we can expect this trend to continue.

Relation between movies and their revenue

Rise of foreign languages

Aside from predominantly hollywood entries, one other language seems to break the charts.Lets enquire.

Back to the bigger picture:

Is there a relation between IMDB score and revenue?

Visual Summaries of distributions

Lets look at an even bigger picture and see how each variable correlates with each other

Correlation Heatmap for continuous variables

This shows overrall correlation between variables. We can see the obvious correlations.

This box plot can tell us the high and lows of revenues, its range and certain outliers.

These scatter plots show a positive relationship between the budget allocated for movies and their revenue. As the budget increases, the revenue tends to increase as well. This trend is suggested by the upward direction of the linear regression line.

Lets try and compute the confidence intervals for Movie Ratings and Revenues

For Revenue:

Manual (CI): the 95% CI for movie revenue is approximately [$247,743,366.72, $258,536,820.12]. This interval suggests that we are 95% confident that the true mean revenue of movies falls between these two values.

T-test Calculation: When using t-test function, the 95% CI for revenue is [$247,742,725, $258,537,462]. This CI aligns closely with the manually calculated CI, reinforcing the confidence in the estimated range for the true mean revenue of movies.

For Movie Ratings:

T-test Calculation: The 95% CI for movie ratings is [$63.23403, $63.76007].

Inference: The 95% CI for movie ratings is relatively narrow, indicating a smaller range in which the true mean rating of movies likely lies. The interval suggests that we are 95% confident that the actual mean movie rating falls between approximately 63.23 and 63.76.

Exploring Time-based Trends in Movie Releases

Let us move on and apply time series to gather insight from the long period of entries.

We choose the response variable as: Score

There is a high density of data points in recent years, suggesting an increase in the number of movies being rated.

Running a simple linear regression using the entire dataset to see if there’s an overall trend:

Suspecting different trends in different time periods, we would subset the data. Lets test if movie ratings trends are different before and after the year 2000.

Linear regression on the entire dataset suggests a slight negative relationship between movie release year and ratings (R-squared: 2.08%).

Pre-2000, ratings show a stronger negative trend (R-squared: 4.5%)

While post-2000 exhibits a weaker one (R-squared: 1.43%). Statistically significant.

These trends indicate decreasing ratings over time.

The low R-squared values in all models suggest that linear regression might not be the best model to capture the relationship between time and movie ratings.

The p-values indicate that there is a statistically significant relationship between time and movie ratings in all models, but the strength of the relationship is weak.

Using smoothing to detect season

Seasonality Detection and ACF/PACF

Auto-Correlation Function (ACF) helps unearth temporal patterns in movie releases, offers insights into evolving audience preferences over time.

Neyman-Pearson Hypothesis Test for Movie Genres’ Ratings

The p-value obtained (p = 0.0001208)<<0.05. Therefore, we reject the null hypothesis.

This indicates strong statistical evidence to suggest that there is a significant difference between the average ratings of movies in Drama and Comedy genres.

Based on the confidence interval (2.014544, 6.179190), we can infer that the mean rating for Drama movies is estimated to be approximately 2.01 to 6.18 points higher than that for Comedy movies. This difference in means is statistically significant at a 95% confidence level.

In summary, there is strong evidence to support that Drama movies, on average, have higher ratings compared to Comedy movies in this dataset.

Lets perform the Fisher’s style test to evaluate the relationship between movie budgets and revenues

The obtained p-value (p < 2.2e-16) << 0.05. Hence, we reject the null hypothesis.

This suggests compelling statistical evidence to support that there is a significant non-zero correlation between movie budgets and revenues.

The correlation coefficient (0.6738296) indicates a strong positive linear relationship between movie budgets and revenues.

This implies that as the budget of a movie increases, there’s a tendency for its revenue to increase as well.

We can assume better organization and effort when involving bigger budgets.

Now lets do an ANOVA for Analyzing Variations in User Ratings among Genres or Languages

ANOVA: User rating vs Genre

The p-value obtained for genres is highly significant (<2e-16), indicating that there are significant variations in user ratings among different movie genres.However, the F-value (1.356) is relatively low, suggesting a weaker relationship between genres and user ratings.

Highly variant but low correlation

ANOVA: User rating vs Language

The p-value for original languages is also highly significant (<2e-16), demonstrating significant variations in user ratings among different languages in which movies are released.

The higher F-value (8.556) indicates a relatively stronger relationship between original languages and user ratings compared to genres.

This suggests that the language in which a movie is originally released might have a more pronounced impact on user ratings compared to its genre.

Inferences after thorough analysis.

Movie budgets have been gradually increasing over years.

There is a a direct correlation between movies and their revenue.

Korean movies seem to be gaining in popularity

There is good correlation between the movie’s IMDB rating and its collection at box office.

As the budget increases, the revenue tends to increase as well.

There is a high density of data points in recent years, suggesting an increase in the number of movies being rated.

Drama movies, on average, have higher ratings compared to Comedy movies in this dataset.

The language in which a movie is originally released might have a more pronounced impact on user ratings compared to its genre.

fin